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Closed Form Solution of Nonlinear-Quadratic Optimal Control Problem by State-control Parameterization using Chebyshev Polynomials

by Hussein Jaddu, Milan Vlach
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 91 - Number 10
Year of Publication: 2014
Authors: Hussein Jaddu, Milan Vlach
10.5120/15914-5281

Hussein Jaddu, Milan Vlach . Closed Form Solution of Nonlinear-Quadratic Optimal Control Problem by State-control Parameterization using Chebyshev Polynomials. International Journal of Computer Applications. 91, 10 ( April 2014), 1-7. DOI=10.5120/15914-5281

@article{ 10.5120/15914-5281,
author = { Hussein Jaddu, Milan Vlach },
title = { Closed Form Solution of Nonlinear-Quadratic Optimal Control Problem by State-control Parameterization using Chebyshev Polynomials },
journal = { International Journal of Computer Applications },
issue_date = { April 2014 },
volume = { 91 },
number = { 10 },
month = { April },
year = { 2014 },
issn = { 0975-8887 },
pages = { 1-7 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume91/number10/15914-5281/ },
doi = { 10.5120/15914-5281 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:12:52.965170+05:30
%A Hussein Jaddu
%A Milan Vlach
%T Closed Form Solution of Nonlinear-Quadratic Optimal Control Problem by State-control Parameterization using Chebyshev Polynomials
%J International Journal of Computer Applications
%@ 0975-8887
%V 91
%N 10
%P 1-7
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper the quasilinearization technique along with the Chebyshev polynomials of the first type are used to solve the nonlinear-quadratic optimal control problem with terminal state constraints. The quasilinearization is used to convert the nonlinear quadratic optimal control problem into sequence of linear quadratic optimal control problems. Then by approximating the state and control variables using Chebyshev polynomials, the optimal control problem can be approximated by a sequence of quadratic programming problems. The paper presents a closed form solution that relates the parameters of each of the quadratic programming problems to the original problem parameters. To illustrate the numerical behavior of the proposed method, the solution of the Van der Pol oscillator problem with and without terminal state constraints is presented.

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Index Terms

Computer Science
Information Sciences

Keywords

Nonlinear optimal control problem Chebyshev polynomials Quasilinearization Iterative method

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