How To Tame Your Sparsity Constraints

TL;DR

This paper presents a simple, iterative method for designing sparse $H_ty$ controllers as FIR filters in discrete-time LTI systems, simplifying the process and enabling robust controller design via system identification.

Contribution

It introduces an alternating convex feasibility approach for FIR $H_ty$ controller synthesis, providing a practical pathway for sparse robust control design.

Findings

The algorithm converges to a suboptimal stable $H_ty$ controller.

FIR filters facilitate easy incorporation of impulse response information.

The method simplifies sparse controller design for continuous-time systems.

Abstract

We show that designing sparse $H_\infty$ controllers, in a discrete (LTI) setting, is easy when the controller is assumed to be an FIR filter. In this case, the problem reduces to a static output feedback problem with equality constraints. We show how to obtain an initial guess, for the controller, and then provide a simple algorithm that alternates between two (convex) feasibility programs until converging, when the problem is feasible, to a suboptimal $H_\infty$ controller that is automatically stable. As FIR filters contain the information of their impulse response in their coefficients, it is easy to see that our results provide a path of least resistance to designing sparse robust controllers for continuous-time plants, via system identification methods.