Adaptive Backstepping Control for a Class of Nonlinear Systems With Unknown Time Delay

In this paper, an adaptive backstepping control scheme is proposed for a class of nonlinear systems with unknown time delay. The unknown time delay in the system depends on all system states, which will inevitably destroy the triangular structure of the control system. Therefore, traditional backstepping can not be used to design the controller. In order to overcome the problem caused by “non-triangular structure”, we construct a linear projection between the state vector and its transform in controller design. Using inequality and adaptive backstepping control, we compensate the uncertainties caused by unknown time delays. Finally, the simulation results show that the proposed algorithm is effective.