Continuous feedback control of perturbed mechanical systems

The problem of synthesizing continuous controls for a Lagrangian scleronomic mechanical system is investigated, on the assumption that the system is subject to uncontrollable bounded perturbations and that the vector of control forces is bounded in norm. a feedback control law is assumed, making it possible to steer the system to a given rest state in a finite time. The approach employed is based on methods of the theory of stability of motion. An implicitly given Lyapunov function is used to construct the control law and justify the construction. The existence of such a function is proved and its properties established. Results of a numerical simulation of the dynamics of various mechanical systems controllable in accordance with the proposed law are presented. It is shown that, for a point mass moving along a horizontal straight line, the control algorithm qualitatively approximates to time-optimal control.