Switched Systems Control via Discreteness-Promoting Regularization

TL;DR

This paper introduces a new regularization-based approach for designing finite-horizon discrete switching signals in linear switched systems, transforming a complex combinatorial problem into a solvable continuous optimization problem.

Contribution

It reformulates the combinatorial control design problem as a non-convex continuous optimization with a regularization term that promotes discreteness, and proves solution equivalence.

Findings

Effective in designing switching signals for linear systems

Numerical examples validate the approach's efficiency

Reformulation simplifies complex combinatorial optimization

Abstract

This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as a continuous optimization problem with a non-convex regularization term that promotes discreteness of the control. We prove that any solution obtained from the relaxed problem is also a solution to the original problem. The resulting non-convex optimization problem is efficiently solved through time discretization. Numerical examples demonstrate the effectiveness of the proposed method.