OPTIMIZATION OF PROPORTIONAL CONTROL PROBLEMS WITH EQUALITY CONSTRAINTS USING PENALTY FUNCTION METHOD

Abstract

The general continuous proportional control problems constrained by ordinary di erential equations with and without delay are considered. We discuss the optimization of proportional control problems with equality constraints and the properties of the Quadratic Penalty Function Method. The discretization of the objective functions and the constraints is carried out using the Composite Simpson's Rule and the Adams-Moulton Technique respectively. The Quadratic Penalty Function Method is used to transform the resulting discretized constrained proportional control problems into unconstrained problems. With this formulation, the associated operators which give the framework for the application of the Conjugate Gradient Method (CGM) for solving the problems are established. The solutions of the new scheme for solving proportional control problems are presented in this thesis and the convergence analysis is conducted to establish the e ectiveness, accuracy and e ciency of the scheme. Five examples are considered and the results of the new scheme compare much more favourably with the analytical solutions than those obtained from existing works. From our analysis, the solution is found to be superlinearly convergent.