Showing 1–42 of 42 results for author: Kar, I

Robust Fixed-Time Model Reference Adaptive Control

Authors: Chayan Kumar Paul, Krishanu Nath, Indra Narayan Kar, Denis Efimov, Rosane Ushirobira

Abstract: This article proposes a Model Reference Adaptive Control (MRAC) strategy to achieve fixed-time convergence of parameter estimation and tracking errors for unknown linear time-invariant systems, without relying on the persistence of excitation condition. Instead, it employs a less restrictive initial/interval excitation condition on the regressor matrix, enhancing practicality and ease of implement… ▽ More This article proposes a Model Reference Adaptive Control (MRAC) strategy to achieve fixed-time convergence of parameter estimation and tracking errors for unknown linear time-invariant systems, without relying on the persistence of excitation condition. Instead, it employs a less restrictive initial/interval excitation condition on the regressor matrix, enhancing practicality and ease of implementation in real-world scenarios. Our primary contribution is a novel parameter update law within the indirect MRAC framework, ensuring that parameter estimates converge within a fixed time, once the initial/interval excitation condition is met. This approach simplifies the practical requirements for adaptive control while guaranteeing robust performance against parameter uncertainty and external disturbances. Simulation results provide a comparison with the current literature to validate the effectiveness of this approach. △ Less

Submitted 22 April, 2026; originally announced April 2026.

Safety in Admittance Control using Reference Trajectory Shaping

Authors: Chayan Kumar Paul, Bhabani Shankar Dey, Indra Narayan Kar

Abstract: This paper presents a switched model reference admittance control framework to achieve safe and compliant human-robot collaboration through reference trajectory shaping. The proposed method generates variable admittance parameters according to task compliance and task-space safety requirements. Additionally, a disturbance bound is incorporated to enhance robustness against disturbances. Safety gua… ▽ More This paper presents a switched model reference admittance control framework to achieve safe and compliant human-robot collaboration through reference trajectory shaping. The proposed method generates variable admittance parameters according to task compliance and task-space safety requirements. Additionally, a disturbance bound is incorporated to enhance robustness against disturbances. Safety guarantees are explicitly established by integrating invariance control, ensuring that the reference trajectory remains within the admissible region. Stability of the switched system is analyzed using a common quadratic Lyapunov function, which confirms asymptotic convergence of the tracking error. The effectiveness of the approach is demonstrated through simulations on a two link manipulator and comparisons with existing methods are also presented. Furthermore, real time implementation on a single link manipulator validates the practical feasibility of the controller, highlighting its ability to achieve both compliance and safety in physical interaction scenarios. △ Less

Submitted 14 March, 2026; originally announced March 2026.

Towards AGI A Pragmatic Approach Towards Self Evolving Agent

Authors: Indrajit Kar, Sammy Zonunpuia, Zonunfeli Ralte

Abstract: Large Language Model (LLM) based agents are powerful yet fundamentally static after deployment, lacking the ability to autonomously expand capabilities, generate new tools, or evolve their reasoning. This work introduces a hierarchical self-evolving multi-agent framework that integrates a Base LLM, an operational SLM agent, a Code-Generation LLM, and a Teacher-LLM to enable continuous adaptation.… ▽ More Large Language Model (LLM) based agents are powerful yet fundamentally static after deployment, lacking the ability to autonomously expand capabilities, generate new tools, or evolve their reasoning. This work introduces a hierarchical self-evolving multi-agent framework that integrates a Base LLM, an operational SLM agent, a Code-Generation LLM, and a Teacher-LLM to enable continuous adaptation. The workflow begins with the agent attempting a task using reasoning and existing tools; if unsuccessful, it escalates to tool synthesis through the Code-Gen LLM, and when failures persist, it triggers an evolution phase using Curriculum Learning (CL), Reward-Based Learning (RL), or Genetic Algorithm (GA) evolution. Using the TaskCraft dataset rich in hierarchical tasks, tool-use traces, and difficulty scaling we evaluate these paradigms. CL delivers fast recovery and strong generalization, RL excels on high-difficulty tasks, and GA offers high behavioral diversity. Across all settings, evolved agents outperform their originals, demonstrating robust, autonomous, self-improving agentic evolution. △ Less

Submitted 15 January, 2026; originally announced January 2026.

Curriculum Guided Massive Multi Agent System Solving For Robust Long Horizon Tasks

Authors: Indrajit Kar, Kalathur Chenchu Kishore Kumar

Abstract: Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operation… ▽ More Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operational region of the grid, ensuring that agents master easier central tasks before tackling harder peripheral ones. To improve reliability, the system integrates Negative Log-Likelihood as a measure of confidence, allowing the curriculum to prioritize regions where agents are both accurate and well calibrated. A Thompson Sampling curriculum manager adaptively chooses training zones based on competence and NLL-driven reward signals. We evaluate the approach on a spatially grounded Tower of Hanoi benchmark, which mirrors the long-horizon structure of many robotic manipulation and planning tasks. Results demonstrate improved stability, reduced oracle usage, and stronger long-range reasoning from distributed agent cooperation. △ Less

Submitted 9 December, 2025; originally announced December 2025.

Comments: 22 pages, 2 tables, 9 figures

Minimum time consensus for damped second order agents using Gröbner basis

Authors: Akansha Rautela, Deepak U. Patil, Ameer Mulla, Indra Narayan Kar

Abstract: A problem of achieving minimum time consensus for a set of $N$ second-order LTI system agents with bounded inputs and fuel constraints is considered. Unlike our other works, here the damping effect in agent dynamics is included. First, the attainable set for each agent with fuel budget constraints is characterized, and its boundary equations are derived. Then, using the convexity property, the min… ▽ More A problem of achieving minimum time consensus for a set of $N$ second-order LTI system agents with bounded inputs and fuel constraints is considered. Unlike our other works, here the damping effect in agent dynamics is included. First, the attainable set for each agent with fuel budget constraints is characterized, and its boundary equations are derived. Then, using the convexity property, the minimum time at which attainable sets of all agents have a non-empty intersection is computed. By applying Helly's theorem, the computation reduces to finding the minimum time to consensus and the corresponding consensus point for each of the triplets separately. △ Less

Submitted 29 October, 2025; originally announced October 2025.

An Event-based State Estimation Approach for Positive Systems with Positive Observers

Authors: Bhargavi Chaudhary, Krishanu Nath, Subashish Datta, Indra Narayan Kar

Abstract: This article addresses the problem of state observer design for continuous-time linear positive networked systems. Considering the bandwidth constraint in the communication network, an event-measurement-based positive observer design is proposed. The physical interpretation of a positive observer differs from that of a general observer. Its primary goal is to ensure that all state estimates remain… ▽ More This article addresses the problem of state observer design for continuous-time linear positive networked systems. Considering the bandwidth constraint in the communication network, an event-measurement-based positive observer design is proposed. The physical interpretation of a positive observer differs from that of a general observer. Its primary goal is to ensure that all state estimates remain non-negative at all times. Using output measurements, a law with weighted sampling error is used to determine the sampling sequence between the system and the observer. The observer dynamics are designed using the standard Luenberger structure with the event-based sampled output information, which is updated only when an event occurs. Assuming observability and sufficient conditions for the positivity of the system, the asymptotic stability of the observer dynamics with sampled information is established. Sufficient conditions of stability and positivity are derived using linear matrix inequalities. Moreover, the design ensures that the event-based architecture is free from Zeno behavior, ensuring a positive minimum bound on the inter-execution time. In addition, numerical simulations on a three-tank system having variable cross-sections are used to demonstrate the efficacy of the proposed event-based positive observer. △ Less

Submitted 5 August, 2025; originally announced August 2025.

