arXiv subjects

Atreyee Kundu

Publications and source records attributed to Atreyee Kundu.

At least 19 recordsLinked to original sources

arXiv2026

On maximum hands-off restricted hybrid control for discrete-time switched linear systems

This paper deals with design of maximum hands-off hybrid control sequences for discrete-time switched linear systems. It is a sparsest combination of a discrete control sequence (i.e. the switching sequence) and a continuous control sequence, both satisfying pre-specified restrictions on the admissible actions, that steers a given initial state of the switched system to the origin of the state-space in a pre-specified duration of time. Given the subsystems dynamics, the sets of admissible continuous and discrete control, the initial state and the time horizon, we present a new algorithm that, under certain conditions on the subsystems dynamics and the admissible control, designs maximum hands-off hybrid control sequences for the resulting switched system. The key apparatuses for our analysis are graph theory and linear algebra. Numerical examples are presented to demonstrate our results.

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arXiv2024

On stability and state-norm estimation of switched systems under restricted switching

This paper deals with the analysis of input/output-to-state stability (IOSS) and construction of state-norm estimators for continuous-time switched nonlinear systems under restricted switching. Our contributions are twofold. First, given a family of systems, possibly containing unstable dynamics, a set of admissible switches between the subsystems and admissible minimum and maximum dwell times on the subsystems, we identify a class of switching signals that obeys the given restrictions and preserves IOSS of the resulting switched system. Second, we design a class of state-norm estimators for switched systems under our class of stabilizing switching signals. These estimators are switched systems themselves with two subsystems -- one stable and one unstable. The key apparatus for our analysis is multiple Lyapunov-like functions. A numerical example is presented to demonstrate the results.

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arXiv2024

Stabilizing switched nonlinear systems under restricted but arbitrary switching signals

This paper deals with input/output-to-state stability (IOSS) of switched nonlinear systems whose switching signals obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems. We present sufficient conditions on the subsystems, admissible switches between them and admissible dwell times on them, such that a switched system generated under all switching signals obeying the given restrictions is IOSS. Multiple Lyapunov-like functions and graph theory are the key apparatuses for our analysis. A numerical example is presented to demonstrate our results.

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arXiv2023

A Sparsity Approach to Scheduling and Control of Networked Systems

We study the design of scheduling logic and control logic for networked control systems (NCSs) where plants communicate with their remotely located controllers over a shared band-limited communication network. Due to a limited capacity of the network, only a subset of the plants can exchange information with their controllers at any instant of time and the remaining plants operate in open-loop. Our key contribution is a new algorithm that co-designs (a) an allocation scheme of the communication network among the plants (scheduling logic) and (b) the control inputs for the plants accessing the network (control logic) under which given non-zero initial states are steered to zero in a given time horizon for all the plants in the NCS. Sparse optimization is the primary apparatus for our analysis. We also provide sufficient conditions on the plant dynamics, capacity of the communication network and the given time horizon that lead to a numerically tractable implementation of our algorithm. A numerical experiment is presented to demonstrate the proposed results.

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arXiv2023

A probabilistic algorithm for scheduling networked control systems under data losses

This paper deals with the design of scheduling logics for networked control systems (NCSs) whose communication networks have limited capacity and are prone to data losses. Our contributions are twofold. First, we present a probabilistic algorithm to generate a scheduling logic that under certain conditions on the plant and the controller dynamics, the capacity of the network and the probability of data losses, ensures stochastic stability of each plant in the NCS. Second, given the plant dynamics, the capacity of the shared communication network and the probability of data losses, we discuss the design of state-feedback controllers such that our stability conditions are obeyed. Numerical examples are presented to demonstrate the results reported in this paper.

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arXiv2023

Yet another stability condition for switched nonlinear systems

This paper deals with input/output-to-state stability (IOSS) of continuous-time switched nonlinear systems. Given a family of systems, possibly containing unstable dynamics, and a set of restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems, we identify a class of switching signals that obeys these restrictions and preserves stability of the resulting switched system. The primary apparatus for our analysis is multiple Lyapunov-like functions. Input-to-state stability (ISS) and global asymptotic stability (GAS) of switched systems under pre-specified restrictions on switching signals fall as special cases of our results when no outputs (resp., also inputs) are considered.

