Penalty function method for optimizing constrained proportional control problems
The general continuous proportional control problems constrained by ordinary differential equations are considered. We discuss the optimization of proportional control problems with equality constraints. The quadratic penalty function method is used to convert the constrained problems into unconstrained problems. Discretization of the objective functions and the constraints is carried out using the Composite Simpson’s Rule and the Fourth-Order Adams-Moulton Technique respectively. The new formulation gives rise to the construction of an operator amenable to the application of the Conjugate Gradient Method (CGM). Analysis of the convergence of the solutions is carried out and the results are found to compare favourably with those obtained from existing algorithms.
CYBERNETICS AND PHYSICS, Vol. 2, No. 3, 177–182.