Control of System Dynamics and Constraints Stabilization

The equations of classical mechanics used for describing a dynamical process of controlled systems containing different elements. The method of constructing differential equations of known partial integrals is used to stabilize the constraints imposed on the mechanical system dynamics which is described by Lagrange equations and Hamilton equations. The problem of constructing the dynamics equations with known properties of motion in the class of Ito stochastic differential equations was investigated by Tleubergenov M.I., Azhymbaev D.T. Assuming that some of the properties of the motion are known and the random perturbing forces belong to the class of processes with independent increments, Lagrange functions, Hamilton functions and Birkhoff functions can be constructed. Stability conditions for solutions of equations of dynamics with respect to the constraint equations are obtained, and an algorithm for constructing equations of constraint perturbations that guarantees the stabilization of constraints in the course of numerical solution is proposed. The problem of controlling the rectilinear motion of a cart with inverted pendulum is solved.