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arXiv2022

A probabilistic scheduling algorithm for networked control systems

This paper deals with the design of scheduling logics for Networked Control Systems (NCSs) whose communication networks have limited capacity. We assume that only a subset of the plants can communicate with their controllers at any time instant. Our contributions are twofold. First, we present a probabilistic algorithm to design scheduling logics that, under certain conditions on the plant and controller dynamics and the capacity of the network, ensure stochastic stability of each plant in an NCS. Second, given the plant dynamics and the capacity of the network, we design static state-feedback controllers such that the conditions for stability under our scheduling logics are satisfied. The main apparatus for our analysis is a Markovian jump linear system representation of the individual plants in an NCS. Our stability conditions involve sets of matrix inequalities. We present numerical experiments to demonstrate our results.

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arXiv2021

A randomized algorithm for the stabilization of switched nonlinear systems under restricted switching

This paper deals with input/output-to-state stability (IOSS) of switched nonlinear systems in the discrete-time setting. We present an algorithm to construct periodic switching signals that obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems, and identify sufficient conditions on the individual subsystems, the admissible switches and admissible dwell times under which a switching signal obtained from our algorithm preserves stability of a switched system with overwhelming probability. We recover our earlier result on probabilistic techniques for the design of switching signals that preserve global asymptotic stability of switched linear systems under sufficient conditions on the properties of the individual subsystems and the admissible dwell times on the subsystems.

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arXiv2021

A scheduling algorithm for networked control systems

This paper deals with the design of scheduling logics for Networked Control Systems (NCSs) whose shared communication networks have limited capacity. We assume that among $N$ plants, only $M\:(< N)$ plants can communicate with their controllers at any time instant. We present an algorithm to allocate the network to the plants periodically such that stability of each plant is preserved. The main apparatus for our analysis is a switched systems representation of the individual plants in an NCS. We rely on multiple Lyapunov-like functions and graph-theoretic arguments to design our scheduling logics. The set of results presented in this paper is a continuous-time counterpart of the results proposed in [15]. We present a set of numerical experiments to demonstrate the performance of our techniques.

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arXiv2020

A note on the existence of stabilizing switching signals for switched linear systems

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set of purely time-dependent switching signals that are allowed to activate all subsystems. The main apparatuses for our analysis are (matrix) commutation relations between certain products of the subsystems matrices and graph-theoretic arguments. We present a numerical experiment to demonstrate our results.

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arXiv2020

Design of periodic scheduling and control for networked systems under random data loss

This paper deals with Networked Control Systems (NCSs) whose shared networks have limited communication capacity and are prone to data losses. We assume that among (N) plants, only (M < N) plants can communicate with their controllers at any time instant. In addition, a control input, at any time instant, is lost in a channel with a probability (p). Our contributions are threefold. First, we identify necessary and sufficient conditions on the open-loop and closed-loop dynamics of the plants that ensure existence of purely time-dependent periodic scheduling sequences under which stability of each plant is preserved for all admissible data loss signals. Second, given the open-loop and closed-loop dynamics of the plants, relevant parameters of the shared network and a period for the scheduling sequence, we present an algorithm that verifies our stability conditions and if satisfied, designs stabilizing scheduling sequences. Otherwise, the algorithm reports non-existence of a stabilizing periodic scheduling sequence with the given period and stability margins. Third, given the plant matrices, the parameters of the network and a period for the scheduling sequence, we present an algorithm that designs static state-feedback controllers such that our stability conditions are satisfied. The main apparatus for our analysis is a switched systems representation of the individual plants in an NCS whose switching signals are time-inhomogeneous Markov chains. Our stability conditions rely on the existence of sets of symmetric and positive definite matrices that satisfy certain (in)equalities.

