A simplified adaptive robust backstepping approach using sliding modes and a z-swapping identifier

An adaptive robust backstepping approach using sliding modes and a z-swapping identifier is presented for a class of nonlinear parameter-varying systems. Each of the first nonlinear-1 virtual control inputs is designed using a zero-order sliding mode controller. Then, in the final step, a general sliding mode controller is used to stabilize the entire closed loop system. The parameter update law is designed using a gain adjusted exponential forgetting least-squares algorithm and a objection operator. The benefits of the approach include a reduction in the overcompensation of uncertainty, a simplification of the control law, and the ability to use linear design techniques to determine the system's transient performance.