HOSM observer for robust output regulator in uncertain nonlinear polynomial systems

This paper studies the problem of a robust optimal regulation for a nonlinear polynomial system based only on output information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favorable value of the unknown parameter. A high order sliding mode observer is designed for the nonlinear plant in such a way that the worst case control can be applied for a system with incomplete information. Additionally a matched type uncertainty is also compensated by means of the same output signal. A numerical example is given to illustrate the effectiveness of the approach.