Adaptive tracking control for a class of strict feedback systems with unknown dead-zone input

This paper proposes an adaptive backstepping control scheme for a class of nonlinear systems with dead-zone input and unknown external disturbances in each state equation. A nonlinear approximation function is constructed for the dead-zone hysteresis. The derivative of this approximation function is cascaded with the plant to form the extended system. The Nussbaum function is used to deal with the difficulty caused by the derivative of the approximate function. Unlike existing methods, the proposed controller fully considers the non-smooth nonlinearity without requiring its inverse. It is shown that the proposed adaptive control scheme ensures all signals in the closed-loop system remain bounded.