Direct Data-Driven Impulsive Control With Average Impulse Interval and Event-Triggered Mechanism

Controlling discrete-time linear systems with unknown model information while reducing control costs poses considerable obstacles. To tackle this issue, this paper proposes two novel data-driven impulsive control (IMC) frameworks for discrete-time linear systems. First, unlike most existing IMC strategies that rely on accurate system models or system identification, the proposed methods can directly design controllers based on measured data. Moreover, for data-driven IMC schemes that respect the average impulsive interval, the exponential stabilization of the system is demonstrated under the strong rank condition by leveraging relevant data and invoking the concepts of Lyapunov functions and the iterative synthesis procedure. Second, to reduce unnecessary impulsive actions during information transmission and thereby enhance control performance, a data-driven event-triggered impulsive control (ETIMC) approach is examined by combining event-triggered control with IMC. To mitigate the requirement for persistent excitation of input data, the concept of data informativity is utilized for analysis, and sufficient criteria for system stabilization under the proposed data-driven ETIMC are established in conjunction with the collected data. Ultimately, the validity of the theoretical results is verified through two illustrative examples.