Comments: 16 pages, 7 figures and 3 tables

On the Contraction Analysis of Nonlinear System with Multiple Equilibrium Points

Authors: Riddhi Mohan Bora, Bhabani Shankar Dey, Indra Narayan Kar

Abstract: In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the 2-contraction theory enables us to analyze the stability of planar nonlinear systems without relying on local equilibrium analysis. By utilizing index theory and 2-co… ▽ More In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the 2-contraction theory enables us to analyze the stability of planar nonlinear systems without relying on local equilibrium analysis. By utilizing index theory and 2-contraction results, we efficiently characterize the nature of equilibrium points and delineate regions in 2-dimensional state space where periodic solutions, closed orbits, or stable dynamics may exist. A key focus of this work is the identification of regions in the state space where periodic solutions may occur, as well as 2-contraction regions that guarantee the nonexistence of such solutions. Additionally, we address a critical problem in engineering the determination of the basin of attraction (BOA) for stable equilibrium points. For systems with multiple equilibria identifying candidate BOAs becomes highly nontrivial. We propose a novel methodology leveraging the 2-contraction theory to approximate a common BOA for a class of nonlinear systems with multiple stable equilibria. Theoretical findings are substantiated through benchmark examples and numerical simulations, demonstrating the practical utility of the proposed approach. Furthermore, we extend our framework to analyze networked systems, showcasing their efficacy in an opinion dynamics problem. △ Less

Submitted 19 February, 2025; originally announced February 2025.

Comments: 14 pages, 10 figures

Monolayer control of spin-charge conversion in van der Waals heterostructures

Authors: K. Abdukayumov, O. Paull, M. Mičica, F. Ibrahim, L. Vojáček, A. Wright, S. Massabeau, F. Mazzola, V. Polewczyk, C. Jego, R. Sharma, C. Vergnaud, A. Marty, I. Gomes de Moraes, A. Ouerghi, H. Okuno, A. Jana, I. Kar, J. Fuji, I. Vobornik, J. Li, F. Bonell, M. Chshiev, M. Bibes, J. -M. George , et al. (3 additional authors not shown)

Abstract: The diversity of 2D materials and their van der Waals (vdW) stacking presents a fertile ground for engineering novel multifunctional materials and quantum states of matter. This permits unique opportunities to tailor the electronic properties of vdW heterostructures by the insertion of only a single 2D material layer. However, such vdW materials engineering at the atomic scale has yet to be invest… ▽ More The diversity of 2D materials and their van der Waals (vdW) stacking presents a fertile ground for engineering novel multifunctional materials and quantum states of matter. This permits unique opportunities to tailor the electronic properties of vdW heterostructures by the insertion of only a single 2D material layer. However, such vdW materials engineering at the atomic scale has yet to be investigated for spin-charge interconversion phenomena. Here, we report on the control of these effects at the monolayer level, where drastic increase in intensity and change in sign of THz spintronic emission are demonstrated by inserting a single layer of MoSe$_2$ between PtSe$_2$ and graphene in a fully epitaxial, large area stacked structure. By using a combination of spin and angle resolved photoemission and density functional theory to reveal the electronic and spin structures, we illustrate two different mechanisms relying on charge transfer and electronic hybridization for the formation of Rashba states, which are responsible for spin-charge conversion and hence the THz spintronic emission. These findings open new pathways to design, at the atomic scale, efficient THz spintronic emitters made of 2D materials and other spintronic devices based on spin-charge interconversion phenomena. △ Less

Submitted 4 January, 2025; originally announced January 2025.

Comments: 16 pages, 4 figures

Journal ref: Phys. Rev. Lett. 135, 016702 (2025)

Minimum Time Consensus of Multi-agent System under Fuel Constraints

Authors: Akansha Rautela, Deepak Patil, Ameer Mulla, Indra Narayan Kar

Abstract: This work addresses the problem of finding minimum time consensus point in the state space for a set of $N$ identical double integrator agents with bounded inputs and fixed fuel budget constraint. To address the problem, characterization of the attainable set for each agent subject to bounded inputs and fixed fuel budget constraints is done. Such attainable set is shown to be a convex set. The min… ▽ More This work addresses the problem of finding minimum time consensus point in the state space for a set of $N$ identical double integrator agents with bounded inputs and fixed fuel budget constraint. To address the problem, characterization of the attainable set for each agent subject to bounded inputs and fixed fuel budget constraints is done. Such attainable set is shown to be a convex set. The minimum time to consensus is the least time when the attainable sets of all agents intersect and the corresponding consensus state is the point of intersection. Using Helly's theorem, it is shown that the intersection is not empty at the time when all triplets of agents exhibit a non-empty intersection. Thus, a closed-form expression for the minimum time to consensus for a triplet of agents is obtained. The calculation of minimum time consensus for each of the triplets is performed independently and is distributed evenly among $N$ agents. The overall minimum time to consensus of $N$ agents is then given by the triplet that has the greatest minimum time to consensus. In the process, the set of initial conditions for agents from which consensus is possible under these input and fuel budget constraints is also characterized. △ Less

Submitted 24 September, 2025; v1 submitted 29 July, 2024; originally announced July 2024.

A Necessary and Sufficient Condition for Local Synchronization in Nonlinear Oscillator Networks

Authors: Sanjeev Kumar Pandey, Shaunak Sen, Indra Narayan Kar

Abstract: Determining conditions on the coupling strength for the synchronization in networks of interconnected oscillators is a challenging problem in nonlinear dynamics. While sophisticated mathematical methods have been used to derive conditions, these conditions are usually only sufficient and/ or based on numerical methods. We addressed the gap between the sufficient coupling strength and numerically o… ▽ More Determining conditions on the coupling strength for the synchronization in networks of interconnected oscillators is a challenging problem in nonlinear dynamics. While sophisticated mathematical methods have been used to derive conditions, these conditions are usually only sufficient and/ or based on numerical methods. We addressed the gap between the sufficient coupling strength and numerically observations using the Lyapunov-Floquet Theory and the Master Stability Function framework. We showed that a positive coupling strength is a necessary and sufficient condition for local synchronization in a network of identical oscillators coupled linearly and in full state fashion. For partial state coupling, we showed that a positive coupling constant results in an asymptotic contraction of the trajectories in the state space, which results in synchronisation for two-dimensional oscillators. We extended the results to networks with non-identical coupling over directed graphs and showed that positive coupling constants is a sufficient condition for synchronisation. These theoretical results are validated using numerical simulations and experimental implementations. Our results contribute to bridging the gap between the theoretically derived sufficient coupling strengths and the numerically observed ones. △ Less

Submitted 20 April, 2026; v1 submitted 10 April, 2024; originally announced April 2024.

