Event-Triggered Control of Nonlinear Discrete-Time System With Unknown Dynamics Based on HDP(λ)

The heuristic dynamic programming (HDP) ( λ )-based optimal control strategy, which takes a long-term prediction parameter λ into account using an iterative manner, accelerates the learning rate obviously. The computation complexity caused by the state-associated extra variable in λ -return value computing of the traditional value-gradient learning method can be reduced. However, as the iteration number increases, calculation costs have grown dramatically that bring huge challenge for the optimal control process with limited bandwidth and computational units. In this article, we propose an event-triggered HDP (ETHDP) ( λ ) optimal control strategy for nonlinear discrete-time (NDT) systems with unknown dynamics. The iterative relation for λ -return of the final target value is derived first. The event-triggered condition ensuring system stability is designed to reduce the computation and communication requirements. Next, we build a model-actor-critic neural network (NN) structure, in which the model NN evaluates the system state for getting λ -return of the current time target value, which is used to obtain the critic NN real-time update errors. The event-triggered optimal control signal and one-step-return value are approximated by actor and critic NN, respectively. Then, the event trigger-based uniformly ultimately bounded (UUB) stability of the system state and NN weight errors are demonstrated by applying the Lyapunov technology. Finally, we illustrate the effectiveness of our proposed ETHDP ( λ ) strategy by two cases.