Adaptive event-triggered PID controllers for linear discrete-time plants

This paper studies adaptive event-triggered PID controllers for 2nd-order linear discrete-time plants for set-point tracking. A new adaptive law is designed by introducing a decay parameter to improve the robustness of the closed-loop system. By utilizing the extra robustness, an absolute type of event-triggering conditions is proposed, where the threshold parameter is co-designed with the adaptive laws. Then, the closed-loop system is formulated into a nonlinear interconnected system among the tracking errors, the differences of outputs, and the parameter estimation errors. A rigorous proof of stability is provided to ensure that the tracking error converges to a vicinity of zero when the initial state belongs to some compact sets. Finally, numerical simulations are given to illustrate the efficiency and feasibility of the proposed results.