Optimal multiplexing of sparse controllers for linear systems
For control theorists and practitioners, this work provides a framework for multiplexing sparse controllers, though it is an incremental extension of existing optimal control and sparsity techniques.
The paper addresses sparse and optimal multiplexing of controllers for linear systems, solving ballistic reachability, LQR, and Mayer problems with sparsity constraints. Numerical experiments validate the proposed methods.
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.