Co-Design Of Delays And Sparse Controllers For Bandwidth-Constrained Cyber-Physical Systems

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 H-2-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 H-2-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 H-2-performance of a LTI system.