On the gradient method applied to optimal control problem

Abstract

The purpose of this paper is to give a direct proof of some convergence results for the gradient and gradient projection methods applied to the optimal control problems. The methods are considered in the continuous approach. In the context of the optimal control problem, direct proofs are given to the results from the point of view of the teaching methods. The gradient projection method is studied in a modified variant, which is programmed in a simpler way in a Computer Algebra System (CAS) environment. For simple optimal control problems, it is possible to use symbolic computations. An example is solved in Mathematica CAS.