# Sparsity-Promoting Optimal Control of Cyber-Physical Systems over Shared Communication Networks

## TL;DR

This paper develops sparse control strategies for cyber-physical systems sharing communication networks, addressing delays and fairness, and introduces algorithms that optimize performance while managing bandwidth and sparsity trade-offs.

## Contribution

It introduces novel sparse H2 control algorithms that incorporate network delays and fairness in shared communication environments, with proven convergence and practical validation.

## Key findings

- Algorithms effectively balance sparsity and performance.
- Delay can be a function of sparsity, affecting control trade-offs.
- Fair bandwidth sharing improves multi-user control performance.

## Abstract

Recent years have seen several new directions in the design of sparse control of cyber-physical systems (CPSs) driven by the objective of reducing communication cost. One common assumption made in these designs is that the communication happens over a dedicated network. For many practical applications, however, communication must occur over shared networks, leading to two critical design challenges, namely - time-delays in the feedback and fair sharing of bandwidth among users. In this paper, we present a set of sparse H2 control designs under these two design constraints. An important aspect of our design is that the delay itself can be a function of sparsity, which leads to an interesting pattern of trade-offs in the H2 performance. We present three distinct algorithms. The first algorithm preconditions the assignable bandwidth to the network and produces an initial guess for a stabilizing controller. This is followed by our second algorithm, which sparsifies this controller while simultaneously adapting the feedback delay and optimizing the H2 performance using alternating directions method of multipliers (ADMM). The third algorithm extends this approach to a multiple user scenario where optimal number of communication links, whose total sum is fixed, is distributed fairly among users by minimizing the variance of their H2 performances. The problem is cast as a difference-of-convex (DC) program with mixed-integer linear program (MILP) constraints. We provide theorems to prove convergence of these algorithms, followed by validation through numerical simulations.