INTERIOR AND EXTERIOR PENALTY FUNCTION METHODS FOR OPTIMAL CONTROL PROBLEMS CONSTRAINED BY ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this research, we considered the general continuous optimal control problems constrained by di erentialalgebraic constraints. Discretization of the objective function and constraints were carried out using the Simpson's Rule and Adams-Bashforth explicit methods respectively. Exterior and Interior penalty function methods were applied to obtain associated unconstrained problems with associated constrained operators. With this formulation,examples with di erential constraints were examined and results compared favourably with existing methods. While the exterior and interior penalty function methods with algebraic constraints agreed analytically , the computational aspect of the interior penalty function method is more involving particularly the presence of linear combination of triangular matrices whose pseudo inverse computation may lead to concepts beyond the scope of this work.