Analytic predictive controllers for nonlinear systems with ill-defined relative degree

The paper addresses the problem of the control of nonlinear systems with ill-defined relative degree. The analytic solution to an optimal tracking problem in terms of a generalised predictive performance index is presented, where the output tracking error is predicted by Taylor series approximation up to an arbitrarily chosen order. It is shown that the optimal control for nonlinear systems with ill-defined relative degree is discontinuous, and the optimal control law is not unique when the system is within the singular point set. Approximate implementation of the optimal predictive control law is discussed. The nonlinear predictive controller presented is successfully demonstrated by an numerical example.