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

• Published in: Fractal and fractional Vol. 4; no. 4; p. 50
• Main Authors: Zhang, Xuefeng, Huang, Wenkai
• Format: Journal Article
• Language: English
• Published: MDPI AG 01.12.2020
• Subjects: adaptive RBF neural network; linear matrix inequality; singular fractional order systems; sliding mode control
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract4040050

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.