Recursive Quantization for $\mathcal{L}_2$ Stabilization of a Finite Capacity Stochastic Control Loop with Intermittent State Observations

TL;DR

This paper develops recursive quantization algorithms to achieve $ ext{L}_2$ stabilization of unstable linear control systems with limited communication capacity and intermittent observations, providing new bounds and methods for such constrained stochastic control problems.

Contribution

It introduces novel recursive quantization schemes and bounds on intermittence parameters for stabilizing unstable LTI systems over finite capacity channels with intermittent observations.

Findings

Derived new bounds on intermittence parameters for stability.

Developed recursive quantization algorithms for constrained stabilization.

Validated results with illustrative examples.

Abstract

The problem of $\mathcal{L}_2$ stabilization of a state feedback stochastic control loop is investigated under different constraints. The discrete time linear time invariant (LTI) open loop plant is chosen to be unstable. The additive white Gaussian noise is assumed to be stationary. The link between the plant and the controller is assumed to be a finite capacity stationary channel, which puts a constraint on the bit rate of the transmission. Moreover, the state of the plant is observed only intermittently keeping the loop open some of the time. In this manuscript both scalar and vector plants under Bernoulli and Markov intermittence models are investigated. Novel bounds on intermittence parameters are obtained to ensure $\mathcal{L}_2$ stability. Moreover, novel recursive quantization algorithms are developed to implement the stabilization scheme under all the constraints. Suitable illustrative examples are provided to elucidate the main results.