Regulating Constraint-following Bound for Uncertain Mechanical Systems: An Indirect Control Approach

This paper proposes an indirect approach of constraint-following control for mechanical systems with (possibly fast) time-varying uncertainty. It proposes to design controller for the system to render bounded constraint-following error. First, it prescribes a desired hard bound for the constraint-following error. The system is required to lie within the bound at all time. Second, the constraint-following error can eventually be sufficiently small. To accomplish this, the original system is transformed into a constructed system. Then a robust control for the constructed system is designed, with renders uniform boundedness and uniform ultimate boundedness, regardless of the uncertainty. It is further proven that when the constructed system is uniformly bounded and uniformly ultimately bounded, the constraint-following error of the original system stays within the pre-determined bounded. In addition, it will become sufficiently small after a finite time. Therefore the desired bounded performance of the constraint-following error can be archived by the robust control. Since the control is not designed based on the original system, the approach is indirect.