Stabilization under round-robin scheduling of control inputs in nonlinear systems

Maheshwari, Chinmay; Sukumar, Srikant; Chatterjee, Debasish

doi:10.1016/j.automatica.2021.109912

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…where the control vector fields g i : R n → R n , 1 ≤ i ≤ m, are sufficiently regular. For the nonlinear system affine in the control that we have described (taken from [MSC21]), the choice of control inputs u 1 , . .…”

Section: Resultsmentioning

confidence: 99%

Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise

Dhama¹,

Pahlajani²

2022

Preprint

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We consider a nonlinear differential equation under the combined influence of small statedependent Brownian perturbations of size ε, and fast periodic sampling with period δ; 0 < ε, δ 1. Thus, state samples (measurements) are taken every δ time units, and the instantaneous rate of change of the state depends on its current value as well as its most recent sample. We show that the resulting stochastic process indexed by ε, δ, can be approximated, as ε, δ 0, by an ordinary differential equation (ode) with vector field obtained by replacing the most recent sample by the current value of the state.We next analyze the fluctuations of the stochastic process about the limiting ode. Our main result asserts that, for the case when δ 0 at the same rate as, or faster than, ε 0, the rescaled fluctuations can be approximated in a suitable strong (pathwise) sense by a limiting stochastic differential equation (sde). This sde varies depending on the exact rates at which ε, δ 0. The key contribution here involves computing the effective drift term capturing the interplay between noise and sampling in the limiting sde. The results essentially provide a first-order perturbation expansion, together with error estimates, for the stochastic process of interest. Connections with the performance analysis of feedback control systems with sampling are discussed and illustrated numerically through a simple example.

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Section: Resultsmentioning

confidence: 99%

Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise

Dhama¹,

Pahlajani²

2022

Preprint

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“…While sensor scheduling problems focus on minimizing (a function of) the estimation error, the actuator scheduling directly affects the controllability and stability of the system as well as the control performance. Therefore, a significant portion of the work on actuator scheduling focuses on studying the effects of actuator scheduling on the controllability and stability of the systems, e.g., [11], [12], [13], [14], [15] and others. It is shown in [11], [12], and [13] that several classes of energy related metrics associated with the controllability Gramian have a structural property (modularity) that allows for an approximation guarantee by using a simple greedy heuristic.…”

Section: Introductionmentioning

confidence: 99%

“…These problems are further investigated in [14], where a framework of sparse actuator schedule design was developed that guarantees performance bounds for a class of controllability metrics. Except [15], these works assume a time invariant scheduling problem, which is likely to be suboptimal and may impose restrictions on controllability for large systems. In [15] the authors use a round robin scheme for selecting the actuators and show that local stability is attained if the switching between the actuators is fast enough.…”

Section: Introductionmentioning

confidence: 99%

“…Except [15], these works assume a time invariant scheduling problem, which is likely to be suboptimal and may impose restrictions on controllability for large systems. In [15] the authors use a round robin scheme for selecting the actuators and show that local stability is attained if the switching between the actuators is fast enough. The efficacy of a time-varying scheduling over a time-invariant one for interconnected systems was also demonstrated in [16].…”

Section: Introductionmentioning

confidence: 99%

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Actuator Scheduling for Linear Systems: A Convex Relaxation Approach

Jiao¹,

Maity²,

Baras³

et al. 2022

Preprint

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In this letter, we investigate the problem of actuator scheduling for networked control systems. Given a stochastic linear system with a number of actuators, we consider the case that one actuator is activated at each time. This problem is combinatorial in nature and NP hard to solve. We propose a convex relaxation to the actuator scheduling problem, and use its solution as a reference to design an algorithm for solving the original scheduling problem. Using dynamic programming arguments, we provide a suboptimality bound of our proposed algorithm. Furthermore, we show that our framework can be extended to incorporate multiple actuators scheduling at each time and actuation costs. A simulation example is provided, which shows that our proposed method outperforms a random selection approach and a greedy selection approach.

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Input-to-state stabilization of networked impulsive systems under communication constraints: A refined Lyapunov functional

Yao,

Wei,

Guo

2024

Applied Mathematics and Computation

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Stabilization under round-robin scheduling of control inputs in nonlinear systems

Cited by 6 publications

References 20 publications

Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise

Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise

Actuator Scheduling for Linear Systems: A Convex Relaxation Approach

Input-to-state stabilization of networked impulsive systems under communication constraints: A refined Lyapunov functional

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