DISCRETIZED PENALTY SCHEMES FOR THE SOLUTION OF OPTIMAL CONTROL PROBLEMS

Abstract

Optimal control problems constrained by ordinary differential equations, delay differential equationsand two-dimensional optimal control problem with vector and matrix coefficients are considered. The Solution of optimal control problems with equality constraints is considered. The discretization of the objective functions and the constraints is carried out using the 1 3 Simpson’s Rule and the Adams-Bashforth Technique respectively. With equality constraints in our research problems, the Conventional Penalty Function Method is then used to transform the resulting discretized constrained optimal control problems with or without delay into unconstrained problems. With thisdevelopment, associated operators are constructed which give the framework for the application of the Conjugate Gradient Method (CGM) for solving the given problems. The solutions of the new scheme are presented in this thesis and the convergence analyses are conducted to establish the efficiency, accuracy and effectiveness of the scheme. Some 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 analyses, the convergence profile of the solutions is super linear.