arXiv subjects

Bhabani Shankar Dey

Publications and source records attributed to Bhabani Shankar Dey.

12 recordsLinked to original sources

arXiv2026

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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arXiv2026

Input-to-State Stabilizing Neural Controllers for Unknown Switched Nonlinear Systems within Compact Sets

This paper develops a neural network based control framework that ensures system safety and input-to-state stability (ISS) for general nonlinear switched systems with unknown dynamics. Leveraging the concept of dwell time, we derive Lyapunov based sufficient conditions under which both safety and ISS of the closed-loop switched system are guaranteed. The feedback controllers and the associated Lyapunov functions are parameterized using neural networks and trained from data collected over a compact state space via deterministic sampling. To provide formal stability guarantees under the learned controllers, we introduce a validity condition based on Lipschitz continuity assumptions, which is embedded directly into the training framework. This ensures that the resulting neural network controllers satisfy provable correctness and stability guarantees beyond the sampled data. As a special case, the proposed framework recovers ISS and safety under arbitrary switching when a common Lyapunov function exists. Simulation results on a representative switched nonlinear system demonstrate the effectiveness of the proposed approach.

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arXiv2025

Neural Controller for Incremental Stability of Unknown Continuous-time Systems

This work primarily focuses on synthesizing a controller that guarantees an unknown continuous-time system to be incrementally input-to-state stable ($δ$-ISS). In this context, the notion of $δ$-ISS control Lyapunov function ($δ$-ISS-CLF) for the continuous-time system is introduced. Combined with the controller, the $δ$-ISS-CLF guarantees that the system is incrementally stable. As the paper deals with unknown dynamical systems, the controller as well as the $δ$-ISS-CLF are parametrized using neural networks. The data set used to train the neural networks is generated from the state space of the system by proper sampling. Now, to give a formal guarantee that the controller makes the system incrementally stable, we develop a validity condition by having some Lipschitz continuity assumptions and incorporate the condition into the training framework to ensure a provable correctness guarantee at the end of the training process. Finally, we demonstrate the effectiveness of the proposed approach through several case studies: a scalar system with a non-affine, non-polynomial structure, a one-link manipulator system, a nonlinear Moore-Greitzer model of a jet engine, a magnetic levitator system and a rotating rigid spacecraft model.

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arXiv2025

Formally Verified Neural Network Controllers for Incremental Input-to-State Stability of Unknown Discrete-Time Systems

This work aims to synthesize a controller that ensures that an unknown discrete-time system is incrementally input-to-state stable ($δ$-ISS). In this work, we introduce the notion of $δ$-ISS control Lyapunov function ($δ$-ISS-CLF), which, in conjunction with the controller, ensures that the closed-loop system is incrementally ISS. To address the unknown dynamics of the system, we parameterize the controller as well as the $δ$-ISS-CLF as neural networks and learn them by utilizing the sampled data from the state space of the unknown system. To formally verify the obtained $δ$-ISS-CLF, we develop a validity condition and incorporate the condition into the training framework to ensure a provable correctness guarantee at the end of the training process. Finally, the usefulness of the proposed approach is proved using multiple case studies - the first one is a scalar system with a non-affine non-polynomial structure, the second example is a one-link manipulator system, the third system is a nonlinear Moore-Grietzer model of the jet engine and the final one is a rotating rigid spacecraft model.

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arXiv2025

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees

Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability notion called incremental input-to-state practical stability (δ-ISpS), ensuring safety guarantees. We also present a feedback linearization based control design scheme that renders a partially unknown system incrementally input-to-state practically stable and safe with formal guarantees. To deal with the unknown dynamics, we utilize Gaussian process regression to approximate the model. Finally, we implement the controller synthesized by the proposed scheme on a manipulator example

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arXiv2025

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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arXiv2025

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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arXiv2025

Formally Verified Neural Lyapunov Function for Incremental Input-to-State Stability of Unknown Systems

This work presents an approach to synthesize a Lyapunov-like function to ensure incrementally input-to-state stability ($δ$-ISS) property for an unknown discrete-time system. To deal with challenges posed by unknown system dynamics, we parameterize the Lyapunov-like function as a neural network, which we train using the data samples collected from the unknown system along with appropriately designed loss functions. We propose a validity condition to test the obtained function and incorporate it into the training framework to ensure provable correctness at the end of the training. Finally, the usefulness of the proposed technique is proved using two case studies: a scalar non-linear dynamical system and a permanent magnet DC motor.

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arXiv2024

Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems

Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class of incremental Lyapunov functions, an incremental stability notion known as Incremental Input-to-State practical Stability (δ-ISpS). Using Gaussian Process, we learn the unknown dynamics of a class of control systems. We then present a backstepping control design scheme that provides state-feedback controllers that render the partially unknown control system δ-ISpS. To show the effectiveness of the proposed controller, we implement it in two case studies.

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arXiv2022

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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arXiv2022

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.

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arXiv2022

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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