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Keywords = singular fractional order systems (SFOS)

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19 pages, 717 KB  
Article
A New Adaptive Robust Sliding Mode Control Approach for Nonlinear Singular Fractional-Order Systems
by Shunan Chen, Wenkai Huang and Qiang Liu
Fractal Fract. 2022, 6(5), 253; https://doi.org/10.3390/fractalfract6050253 - 6 May 2022
Cited by 11 | Viewed by 3562
Abstract
This article focuses on designing an adaptive sliding mode controller via state and output feedback for nonlinear singular fractional-order systems (SFOSs) with mismatched uncertainties. Firstly, on the basis of extending the dimension of the SFOS, a new integral sliding mode surface is constructed. [...] Read more.
This article focuses on designing an adaptive sliding mode controller via state and output feedback for nonlinear singular fractional-order systems (SFOSs) with mismatched uncertainties. Firstly, on the basis of extending the dimension of the SFOS, a new integral sliding mode surface is constructed. Through this special sliding surface, the sliding mode of the descriptor system does not contain a singular matrix E. Then, the sufficient conditions that ensure the stability of sliding mode motion are given by using linear matrix inequality. Finally, the control law based on an adaptive mechanism that is used to update the nonlinear terms is designed to ensure the SFOS satisfies the reaching condition. The applicability of the proposed method is illustrated by a practical example of a fractional-order circuit system and two numerical examples. Full article
(This article belongs to the Special Issue Applications of Fractional Operator in Image Processing and Stability of Control Systems)
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13 pages, 400 KB  
Article
Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties
by Xuefeng Zhang and Wenkai Huang
Fractal Fract. 2020, 4(4), 50; https://doi.org/10.3390/fractalfract4040050 - 22 Oct 2020
Cited by 34 | Viewed by 3939
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue 2020 Selected Papers from Fractal Fract’s Editorial Board Members)
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11 pages, 403 KB  
Article
Admissibility of Fractional Order Descriptor Systems Based on Complex Variables: An LMI Approach
by Xuefeng Zhang and Yuqing Yan
Fractal Fract. 2020, 4(1), 8; https://doi.org/10.3390/fractalfract4010008 - 16 Mar 2020
Cited by 12 | Viewed by 3120
Abstract
This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. [...] Read more.
This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. Then, an observer-based controller is designed to ensure system admissible. Finally, numerical examples are given to reveal the validity of the theoretical conclusions. Full article
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