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arXiv2020

Learning event-driven switched linear systems

We propose an automata theoretic learning algorithm for the identification of black-box switched linear systems whose switching logics are event-driven. A switched system is expressed by a deterministic finite automaton (FA) whose node labels are the subsystem matrices. With information about the dimensions of the matrices and the set of events, and with access to two oracles, that can simulate the system on a given input, and provide counter-examples when given an incorrect hypothesis automaton, we provide an algorithm that outputs the unknown FA. Our algorithm first uses the oracle to obtain the node labels of the system run on a given input sequence of events, and then extends Angluin's $L^*$-algorithm to determine the FA that accepts the language of the given FA. We demonstrate the performance of our learning algorithm on a set of benchmark examples.

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arXiv2020

A reinforcement learning approach to hybrid control design

In this paper we design hybrid control policies for hybrid systems whose mathematical models are unknown. Our contributions are threefold. First, we propose a framework for modelling the hybrid control design problem as a single Markov Decision Process (MDP). This result facilitates the application of off-the-shelf algorithms from Reinforcement Learning (RL) literature towards designing optimal control policies. Second, we model a set of benchmark examples of hybrid control design problem in the proposed MDP framework. Third, we adapt the recently proposed Proximal Policy Optimisation (PPO) algorithm for the hybrid action space and apply it to the above set of problems. It is observed that in each case the algorithm converges and finds the optimal policy.

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arXiv2020

Data-driven switching logic design for switched linear systems

This paper deals with stabilization of discrete-time switched linear systems when explicit knowledge of the state-space models of their subsystems is not available. Given the set of admissible switches between the subsystems, the admissible dwell times on the subsystems and a set of finite traces of state trajectories of the subsystems that satisfies certain properties, we devise an algorithm that designs periodic switching logics which preserve stability of the resulting switched system. We combine two ingredients: (a) data-based stability analysis of discrete-time linear systems and (b) multiple Lyapunov-like functions and graph walks based design of stabilizing switching logics, for this purpose. A numerical example is presented to demonstrate the proposed algorithm.

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arXiv2020

On stabilizability of switched linear systems under restricted switching

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on the subsystems. We derive sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set of purely time-dependent switching signals that obeys the given restrictions. The main apparatuses for our analysis are (matrix) commutation relations between certain products of the subsystems matrices and graph-theoretic arguments.

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arXiv2020

Data-based computation of stabilizing minimum dwell times for discrete-time switched linear systems

We present an algorithm to compute stabilizing minimum dwell times for discrete-time switched linear systems without the explicit knowledge of state-space models of their subsystems. Given a set of finite traces of state trajectories of the subsystems that satisfies certain properties, our algorithm involves the following tasks: first, multiple Lyapunov functions are designed from the given data; second, a set of relevant scalars is computed from these functions; and third, a stabilizing minimum dwell time is determined as a function of these scalars. A numerical example is presented to demonstrate the proposed algorithm.

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arXiv2020

Learning switched systems from simulation models

The design of decision and control strategies for switched systems typically requires complete knowledge of (i) mathematical models of the subsystems and (ii) restrictions on admissible switches between the subsystems. We propose an active learning algorithm that infers (i) and (ii) for discrete-time switched systems whose subsystems dynamics are governed by sets of scalar polynomials and switching signals are constrained by automata. We collect data from gray-box simulation models of the switched systems for this purpose. Our technique for learning (i) involves linear algebraic tools, while for learning (ii) we employ a modified version of the well-known $L^*$-algorithm from machine learning literature. A numerical example is presented to demonstrate our learning algorithm.

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arXiv2020

Scheduling networked control systems under jamming attacks

This paper deals with the design of scheduling policies for networked control systems whose shared networks have limited communication capacity and the controller to plant channels are vulnerable to jamming attacks. We assume that among N plants, only M (< N) plants can communicate with their controllers at any time instant, and the attack sequences follow an (m,k)-firm model, i.e., in any k consecutive time instants, the control inputs sent to some or all of the plants accessing the communication network, are deactivated at most at m (< k) time instants. We devise a new algorithm to allocate the network to the plants periodically such that stability of each plant is preserved under the admissible attack signals. The main apparatus for our analysis is a switched systems representation of the individual plants in an NCS. We rely on matrix commutators (Lie brackets) between the stable and unstable modes of operation of the plants to guarantee stability under our scheduling policies.

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