Control of scleronomous mechanical system with unknown matrix inertia

A scleronomous Lagrangian mechanical system of the general form is considered under the assumption that its matrix of the kinetic energy is not known exactly and the system undergoes undetermined bounded disturbances. A continuous feedback bounded control is proposed which brings the system to a prescribed terminal state in finite time. The approach proposed is based on the Lyapunov direct method. To construct the control law and to justify it, the Lyapunov function given implicitly is used. The algorithm employs a linear feedback control with the gains which are functions of the phase variables. The gains increase and tend to infinity as the phase variables tend to zero; nevertheless, the control forces are bounded and meet the imposed constraint.