On the optimal control problems constrained by delay differential equation using penalty function with B-spline

Abstract

This paper proposes an efficient algorithm using discretization with B-spline polynomial support forthe control. We discretize the objective function and the constraint using trapezoidal rule and Cranck Nilcholson Method respectively. With this development, an unconstrained formulation of the problem viaquadratic penalty function is obtained and the evolution of an associated operator which gives the framework for the application of the conjugate gradient method(CGM) for solving the problem is established.Two examples are considered, tested and the results of the new scheme compared much more favourably to the existing results and the convergence analysis was found to be linear.