Comments: 6 pages, 7 figures, Journal

Comparative study of Kondo effect in Vanadium dichalcogenides VX$_2$ (X=Se & Te)

Authors: Indrani Kar, Susanta Ghosh, Shuvankar Gupta, Sudip Chakraborty, S. Thirupathaiah

Abstract: We report on the electrical transport, magnetotransport, and magnetic properties studies on the transition metal dichalcogenides VSe$_2$ and VTe$_2$ and draw a comprehensive comparison between them. We observe Kondo effect in both systems induced by the exchange interaction between localized moments and conduction electrons at low temperature, resulting into resistance upturn at 6 K for VSe$_2$ an… ▽ More We report on the electrical transport, magnetotransport, and magnetic properties studies on the transition metal dichalcogenides VSe$_2$ and VTe$_2$ and draw a comprehensive comparison between them. We observe Kondo effect in both systems induced by the exchange interaction between localized moments and conduction electrons at low temperature, resulting into resistance upturn at 6 K for VSe$_2$ and 17 K for VTe$_2$. From the field dependent resistance measurements we find that the data is fitted best with modified Hamann equation corrected by the quantum Brillouin function for VSe$_2$, while the data is fitted best with modified Hamann equation corrected by the classical Langevin function for VTe$_2$. Interestingly, we observe a contrasting magnetoresistance (MR) property between these systems across the Kondo temperature. That means, negative MR is found in both systems in the Kondo state. In the normal state MR is positive for VSe$_2$, while it is negligible for VTe$_2$. In addition, both systems show weak ferromagnetism at low temperature due to intercalated V atoms. △ Less

Submitted 1 December, 2023; originally announced December 2023.

Approximate Dynamic Programming based Model Predictive Control of Nonlinear systems

Authors: Keerthi Chacko, Midhun T. Augustine, S. Janardhanan, Deepak U. Patil, I. N. Kar

Abstract: This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the proposed approach, the value function is approximated as a quadratic function for which the parametric matrix is computed using a switched system approximate of the no… ▽ More This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the proposed approach, the value function is approximated as a quadratic function for which the parametric matrix is computed using a switched system approximate of the nonlinear system. The approach is modified further using a multi-stage scheme to improve the control accuracy and an extension to incorporate state constraints. The MPC scheme is validated experimentally on a multi-tank system which is modeled as a third-order nonlinear system. The experimental results show the proposed MPC scheme results in significantly lesser online computation compared to the Nonlinear MPC scheme. △ Less

Submitted 10 December, 2023; originally announced December 2023.

Weak Electronic Correlations Observed in Magnetic Weyl Semimetal Mn$_3$Ge

Authors: Susmita Changdar, Susanta Ghosh, Anumita Bose, Indrani Kar, Achintya Low, Patrick Le Fevre, François Bertran, Awadhesh Narayan, Setti Thirupathaiah

Abstract: Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we systematically studied the electronic band structure of Mn$_3$Ge in the vicinity of the Fermi level. We observe several bands crossing the Fermi level, confirming the metallic nature of the studied system. We further observe several flat bands along various high symmetry directions, consist… ▽ More Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we systematically studied the electronic band structure of Mn$_3$Ge in the vicinity of the Fermi level. We observe several bands crossing the Fermi level, confirming the metallic nature of the studied system. We further observe several flat bands along various high symmetry directions, consistent with the DFT calculations. The calculated partial density of states (PDOS) suggests a dominant Mn $3d$ orbital contribution to the total valence band DOS. With the help of orbital-resolved band structure calculations, we qualitatively identify the orbital information of the experimentally obtained band dispersions. Out-of-plane electronic band dispersions are explored by measuring the ARPES data at various photon energies. Importantly, our study suggests relatively weaker electronic correlations in Mn$_3$Ge compared to Mn$_3$Sn. △ Less

Submitted 1 December, 2023; originally announced December 2023.

Comments: 11 pages, 3 figures. To appear in the Journal of Physics: Condensed Matter

On Incremental Stability of Interconnected Switched Systems

Authors: Bhabani Shankar Dey, Indra Narayan Kar, Pushpak Jagtap

Abstract: In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger property compared to the conventional notion of stability. Even if individual systems in the interconnected setting are stable, guaranteeing stability for the overall… ▽ More In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger property compared to the conventional notion of stability. Even if individual systems in the interconnected setting are stable, guaranteeing stability for the overall system is challenging. However, one of the important features of incremental stability is that the notion is preserved over interconnection. Here, leveraging the contraction-theoretic tools, we derive a set of sufficient conditions for the overall interconnection consisting of bimodal switched systems. To showcase the wider usability of our proposed results, we have also included the effect of external input, which leads to the study of incremental input-to-state stability ($δ$-ISS). For the case of feedback interconnection, the small gain characterisation is presented for the overall system's $δ$-ISS. Further, for a special case of feedback, i.e., cascade interconnection, the results are derived. The derived conditions are based on the matrix measure, making it computationally tractable and general. To make the results more general, a generalised interconnection of bimodal switched systems is studied and corresponding sufficient condition for $δ$-ISS are presented. Two numerical examples are demonstrated and supported with simulation results to verify the theoretical claims. △ Less

Submitted 8 May, 2025; v1 submitted 24 August, 2023; originally announced August 2023.

Characterization of full-scale denial-of-service

Authors: Anindya Basu, Indrani Kar

Abstract: This article investigates the resilient control problem for Cyber-Physical Systems (CPSs) with multiple sensors, where both sides of the communication channels are affected by Denial-of-Service (DoS) attacks. While previous work focused on characterizing Multi-Channel DoS (MCDoS), this study emphasizes the characterization of Full-Scale DoS (FSDoS). First, a partial observer technique is proposed… ▽ More This article investigates the resilient control problem for Cyber-Physical Systems (CPSs) with multiple sensors, where both sides of the communication channels are affected by Denial-of-Service (DoS) attacks. While previous work focused on characterizing Multi-Channel DoS (MCDoS), this study emphasizes the characterization of Full-Scale DoS (FSDoS). First, a partial observer technique is proposed to address the MCDoS condition. Then, an event-triggered control strategy is designed to handle FSDoS. Finally, the frequency and duration of FSDoS are analyzed to ensure the Input-to-State Stability (ISS) of the closed-loop system. △ Less

Submitted 12 February, 2025; v1 submitted 8 June, 2023; originally announced June 2023.

Binomial convolutions for rational power series

Authors: Ira M. Gessel, Ishan Kar

Abstract: The binomial convolution of two sequences $\{a_n\}$ and $\{b_n\}$ is the sequence whose $n$th term is $\sum_{k=0}^{n} \binom{n}{k} a_k b_{n-k}$. If $\{a_n\}$ and $\{b_n\}$ have rational generating functions then so does their binomial convolution. We discuss an efficient method, using resultants, for computing this rational generating function and give several examples involving Fibonacci and trib… ▽ More The binomial convolution of two sequences $\{a_n\}$ and $\{b_n\}$ is the sequence whose $n$th term is $\sum_{k=0}^{n} \binom{n}{k} a_k b_{n-k}$. If $\{a_n\}$ and $\{b_n\}$ have rational generating functions then so does their binomial convolution. We discuss an efficient method, using resultants, for computing this rational generating function and give several examples involving Fibonacci and tribonacci numbers and related sequences. We then describe a similar method for computing Hadamard products of rational generating functions. Finally we describe two additional methods for computing binomial convolutions and Hadamard products of rational power series, one using symmetric functions and one using partial fractions. △ Less

Submitted 12 February, 2024; v1 submitted 20 April, 2023; originally announced April 2023.

