Continuous feedback control for scleronomous mechanical systems

A problem of designing a feedback control for a Lagrangian scleronomous mechanical system is considered. The control forces are assumed to be bounded and the system undergoes uncontrolled disturbances. The continuous feedback control is constructed which drives the system to a prescribed terminal state in a finite time. The proposed 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. The approach developed is based on Lyapunov´s direct method.