Event-Driven Control via Sparsity-Promoting Regularization: A Rollout Approach with Performance Guarantees

Abstract: This paper presents a controller design method aiming to balance control performance and actuation frequency. In this framework, actuation timings are determined in an event-driven manner, resulting in intermittent control actions. Control performance is measured by an infinite-horizon average cost, and input sparsity is promoted through actuation-rate regularization. Since the formulated optimal control problem has a combinatorial nature, we employ a rollout algorithm to find a suboptimal solution. In the proposed scheme, the event-triggering condition is derived through a multistage minimization procedure using a receding-horizon approach. We establish theoretical performance bounds with respect to periodic control and prove the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated through a numerical example.