Design of Adaptive Block Backstepping Controllers for Perturbed Systems with Input Nonlinearity and Dead Zone

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping controllers is proposed in this paper for a class of multi-input systems with input nonlinearity and dead zone to solve regulation problems. According to the number of block (m) in the dynamic equations, virtual inputs are firstly designed from the first block to the (m-1)th block. Then the proposed robust controller is designed from the last block. Adaptive mechanisms are also employed in each of the virtual inputs and the robust controller, hence the least upper bounds of perturbations are not required to be known in advance. The resultant controlled system is able to achieve asymptotic stability if all the control inputs is outside of the dead zone, and uniformly ultimately bounded is achieved if any one of the designed control inputs is inside of the dead zone. A numerical example is given for demonstrating the feasibility of the proposed control scheme.