Adaptive dynamic surface control using the Fourier integral for uncertain nonlinear systems

In this paper, we investigate an adaptive controller for nonlinear systems. Dynamic surface control(DSC) is employed to design an effective controller for following a desired command. The conventional backstepping design generally used for nonlinear systems suffers from the inherent problem of explosion of complexity because it has to repeat differentiations of the virtual control input. By using the DSC approach, this problem is avoided. For designing the adaptive controller, the multi-dimensional Fourier integration is employed in order to estimate non-periodic nonlinear functions. It is shown that the proposed controller design can guarantee the uniformly ultimate boundedness of the closed-loop system solution, and make the tracking error arbitrarily small. The simulation using the longitudinal dynamics of the air-to-air missile model results validate the feasibility of the proposed control law.