Adaptive regulation of uncertain nonlinear systems with dead-zone

This paper deals with the adaptive output control of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone nonlinearity. The nonlinear systems considered are dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An example is presented to show the effectiveness of this methodology.