Comments: 20 pages

MSC Class: 05A19 (Primary) 05A15 (Secondary)

Journal ref: Journal of Integer Sequences, Vol. 27 (2024), Article 24.1.3

Observation of Weak Kondo Effect and Angle Dependent Magnetoresistance in Layered Antiferromagnetic V$_5$S$_8$ Single Crystal

Authors: Indrani Kar, Sayan Routh, Soumya Ghorai, Shubham Purwar, S. Thirupathaiah

Abstract: The compound V$_5$S$_8$ can also be represented by V$_{1.25}$S$_2$, a transition metal dichalcogenide (TMDC) with excess V. Very few TMDCs show magnetism and/or Kondo effect. Among them, the sister compounds VSe$_2$ and VTe$_2$ are recently proved to show ferromagnetism in addition to the low-temperature resistivity upturn due to Kondo effect. In this study, we show Kondo effect in V$_5$S$_8$ orig… ▽ More The compound V$_5$S$_8$ can also be represented by V$_{1.25}$S$_2$, a transition metal dichalcogenide (TMDC) with excess V. Very few TMDCs show magnetism and/or Kondo effect. Among them, the sister compounds VSe$_2$ and VTe$_2$ are recently proved to show ferromagnetism in addition to the low-temperature resistivity upturn due to Kondo effect. In this study, we show Kondo effect in V$_5$S$_8$ originated from the antiferromagnetic exchange interactions among the intercalated V atoms below the N$\acute{e}$el ($T_N$) temperature of 27 K. We find isotropic magnetic properties above $T_N$, while a strong magnetic anisotropy is noticed below $T_N$. In addition, below $T_N$ we find an out-of-plane ($H\parallel c$) spin-flop transition triggered at a critical field of 3.5 T that is absent from the in-plane ($H\perp c$). Angle-dependent magnetoresistance is found to be highly anisotropic in the antiferromagnetic state. △ Less

Submitted 7 February, 2023; originally announced February 2023.

Safe Human Robot-Interaction using Switched Model Reference Admittance Control

Authors: Chayan Kumar Paul, Bhabani Shankar Dey, Udayan Banerjee, Indra Narayan Kar

Abstract: Physical Human-Robot Interaction (pHRI) task involves tight coupling between safety constraints and compliance with human intentions. In this paper, a novel switched model reference admittance controller is developed to maintain compliance with the external force while upholding safety constraints in the workspace for an n-link manipulator involved in pHRI. A switched reference model is designed f… ▽ More Physical Human-Robot Interaction (pHRI) task involves tight coupling between safety constraints and compliance with human intentions. In this paper, a novel switched model reference admittance controller is developed to maintain compliance with the external force while upholding safety constraints in the workspace for an n-link manipulator involved in pHRI. A switched reference model is designed for the admittance controller to generate the reference trajectory within the safe workspace. The stability analysis of the switched reference model is carried out by an appropriate selection of the Common Quadratic Lyapunov Function (CQLF) so that asymptotic convergence of the trajectory tracking error is ensured. The efficacy of the proposed controller is validated in simulation on a two-link robot manipulator. △ Less

Submitted 27 November, 2022; originally announced November 2022.

Robust Artificial Delay based Impedance Control of Robotic Manipulators with Uncertain Dynamics

Authors: Udayan Banerjee, Bhabani Shankar Dey, Indra Narayan Kar, Subir Kumar Saha

Abstract: In this paper an artificial delay based impedance controller is proposed for robotic manipulators with uncertainty in dynamics. The control law unites the time delayed estimation (TDE) framework with a second order switching controller of super twisting algorithm (STA) type via a novel generalized filtered tracking error (GFTE). While time delayed estimation framework eliminates the need for accur… ▽ More In this paper an artificial delay based impedance controller is proposed for robotic manipulators with uncertainty in dynamics. The control law unites the time delayed estimation (TDE) framework with a second order switching controller of super twisting algorithm (STA) type via a novel generalized filtered tracking error (GFTE). While time delayed estimation framework eliminates the need for accurate modelling of robot dynamics by estimating the uncertain robot dynamics and interaction forces from immediate past data of state and control effort, the second order switching control law in the outer loop provides robustness against the time delayed estimation (TDE) error that arises due to approximation of the manipulator dynamics. Thus, the proposed control law tries to establish a desired impedance model between the robot end effector variables i.e. force and motion in presence of uncertainties, both when it is encountering smooth contact forces and during free motion. Simulation results for a two link manipulator using the proposed controller along with convergence analysis are shown to validate the proposition. △ Less

Submitted 20 August, 2022; v1 submitted 18 August, 2022; originally announced August 2022.

Effect on the Electronic and Magnetic Properties of Antiferromagnetic Topological Insulator MnBi$_2$Te$_4$ with Sn Doping

Authors: Susmita Changdar, Susanta Ghosh, Kritika Vijay, Indrani Kar, Sayan Routh, P. K. Maheswari, Soumya Ghorai, Soma Banik, S. Thirupathaiah

Abstract: We thoroughly investigate the effect of nonmagnetic Sn doping on the electronic and magnetic properties of antiferromagnetic topological insulator MnBi$_2$Te$_4$. We observe that Sn doping reduces the out-of-plane antiferromagnetic (AFM) interactions in MnBi$_2$Te$_4$ up to 68\% of Sn concentration and above the system is found to be paramagnetic. In this way, the anomalous Hall effect observed at… ▽ More We thoroughly investigate the effect of nonmagnetic Sn doping on the electronic and magnetic properties of antiferromagnetic topological insulator MnBi$_2$Te$_4$. We observe that Sn doping reduces the out-of-plane antiferromagnetic (AFM) interactions in MnBi$_2$Te$_4$ up to 68\% of Sn concentration and above the system is found to be paramagnetic. In this way, the anomalous Hall effect observed at a very high field of 7.8 T in MnBi$_2$Te$_4$ is reduced to 2 T with 68\% of Sn doping. Electrical transport measurements suggest that all compositions are metallic in nature, while the low-temperature resistivity is sensitive to the AFM ordering and to the doping-induced disorder. Hall effect study demonstrates that Sn actually dopes electrons into the system, thus, enhancing the electron carrier density almost by two orders at 68\% of Sn. In contrast, SnBi$_2$Te$_4$ is found to be a p-type system. Angle-resolved photoemission spectroscopy (ARPES) studies show that the topological properties are intact at least up to 55\% of Sn as the Dirac surface states are present in the valance band, but in SnBi$_2$Te$_4$ we are unable to detect the topological states due to heavy hole doping. Overall, Sn doping significantly affects the electronic and magnetic properties of MnBi$_2$Te$_4$. △ Less

Submitted 27 July, 2022; originally announced July 2022.

Comments: 8 pages and 6 figures

Journal ref: Physica B: Condensed Matter 657, 414799 (2023)

A contraction theory approach to observer-based controller design for glucose regulation in type 1 diabetes with intra-patient variability

Authors: Bhabani Shankar Dey, Anirudh Nath, Abhilash Patel, Indra Narayan Kar

Abstract: While the Artificial Pancreas is effective in regulating the blood glucose in the safe range of 70-180 mg/dl in type 1 diabetic patients, the high intra-patient variability, as well as exogenous meal disturbances, poses a serious challenge. The existing control algorithms thus require additional safety algorithms and feed-forward actions. Moreover, the unavailability of insulin sensors in Artifici… ▽ More While the Artificial Pancreas is effective in regulating the blood glucose in the safe range of 70-180 mg/dl in type 1 diabetic patients, the high intra-patient variability, as well as exogenous meal disturbances, poses a serious challenge. The existing control algorithms thus require additional safety algorithms and feed-forward actions. Moreover, the unavailability of insulin sensors in Artificial Pancreas makes this task more difficult. In the present work, a subcutaneous model of type 1 diabetes (T1D) is considered for observer-based controller design in the framework of contraction analysis. A variety of realistic multiple-meal scenarios for three virtual T1D patients have been investigated with +30 % and -30 % of parametric variability. The average time spent by the three T1D patients is found to be 77 %, 73 % and 76 %, respectively. A significant reduction in the time spent in hyperglycemia (>180 mg/dl) is achieved without any feed-forward action for meal compensation. △ Less

Submitted 29 June, 2022; originally announced June 2022.

