Research Article Open Access

Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

O. Olotu and S.A. Olorunsola

Abstract

The geometric convergence ratio, the main focus of a discretized scheme for constrained quadratic control problem was examined. In order to allow for the numerical applications of the developed scheme, discretizing the time interval and using Euler’s scheme for its differential constraint obtained a finite dimensional approximation. Applying the penalty function method, an unconstrained problem was obtained on function minimization with bilinear form expression. This finally led to the construction of an operator. The Scheme was applied to a sampled problem and it exhibited geometric convergence ratio, α, in the open interval (0, 1) as depicted in column 6 of Table 1.

American Journal of Applied Sciences
Volume 5 No. 2, 2008, 89-92

DOI: https://doi.org/10.3844/ajassp.2008.89.92

Submitted On: 19 February 2007 Published On: 28 February 2008

How to Cite: Olotu, O. & Olorunsola, S. (2008). Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients. American Journal of Applied Sciences, 5(2), 89-92. https://doi.org/10.3844/ajassp.2008.89.92

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Keywords

  • Quadratic
  • discretization
  • bilinear form expression
  • associated operator
  • convergence profile and geometric convergence