DOI number:10.1631/FITEE.1601101

Journal:Frontiers of Information Technology and Electronic Engineering

Key Words:Generalized Hamilton-Jacobi-Bellman equation; Nonlinear optimal control; Galerkin approximation; Legendre polynomials

Abstract:We investigate the use of an approximation method for obtaining near-optimal solutions to a kind of nonlinear continuous-time (CT) system. The approach derived from the Galerkin approximation is used to solve the generalized Hamilton-Jacobi-Bellman (GHJB) equations. The Galerkin approximation with Legendre polynomials (GALP) for GHJB equations has not been applied to nonlinear CT systems. The proposed GALP method solves the GHJB equations in CT systems on some well-defined region of attraction. The integrals that need to be computed are much fewer due to the orthogonal properties of Legendre polynomials, which is a significant advantage of this approach. The stabilization and convergence properties with regard to the iterative variable have been proved. Numerical examples show that the update control laws converge to the optimal control for nonlinear CT systems.

Indexed by:Journal paper

Correspondence Author:Xuesong Chen

Volume:18

Issue:10

Page Number:1479-1487

Translation or Not:no

Date of Publication:2017-10-17

Included Journals:SCI、EI

Links to published journals:https://link.springer.com/article/10.1631/FITEE.1601101