Adaptive and robust controls of uncertain systems with nonlinear parameterization

Two classes of partially known systems are considered in this note; both of them have a fractional parameterization of the unknowns. The first class consists of nonlinear systems whose uncertainties are bounded by a function of fractional parameterization, and the second class compromises those systems whose unknown dynamics can directly, but nonlinearly, be parameterized. It is shown that adaptive robust control can be extended to accommodate nonlinearly parameterized bounding functions and that, with the aid of a robust auxiliary system, new adaptation laws and a simple adaptive control can be designed for the unknowns in the fractional parameterization. Practical stability (in terms of uniform boundedness and ultimate boundedness) is shown; global for adaptive robust control and semiglobal for the new adaptive control.