Implementation of Krotov’s Method for a Type of a Continuous Bilinear Quadratic Optimization Problem

In this study Krotov's method is used for computing a candidate optimum for a constrained optimal control problem that is defined by a continuous time bilinear system, a scalar control input, time varying control bounds and for a quadratic performance index. The use of this method is not trivial and requires solution of two sub-problems before it can be applied. In this study the solutions of these sub-problems are given in two theorems and a suitable Krotov's algorithm is provided. The results are demonstrated by two numerical examples.