Journal of Mathematics and Statistics

On the Discretized Algorithm for Optimal Problems Constrained by Differential Equation with Real Coefficients

O. Olotu

DOI : 10.3844/jmssp.2007.237.242

Journal of Mathematics and Statistics

Volume 3, Issue 4

Pages 237-242

Abstract

A discretized scheme, Discretized Continuous Algorithm (DCA), for solving constrained quadratic optimal control problems was developed to ease the computational cumbersomeness inherent in some existing algorithms, particularly, the Function Space A lgorithm (FSA) by replacing the integral by a series of summation. In order to accomplish this numerical scheme, we resort to a finite approximation of it by discretizing its time interval and using finite difference method for its differential constraint. Using the penalty function method, an unconstrained formulation of the problem was obtained. With the bilinear form expression of the problem, an associated operator was constructed which aided the scheme for the solution of such class of problems. A sample problem was examined to test the effectiveness of the scheme as to convergence with relation to other existing schemes such as Extended Conjugate Gradient Method (ECGM), Multiplier Imbedding Extended Conjugate Gradient Method (MECGM) and Function Space Algorithm (FSA) for solving penalized functional of optimal control problem characterized by non-linear integral quadratic nature.

Copyright

© 2007 O. Olotu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.