Deterministic and Stochastic Approaches to Supervisory Control Design for Networked Systems with Time-Varying Communication Delays

TL;DR

This paper introduces a supervisory control framework for networked systems with time-varying delays, utilizing Lyapunov-Krasovskii functionals and convex optimization to enhance performance and stability.

Contribution

It presents a novel supervisory control design using multiple Lyapunov-Krasovskii functionals and convex optimization, including extensions for Markovian delay modes.

Findings

Improved closed-loop performance over single controllers.

Stability conditions verified via semi-definite programming.

Effective control synthesis using convex optimization.

Abstract

This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwell-time switching and is based on a novel multiple Lyapunov-Krasovskii functional. We develop stability conditions that can be verified by semi-definite programming, and show that the associated state feedback synthesis problem also can be solved using convex optimization tools. Extensions of the analysis and synthesis procedures to the case when the evolution of the delay mode is described by a Markov chain are also developed. Simulations on small and large-scale networked control systems are used to illustrate the effectiveness of our approach.