In this article, an event-triggered adaptive dynamic programming (ETADP) method is proposed for the robust optimal tracking control problem of an uncertain continuous-time nonlinear system with asymmetric input constraints and external disturbances. First, an event-triggered integral reinforcement learning (ETIRL) algorithm is proposed to address the zero-sum game problem for partially unknown dynamical systems. A triggering condition with an interference attenuation level is designed to optimize the process. Second, a single-critic neural network structure is employed to approximate the optimal control law. The control and disturbance laws are updated non-periodically by the event-triggered. The asymptotic stability of the closed-loop system and the uniform ultimate boundedness (UUB) of the critic neural network weights are proven theoretically using the Lyapunov stability theorem. Finally, the feasibility of the algorithm is assessed through pneumatic muscle antagonistic joint experiments.

In this paper, an event-triggered adaptive dynamic programming (ADP) method is proposed to deal with the $H_{\infty }$ problem with unknown dynamic and constrained input. Firstly, the $H_{\infty }$-constrained problem is regarded as the two-player zero-sum game with the nonquadratic value function. Secondly, we develop the event-triggered Hamilton–Jacobi–Isaacs(HJI) equation, and an event-triggered ADP method is proposed to solve the HJI equation, which is equivalent to solving the Nash saddle point of the zero-sum game. An event-based single-critic neural network (NN) is applied to obtain the optimal value function, which reduces the communication resource and computational cost of algorithm implementation. For the event-triggered control, a triggering condition with the level of disturbance attenuation is developed to limit the number of sampling states, and the condition avoids Zeno behavior by proving the existence of events with minimum triggering interval. It is proved theoretically that the closed-loop system is asymptotically stable, and the critic NN weight error is uniformly ultimately boundedness (UUB). The learning performance of the proposed algorithm is verified by two examples.