Synthesis of continuous control of a mechanical system with an unknown inertia matrix

Abstract

The problem of the synthesis of a bounded control for a Lagrange scleronomic system is considered. We assume that the kinetic energy matrix of the system is known with some accuracy and that the system is subjected to uncontrolled bounded perturbations. The feedback control law, which allows us to steer the system to the given state at rest in a finite time, is constructed. The sufficient conditions of this behavior are formulated. The approach applied was proposed earlier for the case of a system with a known kinetic energy matrix. It is based upon the methods of the stability theory of motion. In order to construct the control law and justify it, we use an implicit Lyapunov function. The effectiveness of the control law is demonstrated with the help of numerical modeling of controlled motions of a two-link manipulator, which holds a weight of unknown mass in its hand.