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CLC number: TP13
On-line Access: 2017-12-04
Received: 2016-06-04
Revision Accepted: 2016-10-15
Crosschecked: 2017-11-01
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Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem
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Xue-song Chen. Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(10): 1479-1487.
@article{title="Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem",
author="Xue-song Chen",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="18",
number="10",
pages="1479-1487",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1601101"
}
%0 Journal Article
%T Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem
%A Xue-song Chen
%J Frontiers of Information Technology & Electronic Engineering
%V 18
%N 10
%P 1479-1487
%@ 2095-9184
%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1601101
TY - JOUR
T1 - Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem
A1 - Xue-song Chen
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
IS - 10
SP - 1479
EP - 1487
%@ 2095-9184
Y1 - 2017
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1601101
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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