METHOD OF ITERATIVE APPROXIMATIONS FOR LINEAR OPTIMAL-CONTROL PROBLEM WITH MIXED CONSTRAINTS

The problem of optimal control in a fixed time interval with a terminal functional, described by a system of linear differential equations is considered. Region of the permitted control actions is a polyhedron, given by a system of linear inequalities, for both the control and phase coordinates. A method for the construction of a sequence of approximate solutions is proposed, based on the use of local (with respect to time) optimality conditions. According to its structure the method is similar to the known Krilov-Chernousko method for optimal control problems without mixed constraints. Monotonic nature of the iterative process and its convergence towards the optimal value of the functional is proven.