Abstract
In this paper, an adaptive fuzzy finite-time control problem for pure-feedback switched nonlinear systems with prescribed performance is investigate. By utilizing the prescribed performance technique, we mean that the system output is converge to the predefined bounds. By using the dynamic surface control (DSC) and the backstepping technique, we establish a novel adaptive fuzzy finite-time pure-feedback switching control method. In such a scheme, the Butterworth low-pass filter (LPF) is used to construct the fuzzy observer, which can estimate the immeasurable states and avoid algebraic loop problem. In accordance with the stability theory of common Lyapunov function (CLF), the designed controller can ensures that the tracking error converges to a small neighborhood of the origin in finite time. Finally, an example is given to illustrate this method and verify its validity and effectiveness.
Highlights
Switched nonlinear systems are a kind of complex dynamic systems [1]–[3], which will switch subsystems in the phase space according to certain conditions and rules
The main research approach of switching is the Lyapunov function, which is to solve the periodic oscillation in nonlinear systems, and some valuable results have been achieved in recent decades [8], [9]
Xi,f and uf are the filtered signals which are given by xi,f = EL (s)xi ≈ xi, uf = EL (s)u ≈ u where EL (s) represents a Butterworth low-pass filter (LPF), and filter parameters of Butterworth filter can be obtained in [23]
Summary
Switched nonlinear systems are a kind of complex dynamic systems [1]–[3], which will switch subsystems in the phase space according to certain conditions and rules. P. Zhou et al.: Observer-Based Adaptive Fuzzy Finite-Time Control Design With Prescribed Performance solved successfully [30]. Based on the CLF approach, the DSC and the backstepping technique, an adaptive fuzzy finite time control strategy is proposed for pure-feedback switched nonlinear systems with prescribed performance. (1) Creatively combining prescribed performance with finite-time concept, an adaptive finite-time control strategy for a completely non-affine switched pure-feedback nonlinear systems rather than the original non-switched form is proposed. This article aims to devise an output-feedback controller of system (1) such that: 1), the tracking error (t) = y(t) − yd (t) converges to a small neighborhood of the origin within finite time with prescribed performance for any specified reference signal yd (t); 2), Every signal existing in the closed-loop system is bounded.
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