Controllability and Observability Gramians as Information Metrics for Optimal Design of Networked Control Systems

Abstract

This paper addresses the problem of optimal control and scheduling of Networked Control Systems over limited bandwidth deterministic networks using some insight on the interplay between the control and information theory. The motivation is related to the necessity of choice a communication sequence which maximize control signal impact on the plant behavior. The solution is obtained by decomposing the overall problem in a twofold one. The first level problem aims obtaining the periodic off-line or static scheduling function of control signals based on system properties, communication constrains, periodicity of scheduling sequence, performance criteria and maximization of the degree of reachability/observability of the periodic system. A Mixed Integer Quadratic Programming (MIQP) problem is formulated and solved obtaining a periodic and stable NCS. The solution of the second level problem is based on the structure of the static scheduling function obtained from the first level solution and the dependance of the degree of reachability/observability on the current state of the system.