Projection operator for solving generalized problems of program motions stabilization

Generalization and development of the projection operator method for solving problems of stabilization of given program motions seems to be an actual direction of research in the field of synthesis of optimal control systems for nonlinear dynamic stationary objects with limited phase coordinates and controls. In this paper, we formulate generalized stabilization problems for program motions given by a program-stabilizing vector C0 and a vector of admissible program motions C. We show the derivation of a projection operator for solving the specified class of problems. For a nonlinear locally controlled difference operator, admissible controls are synthesized that stabilize program motions under restrictions on phase coordinates and controls. An operator of a dynamical system is obtained for generalized problems of stabilization of program motions with restrictions on the vectors of phase coordinates and controls. Numerical simulation of the stabilization of the given program motions of a dynamic object is carried out. As an example of a dynamic object, a mathematical model of a synchronous generator is chosen, consisting of a system of bilinear differential equations with parameters corresponding to equations in the form of V. A. Venikov. A computational experiment confirmed the theoretical results obtained in the work.