Lyapunov direct design of robust control for electrical-mechanical systems composed of cascaded nonlinear uncertain subsystems

摘要

Robust control design of nonlinear uncertain systems is investigated. A system under consideration consists of finite nonlinear systems which are cascaded and have significant uncertainties. Such a system arises naturally from many real physicalsystems, especially mechanical systems. An important feature of these systems is that they do not satisfy the assumption of the standard matching conditions required by most existing robust control results. General classes of cascaded uncertain systemsare identified for which robust controllers are obtained explicitly in terms of the bounding junctions of the uncertainties. The resulting robust controllers guarantee stability of global uniform ultimate boundedness or global exponential convergence tozero. The controls are designed by a two-step systematic design procedure. First, design fictitious robust controllers for input of 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 only control of the overall system.