An improved adaptive dynamic surface control approach for uncertain nonlinear systems

Dynamic surface control (DSC) was developed to eliminate the explosion of complexity problem in backstepping procedure. However, as demonstrated in this paper, the obtained results by the existing DSC technique are somewhat conservative, which may pose difficulties in system debugging for realistic applications. This work addresses a modification that yields an improved adaptive DSC approach for tracking control of a class of semi-strict feedback systems. The new method introduces nonlinear adaptive filters instead of the first-order low pass ones to avoid repeatedly differentiating the virtual control signals. Meanwhile, novel flat zone introduced Lyapunov functions, which have dead zones in the prespecified neighborhood of the origin, are employed to design and analyze the improved robust adaptive control law. As a result, the developed control scheme exhibits three distinct features in comparison with the existing DSC strategy as follows: (1) global rather than semiglobal tracking is achieved even in the presence of nonlinear function nonlinearities; (2) the ultimate tracking accuracy can be exactly known before the controller is implemented; and (3) the ranges of the design parameters to guarantee the closed-loop stability and ultimate tracking accuracy can be completely determined a priori, and the design parameters can be freely chosen from the feasible ranges to improve the control performance. Finally, two examples are presented to confirm the effectiveness of the established approach.