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Fast Solution of Dynamic Optimization Problems using Wavelets
by
Saroj Biswas
Department of Electrical and Computer Engineering, Temple University, Philadelphia, USA
Coauthors: Yair Leibovich
This paper presents a method of solution of ordinary differential equations using wavelets, and its application for solving optimization problems. Wavelets with compact support form an orthogonal sequence using which one can express the solution of differential equations to any desired degree of accuracy. In particular, the Haar wavelets and Daubechies wavelets have been found to be particularly simple, yet very efficient for the solution methods. The differential equations are easily converted to a set of algebraic equations which are easily solved. In contrast to conventional serial algorithms, such as Runga-Kutta method, the wavelet method is particularly suitable for parallel computation on vector processors.
The wavelet method is then applied to solving dynamic optimization problems for minimization of a quadratic cost function subject to a state equation described by a matrix differential equation. The results are illustrated by simulation examples.
Date received: December 14, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-47.