Separated design of encoder and controller for networked linear quadratic optimal control

TL;DR

This paper investigates the design of encoders and controllers in networked linear quadratic control systems, demonstrating that a separated design approach is optimal under certain conditions despite the presence of dual effects.

Contribution

It establishes conditions under which encoder and controller design can be separated in networked LQ control, even with dual effects, and explores the impact of design restrictions.

Findings

Separated design minimizes performance cost with dynamic encoder and controller.

Separation holds despite the dual effect in the closed-loop system.

Restricted class designs may not achieve optimality.

Abstract

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising of a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. We consider three basic formats for encoder outputs: quantized samples, real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop system. We also show that this separated design need not be optimal when the controller or encoder are to be chosen from within restricted classes.