An event-triggered adaptive dynamic programming control strategy based on recursive terminal sliding mode

For a class of uncertain nonlinear systems with unknown disturbances and input constraints, a novel event-triggered adaptive dynamic programming control strategy based on recursive terminal sliding mode (ET-ADP-RTSM) is proposed. First, a recursive terminal sliding mode (RTSM) surface composed of a fast non-singular sliding mode surface and an integral sliding mode surface is constructed to ensure that the tracking error converges to zero with faster speed and higher accuracy. Second, the RTSM, the upper bound information of the disturbance function, and the constraint function of the control input are simultaneously incorporated into the utility function to construct an improved performance value function, transforming the robust nonlinear control problem of the system into an approximate optimal control problem. A nested update strategy is adopted when using the neural networks to approximate the optimal value function. An event-triggered (ET) constrained tracking Hamilton-Jacobi-Bellman (HJB) equation is established, and only one critic neural network (NN) is used to learn the optimal value function and obtain the optimal tracking controller. Finally, based on Lyapunov theory, the convergence of the critic NN weights and the stability of the entire closed-loop system are proved. Simulation results and comparative analyses verify the effectiveness of the proposed control strategy.