Adaptive dynamic programming for decentralized neuro‐control of nonlinear systems subject to mismatched interconnections

• Published in: Optimal control applications & methods Vol. 43; no. 5; pp. 1501 - 1519
• Main Authors: Tang, Yuhong, Yang, Xiong, Dong, Na
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.09.2022
• Subjects: Adaptive algorithms; Adaptive control; adaptive dynamic programming; Control methods; Decentralized control; Dynamic programming; Interconnections; mismatched interconnection; Neural networks; Nonlinear control; Nonlinear systems; Optimal control; Policies; reinforcement learning; Subsystems
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2905

This article presents a decentralized neuro‐control scheme for a class of continuous‐time nonlinear systems with mismatched interconnections through an optimal control method. The decentralized control problem of the studied nonlinear‐interconnected systems is transformed into a group of optimal control problems of auxiliary subsystems. First, the value functions of auxiliary subsystems are designed, which are related to the boundaries of interconnected terms. It is proved that, under certain conditions, the decentralized control consisting of optimal control policies of auxiliary subsystems can stabilize the entire interconnected system. Then, an adaptive dynamic programming algorithm is presented to solve the Hamilton–Jacobi–Bellman equations. Critic neural networks (NNs) are employed to approximate the value functions of auxiliary subsystems in order to acquire the optimal control policies. Moreover, the auxiliary subsystems' states and the critic NNs' weight estimation errors are proved to be uniformly ultimately bounded. Finally, a numerical example and an interconnected power system are provided to validate the proposed decentralized neuro‐control strategy.