Design of Information Channels for Optimization and Stabilization in Networked Control

Abstract

In stochastic control, typically a partial observation model/channel is given and one looks for a control policy for optimization or stabilization. Consider a single-agent dynamical system described by the discrete-time equations1)for (Borel measurable) functions f, g, with {w t } being an independent and identically distributed (i.i.d.) system noise process and {v t } an i.i.d. measurement disturbance process, which are independent of x 0 and each other. Here, x t ∈ X, y t ∈ Y, u t ∈ U, where we assume that these spaces are Borel subsets of finite dimensional Euclidean spaces. In (6.2), we can view g as inducing a measurement channel Q, which is a stochastic kernel or a regular conditional probability measure from X to Y in the sense that Q(·|x) is a probability measure on the (Borel) σ -algebra B(Y) on Y for every x ∈ X, and Q(A|·) : ] is a Borel measurable function for every A ∈ B(Y).In networked control systems, the observation channel described above itself is also subject to design. In a more general setting, we can shape the channel input by coding and decoding. This chapter is concerned with design and optimization of such channels.We will consider a controlled Markov model given by (6.1). The observation channel model is described as follows: This system is connected over a noisy channel with a finite capacity to a controller, as shown in Fig. 6.1. The controller has