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Home  >  Volume 46 (May, 2018)

10. A SCHEME FOR OPTIMIZING CONSTRAINED PROPORTIONAL CONTROL PROBLEMS USING PENALTY FUNCTION METHOD by Olusegun Olotua and Afeez Abidemib Volume 46 (May, 2018 Issue), pp75 –86
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A SCHEME FOR OPTIMIZING CONSTRAINED PROPORTIONAL CONTROL PROBLEMS USING PENALTY FUNCTION METHOD

Olusegun Olotua and Afeez Abidemib

Department of Mathematical Sciences, Federal University of Technology, Akure, P.M.B 704, Ondo State, Nigeria.

Abstract

This paper presents the general continuous optimal proportional control problems constrained by ordinary differential equations. The analytical method and numerical technique for solving optimal proportional control problems with equality constraints are discussed. The numerical optimization of the problems adopts the complete discretization technique. Discretization of the objective functions and the constraints is carried out using the Simpson's 3/8 Rule and the Fifth-order Adams-Moulton Technique, respectively. In the presence of equality constraints in our research problems, the discretized form of the constrained proportional control problems is converted to unconstrained problems using the quadratic penalty function method. With the new formulation, the associated operators, which are amenable to the application of Conjugate Gradient Method for solving the problems are constructed. Four real life examples are considered and their analytical and numerical solutions are presented. Analysis of convergence of the results is carried out to demonstrate the accuracy and efficiency of our new scheme over the existing ones. Hence, our results show that the new scheme compares favourably to the existing schemes with a superlinear convergence.

Keyword: Penalty Function, Proportional Control, Conjugate Gradient Method, Discretization, Convergence.

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