Abstract
This paper provides a disturbance observer-based prescribed performance control method for uncertain strict-feedback systems. To guarantee that the tracking error meets a design prescribed performance boundary (PPB) condition, an improved prescribed performance function is introduced. And radial basis function neural networks (RBFNNs) are used to approximate nonlinear functions, while second-order filters are employed to eliminate the “explosion-complexity” problem inherent in the existing method. Meanwhile, disturbance observers are constructed to estimate the compounded disturbance which includes time-varying disturbances and network construction errors. The stability of the whole closed-loop system is guaranteed via Lyapunov theory. Finally, comparative simulation results confirm that the proposed control method can achieve better tracking performance.
Highlights
Backstepping technology is widely used for nonlinear systems with the strict-feedback structure [1,2,3]. is method requires repeated differentiation of the virtual controller, which leads to the problem of “explosion-complexity.”
It can be seen from the above literature that the nonlinear system contains unknown nonlinear function terms and external disturbances
In order to ensure that the tracking error e is limited within prescribed performance boundary (PPB) (10), we introduce the following transformation variable z1: h(t) z1 ln1 −
Summary
Backstepping technology is widely used for nonlinear systems with the strict-feedback structure [1,2,3]. is method requires repeated differentiation of the virtual controller, which leads to the problem of “explosion-complexity.” In order to solve this problem and estimate the virtual controller, dynamic surface control (DSC) technique [4,5,6,7] is applied. By applying the same differentiator, Yu et al [9] proposed a backstepping approach, which enables the tracking error to converge to a small neighborhood in finite time It can be seen from the above literature that the nonlinear system contains unknown nonlinear function terms and external disturbances. Erefore, it is necessary to discuss that how to accurately estimate unknown nonlinear functions and external disturbances under the condition that the tracking error meets the PPB. E main contributions of this paper are summarized as follows: (1) the proposed PPC method guarantees a small convergence overshoot of the tracking error; (2) system uncertainties (include unknown nonlinear functions and external disturbances) can be effectively estimated by the disturbance observer and RBFNNs; and (3) compared with the traditional PPC method, the proposed method has better control performance.
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