Estimating error of the optimal grid design in the problems of nonlinear optimal control of prescribed duration

Presented was a new grid method for design the feedback-optimal control law (optimal design) in the problem of optimal control of prescribed duration. The difference between the optimal result and the result of control based on the proposed grid design was estimated for any initial state of the controlled system. These estimates were illustrated by the solutions of nonlinear model problems of control on plane where the graph of the cost function (optimal result) at the given time instant is compared with the graph of the results of control using the proposed construction.