Stochastic Sensor Scheduling for Networked Control Systems

TL;DR

This paper develops an optimal sensor scheduling method for networked control systems using Markov chain models, balancing sampling frequency and switching effort to improve resource allocation and system performance.

Contribution

It introduces a novel Markov chain-based approach for optimal sensor scheduling that extends Brockett's control method, optimizing resource use in networked control systems.

Findings

Derived an optimal scheduling policy minimizing a combined cost function.

Provided bounds on system performance under the proposed scheduling.

Validated the approach with numerical simulations on water tank systems.

Abstract

Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost function for this Markov chain as the summation of terms depending on the average sampling frequencies of the subsystems and the effort needed for changing the parameters of the underlying Markov chain. By minimizing this cost function through extending Brockett's recent approach to optimal control of Markov chains, we extract an optimal scheduling policy to fairly allocate the network resources among the control loops. We study the statistical properties of this scheduling policy in order to compute upper bounds for the closed-loop performance of the networked system, where several decoupled scalar subsystems are connected to their corresponding estimator or controller through a shared communication medium. We generalize the estimation results to observable subsystems of arbitrary order. Finally, we illustrate the developed results numerically on a networked system composed of several decoupled water tanks.