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Indra Narayan Kar

Publications and source records attributed to Indra Narayan Kar.

At least 19 recordsLinked to original sources

Robust Fixed-Time Model Reference Adaptive Control

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.

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

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.

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Safety in Admittance Control using Reference Trajectory Shaping

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.

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Minimum time consensus for damped second order agents using Gröbner basis

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.

math.OC

Minimum Time Consensus of Multi-agent System under Fuel Constraints

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.

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

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.

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On Incremental Stability of Interconnected Switched Systems

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.

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On the Contraction Analysis of Nonlinear System with Multiple Equilibrium Points

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.

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Safe Human Robot-Interaction using Switched Model Reference Admittance Control

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.

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

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.

cs.RO

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

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.

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Characterization of Minimum Time-Fuel Optimal Control for LTI Systems

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.

math.OC

Efficient detection of adversarial images

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.

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

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.

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Analysis of higher order time delay systems using Lambert W function

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.

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

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.

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Memory-Based Data-Driven MRAC Architecture Ensuring Parameter Convergence

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.

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

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.

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