Dynamic Surface Control for a Class of Strict-Feedback MIMO Systems in Nonlinear Block Controllable Form

A robust dynamic surface control law design method with guaranteed L_∞tracking performance is proposed for a class of strict-feedback MIMO(multiple-input multiple-output) systems in nonlinear block controllable form with unknown uncertainty.A nonlinear damping item is employed to compensate unknown uncertainty.The problem of explosion of terms in backstepping design caused by repeated derivations of certain nonlinear functions in virtual control,is overcome by the dynamic surface control method.All signals in the closed loop are guaranteed to be semi-globally uniformly ultimately bounded by Lyapunov stability theorem.The output tracking error is proved to converge to an arbitrarily small neighborhood around zero and the L_∞performance of system tracking error can be guaranteed by appropriately choosing design parameters and initializing the dynamic surfaces.Simulation results demonstrate the effectiveness of the proposed method.