Data-Driven Self-Triggering Mechanism for State Feedback Control

Abstract

This paper presents a novel approach for data-driven self-triggered state feedback control of unknown linear systems using noisy data gathered offline. The self-triggering mechanism determines the next triggering time by checking whether the difference between the predicted state and the current state is significant or not. However, when the system matrices are unknown, the challenge lies in characterizing the distance between future states and the current state using only data. To address this, we put forth a data-driven online optimization problem for trajectory prediction by using noisy input-state data. Its optimal solution, together with another unknown parameter that reflects the open-loop divergence rate, is shown sufficient for explicitly quantifying the distance. Moreover, a data-driven set-based over-approximating algorithm using matrix zonotopes is subsequently proposed to upper-bound the open-loop divergence rate. Leveraging the optimal solution and the upper bound, a self-triggering mechanism is devised for state feedback control systems, which is proven to ensure input-to-state stability. Numerical examples are presented to validate the effectiveness of the proposed method.