Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties

Xuefeng Zhang,Wenkai Huang

doi:10.3390/fractalfract4040050

Xuefeng Zhang, Wenkai Huang

Open Access

https://doi.org/10.3390/fractalfract4040050

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Journal: Fractal and Fractional	Publication Date: Oct 22, 2020
Citations: 28	License type: CC BY 4.0

Affiliation: Northeastern University

Abstract

This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.

Highlights

Fractional order systems (FOSs) have been developed greatly in the past few decades
When the fractional order α is equal to the integer, the FOSs reduce to integer order systems
Many scholars have carried out further research on FOSs

Summary

Introduction

Fractional order systems (FOSs) have been developed greatly in the past few decades. When the fractional order α is equal to the integer, the FOSs reduce to integer order systems. In [13], the robust stabilization of uncertain singular time-delay systems is considered, and sufficient conditions are given to ensure the system is regular, impulse-free, and asymptotically stable. By design the integral sliding surface, Wang et al in [29] study the adaptive SMC for the T-S fuzzy singular systems. In [40], Wang et al find that the control law based on the fractional order reaching law can reduce the time for the FOSs to reach the sliding surface. In [45], the admissibility of T-S fuzzy singular systems is considered by using a RBF neural network sliding mode observer. Where x(t) ∈ Rn is the system state, u(t) ∈ Rl is the control input, and α (0 < α < 1) is the fractional order, E ∈ Rn×n is a singular matrix such that rank(E) = r < n.

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Main Results

Simulation Example

Conclusions