Characterization of Minimum Time-Fuel Optimal Control for LTI Systems

Authors: Rajasree Sarkar, Deepak U. Patil, Indra Narayan Kar

Abstract: A problem of computing time-fuel optimal control for state transfer of a single input linear time invariant (LTI) system to the origin is considered. The input is assumed to be bounded. Since, the optimal control is bang-off-bang in nature, it is characterized by sequences of +1 , 0 and -1 and the corresponding switching time instants. All (candidate) sequences satisfying the Pontryagin's maximum… ▽ More A problem of computing time-fuel optimal control for state transfer of a single input linear time invariant (LTI) system to the origin is considered. The input is assumed to be bounded. Since, the optimal control is bang-off-bang in nature, it is characterized by sequences of +1 , 0 and -1 and the corresponding switching time instants. All (candidate) sequences satisfying the Pontryagin's maximum principle (PMP) necessary conditions are characterized. The number of candidate sequences is obtained as a function of the order of system and a method to list all candidate sequences is derived. Corresponding to each candidate sequence, switching time instants are computed by solving a static optimization problem. Since the candidate control input is a piece-wise constant function, the time-fuel cost functional is converted to a linear function in switching time instants. By using a simple substitution of variables, reachability constraints are converted to polynomial equations and inequalities. Such a static optimization problem can be solved separately for each candidate sequence. Finally, the optimal control input is obtained from candidate sequences which gives the least cost. For each sequence, optimization problem can be solved by converting it to a generalized moment problem (GMP) and then solving a hierachical sequence of semidefinite relaxations to approximate the minima and minimizer [1]. Lastly, a numerical example is presented for demonstration of method. △ Less

Submitted 22 February, 2021; originally announced February 2021.

Consensus of Multi-Agent Systems Using Back-Tracking and History Following Algorithms

Authors: Yanumula V. Karteek, Indrani Kar, Somanath Majhi

Abstract: This paper proposes two algorithms, namely "back-tracking" and "history following", to reach consensus in case of communication loss for a network of distributed agents with switching topologies. To reach consensus in distributed control, considered communication topology forms a strongly connected graph. The graph is no more strongly connected whenever an agent loses communication.Whenever an age… ▽ More This paper proposes two algorithms, namely "back-tracking" and "history following", to reach consensus in case of communication loss for a network of distributed agents with switching topologies. To reach consensus in distributed control, considered communication topology forms a strongly connected graph. The graph is no more strongly connected whenever an agent loses communication.Whenever an agent loses communication, the topology is no more strongly connected. The proposed back-tracking algorithm makes sure that the agent backtracks its position unless the communication is reestablished, and path is changed to reach consensus. In history following, the agents use their memory and move towards previous consensus point until the communication is regained. Upon regaining communication, a new consensus point is calculated depending on the current positions of the agents and they change their trajectories accordingly. Simulation results, for a network of six agents, show that when the agents follow the previous history, the average consensus time is less than that of back-tracking. However, situation may arise in history following where a false notion of reaching consensus makes one of the agents stop at a point near to the actual consensus point. An obstacle avoidance algorithm is integrated with the proposed algorithms to avoid collisions. Hardware implementation for a three robots system shows the effectiveness of the algorithms. △ Less

Submitted 17 November, 2020; originally announced November 2020.

Journal ref: International Journal of Robotics and Automation, 32(4), 2017

Experimental Evidence of Stable 2$H$ Phase on the Surface of Layered 1$T'$-TaTe$_2$

Authors: Indrani Kar, Kapildeb Dolui, Luminita Harnagea, Y. Kushnirenko, G. Shipunov, N. C. Plumb, M. Shi, B. Büchner, S. Thirupathaiah

Abstract: We report on the low-energy electronic structure of Tantalum ditelluride (1$T'$-TaTe$_2$), one of the charge density wave (CDW) materials from the group V transition metal dichalcogenides using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT). We find that the Fermi surface topology of TaTe$_2$ is quite complicated compared to its isovalent compounds such as Ta… ▽ More We report on the low-energy electronic structure of Tantalum ditelluride (1$T'$-TaTe$_2$), one of the charge density wave (CDW) materials from the group V transition metal dichalcogenides using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT). We find that the Fermi surface topology of TaTe$_2$ is quite complicated compared to its isovalent compounds such as TaS$_2$, TaSe$_2$, and isostructural compound NbTe$_2$. More importantly, we discover that the surface electronic structure of 1$T'$-TaTe$_2$ has more resemblance to the 2$H$-TaTe$_2$, while the bulk electronic structure has more resemblance to the hypothetical 1$T$-TaTe$_2$. These experimental observations are thoroughly compared with our DFT calculations performed on 1$T$-, 2$H$- and 2$H$ (monolayer)/1$T$- TaTe$_2$. We further notice that the Fermi surface topology is temperature independent up to 180 K, confirming that the 2$H$ phase on the surface is stable up to 180 K and the CDW order is not due to the Fermi surface nesting. △ Less

Submitted 22 December, 2020; v1 submitted 2 September, 2020; originally announced September 2020.

Comments: 5 figures, 22 pages, Accepted for publication in JPCC

Journal ref: J. Phys. Chem. C 125, 1150 (2021)

Efficient detection of adversarial images

Authors: Darpan Kumar Yadav, Kartik Mundra, Rahul Modpur, Arpan Chattopadhyay, Indra Narayan Kar

Abstract: In this paper, detection of deception attack on deep neural network (DNN) based image classification in autonomous and cyber-physical systems is considered. Several studies have shown the vulnerability of DNN to malicious deception attacks. In such attacks, some or all pixel values of an image are modified by an external attacker, so that the change is almost invisible to the human eye but signifi… ▽ More In this paper, detection of deception attack on deep neural network (DNN) based image classification in autonomous and cyber-physical systems is considered. Several studies have shown the vulnerability of DNN to malicious deception attacks. In such attacks, some or all pixel values of an image are modified by an external attacker, so that the change is almost invisible to the human eye but significant enough for a DNN-based classifier to misclassify it. This paper first proposes a novel pre-processing technique that facilitates the detection of such modified images under any DNN-based image classifier as well as the attacker model. The proposed pre-processing algorithm involves a certain combination of principal component analysis (PCA)-based decomposition of the image, and random perturbation based detection to reduce computational complexity. Next, an adaptive version of this algorithm is proposed where a random number of perturbations are chosen adaptively using a doubly-threshold policy, and the threshold values are learnt via stochastic approximation in order to minimize the expected number of perturbations subject to constraints on the false alarm and missed detection probabilities. Numerical experiments show that the proposed detection scheme outperforms a competing algorithm while achieving reasonably low computational complexity. △ Less

Submitted 9 July, 2020; originally announced July 2020.

