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We address the problem of sparsity-promoting optimal control ofcyber-physical systems with feedback delays. The delays are categorized intotwo classes - namely, intra-layer delay, and inter-layer delay between thecyber and the physical layers. Our objective is to minimize the H2-norm of theclosed-loop system by designing an optimal combination of these two delaysalong with a sparse state-feedback controller, while respecting a givenbandwidth 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 increasingsparsity of the controller. The outer loop comprises of semidefinite program(SDP)-based relaxations of non-convex inequalities necessary for stableco-design of the delays with the controller. We illustrate this algorithm usingsimulations that highlight various aspects of how delays and sparsity impactthe stability and $\mc{H}_2$ performance of a LTI system.

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