Data-Driven Sparse Event-Triggered Control of Unknown Systems

In event-triggered control, we often face the situation where the control input must be sparse. We consider sparse event-triggered control, in which the control input is sparse and updated in an event-triggered manner. In this paper, we propose a data-driven method for unknown linear systems. First, as a preliminary result for the proposed method, we present a method for constructing a quadratic Lyapunov function for an unknown stable linear system; this method utilizes a data set of several segments of state trajectories. Based on this result, we derive a data-driven sparse event-triggered control. In this method, the event-triggering condition, which is defined by a Lyapunov function, is updated by online data on the state trajectory. The data are collected on the periods when state feedback control is applied and the state is reset on the other periods; this structure helps us to obtain data set including sufficient information on the plant dynamics. Consequently, the control system is driven by sparse input and is globally asymptotically stable. The performance is demonstrated by numerical simulation.