Comments: 10 pages, 3 figures, 3 algorithms, 8 tables. Extension of the Conference paper:- Kartik Mundra, Rahul Modpur, Arpan Chattopadhyay, and Indra Narayan Kar. Adversarial image detection in cyber-physical systems. In Proceedings of the 1st ACM Workshop on Autonomous and Intelligent Mobile Systems, pages 1-5, 2020. Can be found at https://dl.acm.org/doi/abs/10.1145/3377283.3377285

Metal-chalcogen bond-length induced electronic phase transition from semiconductor to topological semimetal in ZrX$_2$ (X = Se and Te)

Authors: I. Kar, Joydeep Chatterjee, Luminita Harnagea, Y. Kushnirenko, A. V. Fedorov, Deepika Shrivastava, B. Büchner, P. Mahadevan, S. Thirupathaiah

Abstract: Using angle resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations we studied the low-energy electronic structure of bulk ZrTe$_2$. ARPES studies on ZrTe$_2$ demonstrate free charge carriers at the Fermi level, which is further confirmed by the DFT calculations. An equal number of hole and electron carrier density estimated from the ARPES data, points ZrTe… ▽ More Using angle resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations we studied the low-energy electronic structure of bulk ZrTe$_2$. ARPES studies on ZrTe$_2$ demonstrate free charge carriers at the Fermi level, which is further confirmed by the DFT calculations. An equal number of hole and electron carrier density estimated from the ARPES data, points ZrTe$_2$ to a semimetal. The DFT calculations further suggest a band inversion between Te $p$ and Zr $d$ states at the $Γ$ point, hinting at the non-trivial band topology in ZrTe$_2$. Thus, our studies for the first time unambiguously demonstrate that ZrTe$_2$ is a topological semimetal. Also, a comparative band structure study is done on ZrSe$_2$ which shows a semiconducting nature of the electronic structure with an indirect band gap of 0.9 eV between $Γ(A) $ and $M (L)$ high symmetry points. In the below we show that the metal-chalcogen bond-length plays a critical role in the electronic phase transition from semiconductor to a topological semimetal ingoing from ZrSe$_2$ to ZrTe$_2$. △ Less

Submitted 9 July, 2019; originally announced July 2019.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. B 101, 165122 (2020)

Artificial Delay Based ARC of a Class of Uncertain EL Systems with Only Position Feedback

Authors: Spandan Roy, Indra Narayan Kar, Jinoh Lee, Nikos Tsagarakis, Darwin G. Caldwell

Abstract: In this paper, the tracking control problem of an Euler-Lagrange system is addressed with regard to parametric uncertainties, and an adaptive-robust control strategy, christened Time-Delayed Adaptive Robust Control (TARC), is presented. TARC approximates the unknown dynamics through the time-delayed estimation, and the adaptive-robust control provides robustness against the approximation error. Th… ▽ More In this paper, the tracking control problem of an Euler-Lagrange system is addressed with regard to parametric uncertainties, and an adaptive-robust control strategy, christened Time-Delayed Adaptive Robust Control (TARC), is presented. TARC approximates the unknown dynamics through the time-delayed estimation, and the adaptive-robust control provides robustness against the approximation error. The novel adaptation law of TARC, in contrast to the conventional adaptive-robust control methodologies, requires neither complete model of the system nor any knowledge of predefined uncertainty bounds to compute the switching gain, and circumvents the over- and underestimation problems of the switching gain. Moreover, TARC only utilizes position feedback and approximates the velocity and acceleration terms from the past position data. The adopted state-derivatives estimation method in TARC avoids any explicit requirement of external low pass filters for the removal of measurement noise. A new stability notion in continuous-time domain is proposed considering the time delay, adaptive law, and state-derivatives estimation which in turn provides a selection criterion for gains and sampling interval of the controller. △ Less

Submitted 3 November, 2017; originally announced November 2017.

Journal ref: IEEE Transactions on Control Systems Technology, 2018

Consensus of second order multi-agents with actuator saturation and asynchronous time-delays

Authors: Venkata Karteek Yanumula, Indrani Kar, Somanath Majhi

Abstract: This article presents the consensus of a saturated second order multi-agent system with non-switching dynamics that can be represented by a directed graph. The system is affected by data processing (input delay) and communication time-delays that are assumed to be asynchronous. The agents have saturation nonlinearities, each of them is approximated into separate linear and nonlinear elements. Nonl… ▽ More This article presents the consensus of a saturated second order multi-agent system with non-switching dynamics that can be represented by a directed graph. The system is affected by data processing (input delay) and communication time-delays that are assumed to be asynchronous. The agents have saturation nonlinearities, each of them is approximated into separate linear and nonlinear elements. Nonlinear elements are represented by describing functions. Describing functions and stability of linear elements are used to estimate the existence of limit cycles in the system with multiple control laws. Stability analysis of the linear element is performed using Lyapunov-Krasovskii functions and frequency domain analysis. A comparison of pros and cons of both the analyses with respect to time-delay ranges, applicability and computation complexity is presented. Simulation and corresponding hardware implementation results are demonstrated to support theoretical results. △ Less

Submitted 23 November, 2017; v1 submitted 4 September, 2017; originally announced September 2017.

Comments: 10 pages

Journal ref: IET Control Theory Appl., 2017, Vol. 11 Iss. 17, pp. 3201-321

Theory and Application on Adaptive-Robust Control of Euler-Lagrange Systems with Linearly Parametrizable Uncertainty Bound

Authors: Spandan Roy, Sayan Basu Roy, Indra Narayan Kar

Abstract: This work proposes a new adaptive-robust control (ARC) architecture for a class of uncertain Euler-Lagrange (EL) systems where the upper bound of the uncertainty satisfies linear in parameters (LIP) structure. Conventional ARC strategies either require structural knowledge of the system or presume that the overall uncertainties or its time derivative are norm bounded by a constant. Due to unmodell… ▽ More This work proposes a new adaptive-robust control (ARC) architecture for a class of uncertain Euler-Lagrange (EL) systems where the upper bound of the uncertainty satisfies linear in parameters (LIP) structure. Conventional ARC strategies either require structural knowledge of the system or presume that the overall uncertainties or its time derivative are norm bounded by a constant. Due to unmodelled dynamics and modelling imperfection, true structural knowledge of the system is not always available. Further, for the class of systems under consideration, prior assumption regarding the uncertainties (or its time derivative) being upper bounded by a constant, puts a restriction on states beforehand. Conventional ARC laws invite overestimation-underestimation problem of switching gain. Towards this front, Adaptive Switching-gain based Robust Control (ASRC) is proposed which alleviates the overestimation-underestimation problem of switching gain. Moreover, ASRC avoids any presumption of constant upper bound on the overall uncertainties and can negotiate uncertainties regardless of being linear or nonlinear in parameters. Experimental results of ASRC using a wheeled mobile robot notes improved control performance in comparison to adaptive sliding mode control. △ Less

Submitted 4 August, 2017; originally announced August 2017.

Comments: 10 pages, 9 figures

Journal ref: IEEE Transactions on Control Systems Technology, 2018

Analysis of higher order time delay systems using Lambert W function

Authors: Niraj Choudhary, Janardhanan Sivaramakrishnan, Indra Narayan Kar

Abstract: In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The eigenvalues of a time delay system are either real or complex conjugate pairs and therefore, the whole eigenspectrum can be associated with only two real branches of… ▽ More In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The eigenvalues of a time delay system are either real or complex conjugate pairs and therefore, the whole eigenspectrum can be associated with only two real branches of the Lambert W function. A new class of time delay systems is characterized to extend the applicability of the above said method. A state variable transformation is used to transform the proposed class of systems into the common canonical form. Moreover, this approach has been exploited to design a controller which places a subset of eigenvalues at desired locations. Stability is analyesed by the help of Nyquist plot. The approach is validated through an example. △ Less

Submitted 7 April, 2016; originally announced April 2016.

