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Backstepping

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IEEE Transactions on Automatic Control

This article is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example.

Command Filter Adaptive Asymptotic Tracking of Uncertain Nonlinear Systems With Time-Varying Parameters and Disturbances