This paper describes a systematic procedure to design robust adaptive controllers for a class of nonlinear systems with unknown functions of unknown bounds based on backstepping and sliding mode techniques. These unknown functions can be unmodeled system nonlinearities, uncertainties and disturbances with unknown bounds. Both state feedback and output feedback designs are addressed. In the design procedure, the upper bounds of the unknown functions are estimated using an adaptation strategy, and the estimates are used to design stabilizing functions and control inputs based on the backstepping design methodology. The proposed controllers guarantee that the tracking errors converge to a residual set close to zero exponentially for both state feedback and output feedback designs, while maintaining the boundedness of all other variables.
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