Report number: DS-16-1549

Journal ref: J. Dyn. Sys., Meas., Control 139(11), Aug 08, 2017

Memory-Based Data-Driven MRAC Architecture Ensuring Parameter Convergence

Authors: Sayan Basu Roy, Shubhendu Bhasin, Indra Narayan Kar

Abstract: Convergence of controller parameters in standard model reference adaptive control (MRAC) requires the system states to be persistently exciting (PE), a restrictive condition to be verified online. A recent data-driven approach, concurrent learning, uses information-rich past data concurrently with the standard parameter update laws to guarantee parameter convergence without the need of the PE cond… ▽ More Convergence of controller parameters in standard model reference adaptive control (MRAC) requires the system states to be persistently exciting (PE), a restrictive condition to be verified online. A recent data-driven approach, concurrent learning, uses information-rich past data concurrently with the standard parameter update laws to guarantee parameter convergence without the need of the PE condition. This method guarantees exponential convergence of both the tracking and the controller parameter estimation errors to zero, whereas, the classical MRAC merely ensures asymptotic convergence of tracking error to zero. However, the method requires knowledge of the state derivative, at least at the time instances when the state values are stored in memory. The method further assumes knowledge of the control allocation matrix. This paper addresses these limitations by using a memory-based finite-time system identifier in conjunction with a data-driven approach, leading to convergence of both the tracking and the controller parameter estimation errors without the PE condition and knowledge of the system matrices and the state derivative. A Lyapunov based stability proof is included to justify the validity of the proposed data-driven approach. Simulation results demonstrate the efficacy of the suggested method. △ Less

Submitted 1 February, 2016; originally announced February 2016.

Event-triggered Communication in Wide-area Damping Control: A Limited Output Feedback Based Approach

Authors: Mahendra Bhadu, Niladri Sekhar Tripathy, I. N. Kar, Nilanjan Senroy

Abstract: A conceptual design methodology is proposed for event-triggered based power system wide area damping controller. The event-triggering mechanism is adopted to reduce the communication burden between origin of the remote signal and the wide area damping controller (WADC) location. The remote signal is transmitted to the WADC only when an event-triggering condition based on a predefined system output… ▽ More A conceptual design methodology is proposed for event-triggered based power system wide area damping controller. The event-triggering mechanism is adopted to reduce the communication burden between origin of the remote signal and the wide area damping controller (WADC) location. The remote signal is transmitted to the WADC only when an event-triggering condition based on a predefined system output, is satisfied. The triggering condition is derived from a stability criterion, and is monitored continuously by a separate event-monitoring unit located at the origin of the remote signal. The stability of the resulting closed loop system is guaranteed via the input-to-state stability (ISS) technique. The proposed event triggered WADC (ET-WADC) is implemented on two typical test power systems - two area four machine and IEEE 39 bus 10 machine. The validation of proposed mechanism is carried out through non-linear simulation studies on MATLAB/Simulink platform. The numerical results show the efficacy of the controller in managing the communication channel usage without compromising the stated system stability objectives. △ Less

Submitted 3 January, 2016; originally announced January 2016.

Comments: 8 pages, 9 figures

Stabilization of Uncertain Discrete-time Linear System via Limited Information

Authors: Niladri Sekhar Tripathy, I. N. Kar, Kolin Paul

Abstract: This paper proposes a procedure to control an uncertain discrete-time networked control system through a limited stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. The input information is limited due to unreliability of communicating networks. An event-triggered based robust control strategy is adopted to capture t… ▽ More This paper proposes a procedure to control an uncertain discrete-time networked control system through a limited stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. The input information is limited due to unreliability of communicating networks. An event-triggered based robust control strategy is adopted to capture the network unreliability. In event-triggered control the control input is computed and updated at the system end only when a pre-specified event condition is violated. The robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost-functional. The designed robust control law with limited information ensures input-to-sate stability (ISS) of original system under presence of mismatched uncertainty. Deriving the event-triggering condition for discrete-time uncertain system and ensuring the stability of such system analytically are the key contributions of this paper. A numerical example is given to prove the efficacy of the proposed event-based control algorithm over the conventional periodic one. △ Less

Submitted 22 December, 2015; originally announced December 2015.

Comments: 6 pages, 3 figures

Contraction based stabilization of nonlinear singularly perturbed systems and application to high gain feedback

Authors: Madan Mohan Rayguru, I N Kar

Abstract: Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for stabilization of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard and… ▽ More Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for stabilization of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard and non-standard singularly perturbed systems. This framework provides relaxation over traditional quadratic Lyapunov based method as there is no need to satisfy interconnection conditions during controller design algorithm. Moreover, the stability bound does not depend on smallness of singularly perturbed parameter. Combined with high gain scaling, the proposed technique is shown to assure contraction of approximate feedback linearizable systems. These findings extend the class of nonlinear systems which can be made contracting. △ Less

Submitted 3 December, 2015; originally announced December 2015.

A Contraction Theory Approach for Analysis of Performance Recovery in Dynamic Surface Control

Authors: M M Rayguru, I N kar

Abstract: Dynamic surface control (DSC) method uses high gain filters to avoid the "explosion of complexity" issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale separation between them. This paper attempts to design a novel disturbance observer based dynamic surface controller using contraction framework. In doing so the steady… ▽ More Dynamic surface control (DSC) method uses high gain filters to avoid the "explosion of complexity" issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale separation between them. This paper attempts to design a novel disturbance observer based dynamic surface controller using contraction framework. In doing so the steady state error bounds are obtained in terms of design parameters which are exploited to tune the closed loop system performance. The results not only show that DSC technique recover the performance of a backstepping controller for a small range of filter parameter but also derive the maximum bound for it. Furthermore the stability bounds are also derived in the presence of disturbances and convergence of trajectories to a small penultimate bound is proved. The convergence results are shown to hold for less conservative choice of filter parameter and observer gain. The effectiveness of the proposed controller is verified through simulation example. △ Less

Submitted 31 October, 2015; originally announced November 2015.

Adaptive-Robust Control of a Class of Uncertain Nonlinear Systems Utilizing Time-Delayed Input and Position Feedback

Authors: Spandan Roy, Indra Narayan Kar

Abstract: In this paper, the tracking control problem of a class of Euler-Lagrange systems subjected to unknown uncertainties is addressed and an adaptive-robust control strategy, christened as Time-Delayed Adaptive Robust Control (TARC) is presented. The proposed control strategy approximates the unknown dynamics through time-delayed logic, and the switching logic provides robustness against the approximat… ▽ More In this paper, the tracking control problem of a class of Euler-Lagrange systems subjected to unknown uncertainties is addressed and an adaptive-robust control strategy, christened as Time-Delayed Adaptive Robust Control (TARC) is presented. The proposed control strategy approximates the unknown dynamics through time-delayed logic, and the switching logic provides robustness against the approximation error. The novel adaptation law for the switching gain, in contrast to the conventional adaptive-robust control methodologies, does not require either nominal modelling or predefined bounds of the uncertainties. Also, the proposed adaptive law circumvents the overestimation-underestimation problem of switching gain. The state derivatives in the proposed control law is estimated from past data of the state to alleviate the measurement error when state derivatives are not available directly. Moreover, a new stability notion for time-delayed control is proposed which in turn provides a selection criterion for controller gain and sampling interval. Experimental result of the proposed methodology using a nonholonomic wheeled mobile robot (WMR) is presented and improved tracking accuracy of the proposed control law is noted compared to time-delayed control and adaptive sliding mode control. △ Less

Submitted 11 February, 2016; v1 submitted 24 September, 2015; originally announced September 2015.

