Lyapunov direct design of robust tracking control for classes of cascaded nonlinear uncertain systems without matching conditions

Robust tracking control of nonlinear uncertain cascaded systems is investigated without the assumption of matching conditions. The system under consideration consists of finite nonlinear systems which are cascaded and have significant uncertainties. Several general classes of cascaded uncertain systems are identified for which robust controllers are obtained explicitly in terms of the bounding functions of the uncertainties. These classes of uncertain systems do not satisfy the matching conditions while incorporating many real physical systems, especially mechanical systems. The authors greatly broaden the applicability of robust control. The resulting controllers guarantee global uniform ultimate bounded stability or global exponential stability. The controls are designed by a two-step systematic design procedure. First, fictitious robust controllers are designed for input of the individual subsystem as if every subsystem had an independent control. Then, a recursive mapping is proposed which maps the individual fictitious controls recursively into the unique overall control. As an example, a one-link rigid robot with motor dynamics is considered