Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem
点击次数：
DOI码：10.1631/FITEE.1601101
发表刊物：Frontiers of Information Technology and Electronic Engineering
关键字：Generalized Hamilton-Jacobi-Bellman equation; Nonlinear optimal control; Galerkin approximation; Legendre polynomials
摘要：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.
论文类型：期刊论文
通讯作者：Xuesong Chen
卷号：18
期号：10
页面范围：1479-1487
是否译文：否
发表时间：2017-10-17
收录刊物：SCI、EI
发布期刊链接：https://link.springer.com/article/10.1631/FITEE.1601101
附件：