Online Robust Adaptive Dynamic Programming Control of a Class of Affine Nonlinear Systems Subject to Unknown Bounded External Disturbances

ABSTRACT Disturbance suppression has long been a challenging issue in the study of adaptive dynamic programming (ADP) algorithms. This paper introduces a novel critic neural network (NN)‐based robust ADP algorithm for a class of continuous‐time affine nonlinear systems to handle the unknown bounded external disturbances. The algorithm adopts an improved robust cost function (RCF), which simultaneously enhances the capability of rejecting the disturbances and reduces the controller's energy consumption. Based on this, a disturbance compensator is further proposed to achieve asymptotic stability of the closed‐loop system. To facilitate the application of the proposed control algorithm to practical engineering problems, a critic‐only NN is employed to approximate the optimal cost function using a novel tuning law. Consequently, the proposed critic NN and RCF‐based optimal control algorithm, combined with the RCF‐based disturbance compensator and NN tuning law, ensures the uniform ultimate boundedness (UUB) of the system's state trajectory. The effectiveness of our algorithm is demonstrated through software simulations.