Discounted near‐optimal regulation of constrained nonlinear systems via generalized value iteration. (18th August 2021)

• Record Type: Journal Article
• Authors: Wang, Ding; Zhao, Mingming; Ha, Mingming; Qiao, Junfei
• Other Names: Sename Olivier guestEditor.; Rotondo Damiano guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 31:Number 17(2021)
• Page Start: 8481
• Page End: 8503
• Publication Date: 2021-08-18
• Subjects: adaptive critic -- control constraints -- convergence analysis -- discounted optimal control -- generalized value iteration; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5729
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: In this article, a generalized value iteration algorithm is developed to address the discounted near‐optimal control problem for discrete‐time systems with control constraints. The initial cost function is permitted to be an arbitrary positive semi‐definite function without being zero. First, a nonquadratic performance functional is utilized to overcome the challenge caused by saturating actuators. Then, the monotonicity and convergence of the iterative cost function sequence with the discount factor are analyzed. For facilitating the implementation of the iterative algorithm, two neural networks with Levenberg–Marquardt training algorithm are constructed to approximate the cost function and the control law. Furthermore, the initial control law is obtained by employing the fixed point iteration approach. Finally, two simulation examples are provided to validate the feasibility of the present strategy. It is emphasized that the established control laws are successfully constrained for randomly given initial state vectors.