ON EFFICIENCY OF THE GRID OPTIMAL SYNTHESIS TO CONTROL PROBLEMS OF PRESCRIBED DURATION
The subject of the paper is estimation of new method for constructing feedbacks. The researches follow to N.N. Krasovskii formalization of feedbacks. We consider optimal control problems of prescribed duration on the plane. Dynamics of controlled systems are nonlinear. Values of controls are restricted by geometrical constrains. Running cost functionals of the Bolza type are minimized along trajectories of the systems on time intervals of prescribed duration. A new numerical method for solving optimal control problems of prescribed duration is suggested. It based on a generalization of the method of characteristics for the Hamilton - Jacobi - Bellman equation. The data of problems are assumed to be Lipschitz continuous. Constructions of optimal grid synthesis are provided and numerical algorithms are created. Efficiency of the algorithms is discussed. Estimations for difference between the optimal result and the result of control via suggested grid synthesis are obtained. Examples of solving model problems on the plane are exposed to illustrate the work of algorithms and to compare results of the new method with other known methods.