Compensator-based approximate optimal control for affine nonlinear systems with input constraints and unmatched disturbances. (November 2020)

• Record Type: Journal Article
• Authors: Lu, Ke; Liu, Chunsheng; Sun, Jingliang; Li, Chunhua; Ma, Chengcheng
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 42:Number 15(2020)
• Page Start: 3024
• Page End: 3034
• Publication Date: 2020-11
• Subjects: Adaptive dynamic programming (ADP) -- input constraints -- unmatched disturbances -- auxiliary dynamic compensator -- asymptotically stable; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331220940161
• Languages: English
• ISSNs: 0142-3312

Abstract

This paper develops a novel approximate optimal control method for a class of constrained continuous-time nonlinear systems in the presence of disturbances via adaptive dynamic programming (ADP) technique. First, an auxiliary dynamic compensator is introduced to deal with the input constraints. Through augmenting the original system with the designed auxiliary compensator, the design of constrained optimal controller is circumvented by stabilizing the equivalent augmented system. Then, the cost function is appropriately redefined by introducing an additional function connected with disturbances for the augmented nominal system in order to compensate the effect of unmatched disturbances. Next, the solution of associated Hamilton-Jacobi-Bellman (HJB) equation is solved online with weight adaptation law using neural networks (NNs). Furthermore, an additional robustifying term is utilized to compensate the effect of the approximation error of NNs, and thus the asymptotic stability of the closed-loop system is guaranteed. Finally, all signals of the closed-loop system are proved to be asymptotic convergence by using Lyapunov method. Simulation examples demonstrate the effectiveness of the proposed scheme.