Abstract
An improved dynamic surface control (IDSC) approach is presented for a class of strict-feedback nonlinear systems with unknown functions. The proposed method makes the state errors get rid of the influence of first-order filters, which simplifies the design of control. By employing neural networks to account for system uncertainties, the virtual control signal of the IDSC is directly used to construct the state error instead of the signal generated by the first-order filter in the dynamic surface control (DSC) method. The stability of the method is proved by Lyapunov stability theory, and the semi-global uniform ultimate boundedness of all signals in the closed-loop system is guaranteed. Simulation results demonstrate the IDSC method has better tracking performance and stability than traditional DSC method.
Highlights
During the past decades, Approximation-based adaptive control for uncertain nonlinear systems has received much attentions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
Neural networks (NNs) and fuzzy-logic systems (FLS) are used to approximate uncertain nonlinear functions without superfluous knowledge about controlled system, which has effectively removed the restrictive conditions for system uncertainties
The bounds of control gain functions are always assumed to be constants while using dynamic surface control (DSC) method. This restrictive condition has been weakened that the control gain functions can be unbounded functions in [34], where a DSC-based adaptive neural control method is designed for a class of non-strict-feedback nonlinear systems
Summary
Approximation-based adaptive control for uncertain nonlinear systems has received much attentions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. A DSC-based robust adaptive neural control approach has been proposed for strict-feedback nonlinear systems in [33]. The improved algorithm introduces nonlinear adaptive filters instead of the first-order low pass ones to avoid repeatedly differentiating the virtual control signals It can realize global tracking instead of semi global tracking. When we turn our attention back to DSC method, it should be noted that the state errors and actual controller for the DSC method are constructed based on the signals produced by passing virtual control signals through first-order filters, which implies the convergence of state errors heavily depends on the first-order filters This fact will result in the problem that the tracking performance or even the stability of system may degrade rapidly when the time constants are changed. The simulation examples are given to demonstrate the effectiveness of the proposed method in Section V and followed by Section VI which concludes this paper
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