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Frontiers of Information Technology & Electronic Engineering >> 2017, Volume 18, Issue 10 doi: 10.1631/FITEE.1601101

Galerkin approximationwith Legendre polynomials for a continuous-time nonlinear optimal control problem

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

Available online: 2018-01-18

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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.

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