Robust control for a class of nonlinear systems with input constraints based on actor‐critic learning

• Published in: International journal of robust and nonlinear control Vol. 34; no. 12; pp. 7635 - 7654
• Main Authors: Li, Dongdong, Dong, Jiuxiang
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.08.2024
• Subjects: actor‐critic neural networks; adaptive dynamic programming; Algorithms; Control systems design; Controllers; Cost function; Distance learning; input constraints; Liapunov direct method; Machine learning; Neural networks; Nonlinear systems; Optimal control; Robust control
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6190

This article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm.