Control of system dynamics and constraints stabilization

Problems of program control for dynamic systems with elements of various physical natures are considered. The equations of classical mechanics is used for describing a dynamical process of controlled systems. The method of constructing differential equations of the known particular integrals is used to stabilize the constraints imposed on the dynamical system, which is described with the Lagrange or Hamilton equations. Stability conditions for solutions of dynamics equations with respect to the constraint equations are obtained. An algorithm for constructing equations of constraint perturbations that guarantees stabilization of constraints in the course of numerical solution by the Runge-Kutta method is proposed. The proposed methods are used for solving problems of control of production, logistics and technical systems: a discrete adaptive optical system, an electromechanical system consisting of a power supply unit and a direct current motor, which controls the crank mechanism, a unit controlling wheel system's movement along a given trajectory with avoidance of moving bodies; enterprise consisting of two plants; rectilinear motion of a cart with inverted pendulum. The content of the work distributed in the following titles: Introduction; Statement of the problem; Construction of dynamics equations; Stability and stabilization; Applications. © 2016 IEEE.