Extended adaptive backstepping method using dynamic surface control

An extended adaptive backstepping method is proposed for nonlinear systems with strict feedback form. The parameters' update laws are designed on uncertainty equivalence. The uncertain parameters converge quickly. The method utilizes the differentiation of the first-order filter to replace the quantity of the differentiation of the virtual control in determining the next virtual control at each step of recursion. Therefore, the problem of explosion of complexity in traditional backstepping design, which is caused by repeated differentiations of certain nonlinear functions such as virtual control, is overcome by introducing the firs-order filter. The response of system is quick. The parameters converge quickly. The control law is simpler. Simulation results demonstrate the proposed method is validity.