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A WAVELET COLLOCATION SCHEME FOR SOLVING SOME OPTIMAL PATH PLANNING PROBLEMS

Part of: Existence theories Numerical methods in Fourier analysis

Published online by Cambridge University Press:  12 May 2016

MARZIYEH MORTEZAEE  and
ALIREZA NAZEMI
MARZIYEH MORTEZAEE*
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran email mortezaee91@gmail.com, nazemi20042003@yahoo.com
ALIREZA NAZEMI
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran email mortezaee91@gmail.com, nazemi20042003@yahoo.com
*
✉ mortezaee91@gmail.com
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Abstract

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We consider an approximation scheme using Haar wavelets for solving optimal path planning problems. The problem is first expressed as an optimal control problem. A computational method based on Haar wavelets in the time domain is then proposed for solving the obtained optimal control problem. A Haar wavelets integral operational matrix and a direct collocation method are used to find an approximate optimal trajectory of the original problem. Numerical results are also presented for several examples to demonstrate the applicability and efficiency of the proposed method.

Keywords

optimal path planning problemsapproximationrationalized Haar functionsnonlinear programming

MSC classification

Primary: 49J15: Optimal control problems involving ordinary differential equations
Secondary: 65T60: Wavelets 90C30: Nonlinear programming

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 4 , April 2016 , pp. 461 - 481
Copyright
© 2016 Australian Mathematical Society 

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