New Methods of Synthesis and Calculation of Optimal Terminal Control

Abstract

The article deals with the problem of optimal terminal control synthesis. A functional, a nonlinear mathematical model, and restrictions on the maximum permissible control values are specified. The control law is synthesized. The main problem that arises in the synthesis of the optimal control law for nonlinear dynamical systems is the solution of the boundary value problem. The following statements are proved: 1) the optimal trajectory of a dynamical system is the envelope of a parametric family of singular curves called instantaneous solutions, 2) the optimal control can be found on the family of instantaneous solutions. The use of instantaneous solutions avoids the explicit solution of the boundary value problem. To simplify the control calculations, it is shown that the synthesis of optimal control is carried out using the entire initial mathematical model of the dynamic system, but for calculating the control at any given time, it is possible to use a reduced (truncated) model. Thus, there is an information dualism of the optimal control problem. This approach is an extension of the Yu. B. Hermeyer's information redefinition principle to the domain of optimal terminal control.