A numerical method for network operator for synthesis of a control system with uncertain initial values

Abstract

The problem of synthesis of a control system in which the control is found as a function of coordinates of the state space is considered. It is shown that the solution of the synthesis problem for one given initial state may not provide conservation of the optimal value of the functional under variation of the initial state. A problem of control synthesis is formulated, in which it is necessary to find an optimal control for initial values belonging to a given region. It is proved that if the region of initial values is discrete and contains a finite number of points, then a solution to this synthesis problem exists. To solve the synthesis problem, a constructive computational method is proposed, based on the network operator. An example of solving an applied control synthesis problem is presented.