Predictive control of nonlinear systems with ill-defined relative degrees: an analytic approach [published as: Analytic predictive controllers for nonlinear systems with Ill-defined relative degree]

This paper addresses the problem of control of nonlinear systems with ill-defined relative degrees. The solution to an optimal tracking problem in terms of a generalised predictive performance index is presented when the output tracking error is predicted by Taylor series approximation up to an arbitrary chosen order. It is shown that the optimal control law for nonlinear systems with ill-defined relative degrees leads to a switch control scheme is resulted . It is shown that similar to conventional predictive control, analytic model predictive control provides a natural tool to deal with systems with ill-defined relative degrees. A novel scheme is developed with the frame of model predictive control It is shown that the closed-loop system is asymptotically stable.