Synthesis of Bounded Control for Nonlinear Uncertain Mechanical Systems

A problem of designing a control for Lagrange mechanical systems of a general form under uncertainty is investigated. A rheonomic system is considered under the assumption that the coefficients of a quadratic polynomial which represents the kinetic energy are unknown but lie within given bounds and the system undergoes uncontrolled bounded disturbances. Stability theory based control is constructed which enables one to drive the system to a prescribed terminal state in finite time. The proposed algorithm can be treated as a linear feedback control with the gains which are differentiable 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.