Co-Design of Delays and Sparse Controllers for Bandwidth-Constrained Cyber-Physical Systems

TL;DR

This paper presents a co-design approach for delays and sparse controllers in cyber-physical systems, optimizing bandwidth use while maintaining stability and performance through a novel two-loop algorithm.

Contribution

It introduces a new two-loop optimization algorithm combining ADMM and SDP relaxations for co-designing delays and sparse controllers under bandwidth constraints.

Findings

Delays and sparsity significantly affect system stability.

The proposed method effectively balances delay, sparsity, and performance.

Simulations demonstrate improved H2-norm performance with co-designed delays and controllers.

Abstract

We address the problem of sparsity-promoting optimal control of cyber-physical systems with feedback delays. The delays are categorized into two classes - namely, intra-layer delay, and inter-layer delay between the cyber and the physical layers. Our objective is to minimize the H2-norm of the closed-loop system by designing an optimal combination of these two delays along with a sparse state-feedback controller, while respecting a given bandwidth constraint. We propose a two-loop optimization algorithm for this. The inner loop, based on alternating directions method of multipliers (ADMM), handles the conflicting directions of decreasing H2-norm and increasing sparsity of the controller. The outer loop comprises of semidefinite program (SDP)-based relaxations of non-convex inequalities necessary for stable co-design of the delays with the controller. We illustrate this algorithm using simulations that highlight various aspects of how delays and sparsity impact the stability and $\mc{H}_2$ performance of a LTI system.