Improvement and estimation of the approximate optimal positional control

Iterative procedures for improvement and approximate optimization of the positional controls with the use of the Krotov estimation functions generated by them at the iterations by means of the linear partial derivative equations and their discrete counterparts were considered, substantiated, and shown to converge to the solutions of the Bellman relations. The corresponding constructive schemes leading to approximate optimal solutions with the upper estimates were constructed, their relations were established, and comparison was made with the existing schemes of the approximate optimal design of controls.