The Method of Reflection for Solving the Time-Optimal Hamilton-Jacobi-Bellman Equation on the Interval Using Wavelets

Author

Jain, S. ; Tsiotras, P.

Author_Institution

Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA

fYear

2005

fDate

27-29 June 2005

Firstpage

1062

Lastpage

1067

Abstract

In this paper we use the antiderivatives of wavelets to efficiently represent functions which are defined over a bounded interval and which satisfy a boundary condition in the interior of this interval. The functions we want to approximate are typically nonsmooth at the origin. Such functions appear as solutions to Hamilton-Jacobi-Bellman (HJB) equations for time-optimal control problems. We first give the degree of approximation of the antiderivatives and then propose a wavelet reflection algorithm (WRA) to solve numerically the time-optimal HJB equation on the interval. Several numerical examples demonstrate the advantages of the technique developed in this paper over polynomial expansions

Keywords

Jacobian matrices; optimal control; wavelet transforms; boundary condition; bounded interval; polynomial expansions; time-optimal Hamilton-Jacobi-Bellman equation; time-optimal control problem; wavelet reflection algorithm; Aerospace engineering; Approximation algorithms; Boundary conditions; Boundary value problems; Frequency domain analysis; Integral equations; Polynomials; Reflection; Wavelet coefficients; Wavelet domain;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Control, 2005. Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation

Conference_Location

Limassol

ISSN

2158-9860

Print_ISBN

0-7803-8936-0

Type

conf

DOI

10.1109/.2005.1467162

Filename

1467162