Optimal multiplexing of sparse controllers for linear systems

This article treats three problems of sparse and optimal multiplexing a finite ensemble of linear control systems. Given an ensemble of linear control systems, multiplexing of the controllers consists of an algorithm that selects, at each time $t$, only one from the ensemble of linear systems is actively controlled whereas the other systems evolve in open-loop. The first problem treated here is a ballistic reachability problem where the control signals are required to be maximally sparse and multiplexed, the second concerns sparse and optimally multiplexed linear quadratic control, and the third is a sparse and optimally multiplexed Mayer problem. Numerical experiments are provided to demonstrate the efficacy of the techniques developed here.