Comments: 9 pages

Journal ref: IEEE Transactions on Control Systems Technology, 2018

Adaptive-Robust Control of a Class of Nonlinear Systems with Unknown Input Delay

Authors: Spandan Roy, Indra Narayan Kar

Abstract: In this paper, the tracking control problem of a class of uncertain Euler-Lagrange systems subjected to unknown input delay and bounded disturbances is addressed. To this front, a novel delay dependent control law, referred as Adaptive Robust Outer Loop Control (AROLC) is proposed. Compared to the conventional predictor based approaches, the proposed controller is capable of negotiating any input… ▽ More In this paper, the tracking control problem of a class of uncertain Euler-Lagrange systems subjected to unknown input delay and bounded disturbances is addressed. To this front, a novel delay dependent control law, referred as Adaptive Robust Outer Loop Control (AROLC) is proposed. Compared to the conventional predictor based approaches, the proposed controller is capable of negotiating any input delay, within a stipulated range, without knowing the delay or its variation. The maximum allowable input delay is computed through Razumikhin-type stability analysis. AROLC also provides robustness against the disturbances due to input delay, parametric variations and unmodelled dynamics through switching control law. The novel adaptive law allows the switching gain to modify itself online in accordance with the tracking error without any prerequisite of the uncertainties. The uncertain system, employing AROLC, is shown to be Uniformly Ultimately Bounded (UUB). As a proof of concept, experimentation is carried out on a nonholonomic wheeled mobile robot with various time varying as well as fixed input delay, and better tracking accuracy of the proposed controller is noted compared to predictor based methodology. △ Less

Submitted 22 September, 2015; originally announced September 2015.

Journal ref: Nonlinear Dynamics (2016)

Formation Stabilization with Collision Avoidance of Complex Systems

Authors: Soumic Sarkar, Indra Narayan Kar

Abstract: Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half as opposed to the vector representation in Cartesian coordinate system. We first design a stable formation controller in an attempt to solve the formation contro… ▽ More Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half as opposed to the vector representation in Cartesian coordinate system. We first design a stable formation controller in an attempt to solve the formation control turned to stabilization problem and then find a collision avoidance controller in the transformed domain, respectively. Different linear transformations are used to facilitate the formation control task in a different way. For example Jacobi transformation is used to separate the shape control and trajectory control. The inverse of the transformation must have nonzero eigenvalues with both positive and negative real parts which may lead the system to instability. If the inverse of the transformation appears in closed loop then a diagonal stabilizing matrix is required to reassign the eigenvalues of the inverse of transformation in the right half of complex plane. The algorithm to find such stabilizing matrix is provided. We then define a matrix of potential in the actual domain which is the stepping stone to find a matrix of potential in the transformed domain. Thus collision avoidance controller can be designed directly in the transformed domain. The mathematical proof is given that both the actual and transformed system behaves identically. Simulation results are provided to support our claim. △ Less

Submitted 1 June, 2015; v1 submitted 29 May, 2015; originally announced May 2015.

Model Based Robust Control Law for Linear Event-triggered System

Authors: Niladri Sekhar Tripathy, I. N. Kar, Kolin Paul

Abstract: This paper proposes a framework to design an event-triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event-triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and unmatched system uncertainties. Derivation of event-trig… ▽ More This paper proposes a framework to design an event-triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event-triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and unmatched system uncertainties. Derivation of event-triggering rule with a non-zero positive inter-event time and corresponding stability criteria for uncertain event-triggered system are the key contributions of this paper. The efficacy of proposed algorithm is carried out through a comparative study of simulation results. △ Less

Submitted 7 September, 2015; v1 submitted 29 December, 2014; originally announced December 2014.

Comments: 13 pages, 11 figures

Multi Time Scale Behaviour of The Formation of Multiple Groups of Nonholonomic Wheeled Mobile Robots

Authors: Soumic Sarkar, Indra Narayan Kar

Abstract: Different geometric patterns and shapes are generated using groups of agents, and this needs formation control. In this paper, Centroid Based Transformation (CBT), has been applied to decompose the combined dynamics of nonholonomic Wheeled Mobile Robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. The intra group shape dynamics can further b… ▽ More Different geometric patterns and shapes are generated using groups of agents, and this needs formation control. In this paper, Centroid Based Transformation (CBT), has been applied to decompose the combined dynamics of nonholonomic Wheeled Mobile Robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. The intra group shape dynamics can further be partitioned into the shape dynamics of each group, giving the notion of multiple group. Thus separate controllers have been designed for each subsystem. The gains of the controllers are such chosen that the overall system becomes singularly perturbed system, and different subsystems converge to their desired values at different times. Then multi-time scale convergence analysis has been carried out in this paper. Negative gradient of a potential based function has been added to the controller to ensure collision avoidance among the robots. Simulation results have been provided to demonstrate the effectiveness of the proposed controller. △ Less

Submitted 25 December, 2014; originally announced December 2014.

Comments: arXiv admin note: text overlap with arXiv:1412.6164

Formation of Multiple Groups of Mobile Robots Using Sliding Mode Control

Authors: Soumic Sarkar, Indra Narayan Kar

Abstract: Formation control of multiple groups of agents finds application in large area navigation by generating different geometric patterns and shapes, and also in carrying large objects. In this paper, Centroid Based Transformation (CBT) \cite{c39}, has been applied to decompose the combined dynamics of wheeled mobile robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dyn… ▽ More Formation control of multiple groups of agents finds application in large area navigation by generating different geometric patterns and shapes, and also in carrying large objects. In this paper, Centroid Based Transformation (CBT) \cite{c39}, has been applied to decompose the combined dynamics of wheeled mobile robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. Separate controllers have been designed for each subsystem. The gains of the controllers are such chosen that the overall system becomes singularly perturbed system. Then sliding mode controllers are designed on the singularly perturbed system to drive the subsystems on sliding surfaces in finite time. Negative gradient of a potential based function has been added to the sliding surface to ensure collision avoidance among the robots in finite time. The efficacy of the proposed controller is established through simulation results. △ Less

Submitted 29 May, 2015; v1 submitted 11 October, 2014; originally announced December 2014.

Comments: 8 pages, 5 figures

Quantum Brain: A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets

Authors: Laxmidhar Behera, Indrani Kar, Avshalom Elitzur

Abstract: A theoretical quantum brain model is proposed using a nonlinear Schroedinger wave equation. The model proposes that there exists a quantum process that mediates the collective response of a neural lattice (classical brain). The model is used to explain eye movements when tracking moving targets. Using a Recurrent Quantum Neural Network(RQNN) while simulating the quantum brain model, two very int… ▽ More A theoretical quantum brain model is proposed using a nonlinear Schroedinger wave equation. The model proposes that there exists a quantum process that mediates the collective response of a neural lattice (classical brain). The model is used to explain eye movements when tracking moving targets. Using a Recurrent Quantum Neural Network(RQNN) while simulating the quantum brain model, two very interesting phenomena are observed. First, as eye sensor data is processed in a classical brain, a wave packet is triggered in the quantum brain. This wave packet moves like a particle. Second, when the eye tracks a fixed target, this wave packet moves not in a continuous but rather in a discrete mode. This result reminds one of the saccadic movements of the eye consisting of 'jumps' and 'rests'. However, such a saccadic movement is intertwined with smooth pursuit movements when the eye has to track a dynamic trajectory. In a sense, this is the first theoretical model explaining the experimental observation reported concerning eye movements in a static scene situation. The resulting prediction is found to be very precise and efficient in comparison to classical objective modeling schemes such as the Kalman filter. △ Less

Submitted 2 July, 2004; originally announced July 2004.

Comments: 7 pages, 7 figures submitted to Physical Review Letters