Event-triggered adaptive optimal tracking control with error derivatives for state-constrained nonlinear strict-feedback systems

The paper presents an adaptive control method with tracking error derivatives in the cost function for nonlinear strict-feedback systems under full state constraints. Within the framework of the backstepping method, the barrier-type optimal cost function is constructed to prevent the state variables from exceeding a predefined range. In the cost function, control inputs are introduced into the tracking error derivatives, ensuring that the cost function remains bounded over infinite time and that the error signal converges. An adaptive reinforcement learning (RL) algorithm is executed using the actor-critic architecture to obtain virtual and actual optimal controllers. Additionally, a dynamic event-triggering mechanism is designed to adjust the triggering threshold online, further shortening the triggering time to save communication resources. It is proven using the Lyapunov method that the signals of the closed-loop system remain bounded. Finally, a simulation example is provided to verify the effectiveness of the proposed optimal control method.