Event‐triggered adaptive dynamic programming of nonlinear system with asymmetric input constraints and uncertain disturbances

In this article, an uncertain disturbance rejection control problem for the affine system in the presence of asymmetric input constraints is addressed using an event‐triggered control method. The disturbance rejection control is converted to an H∞$$ {H}_{\infty } $$ optimal control problem, and a zero‐sum game‐based method is proposed to solve this H∞$$ {H}_{\infty } $$ optimal control problem. To deal with the input constraints, a new cost function is proposed. The event‐triggered controller is updated only when the triggering condition is satisfied, which can reduce the computational complexity.In order to obtain a controller that minimizes the performance index function in the worst‐case disturbance, we use a critic‐only network to solve the Hamilton–Jacobi–Isaacs (HJI) equation, and the critic network weight is tuned through a gradient descent method with the historical state data. The stability of the closed‐loop system and the uniform ultimate boundedness of the critic network parameters are proved by the Lyapunov method. Two numerical examples are provided to verify the effectiveness of the proposed methods.