Tracking Control of Discrete-Time System With Dynamic Event-Based Adaptive Dynamic Programming

Abstract

In this brief, a novel formulation of the value function with dynamic event-triggered strategy is introduced for the optimal tracking problem (TP) of nonlinear discrete-time systems to eliminate the tracking error by using adaptive dynamic programming (ADP). Firstly, different from the existing ADP methods, a creative formulation of the cost function introduces the control input into the tracking error, and ignores the quadratic form of the control input directly. Second, a novel static triggering mechanism is designed. The proposed approach samples the states and updates the control signal only when the triggered condition is satisfied, and critic-actor Neural network (NN) is designed to approach the performance index and control input. The stability analysis of the closed-loop system is provided based on the Lyapunov’s theorem. Finally, in order to obtain a larger event triggering time interval, a dynamic triggering mechanism is given. Theoretical results show that the system state and the network weight errors are uniformly ultimately bounded (UUB). A simulation result also verify the theoretical claims.