Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach

2015 ◽  
Author(s):  
Bijnan Bandyopadhyay ◽  
Shyam Kamal
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Fractional Order Systems ◽  
And Control

Sliding mode control of uncertain fractional order systems with delay

2019 ◽  
Vol 93 (4) ◽  
pp. 934-943 ◽  
Author(s):  
Niraj Choudhary ◽  
Janardhanan Sivaramakrishnan ◽  
Indra Narayan Kar
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Fractional Order Systems ◽  
Mode Control

scholarly journals Stability of Fractional Order Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Margarita Rivero ◽  
Sergei V. Rogosin ◽  
José A. Tenreiro Machado ◽  
Juan J. Trujillo
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
State Of The Art ◽  
Point Of View ◽  
Fractional Order Systems ◽  
Short Period ◽  
Systems And Control ◽  
Different Types ◽  
The Stability ◽  
And Control

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

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

2020 ◽  
Vol 4 (4) ◽  
pp. 50
Author(s):  
Xuefeng Zhang ◽  
Wenkai Huang
Keyword(s):  
Neural Network ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Rbf Neural Network ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Sliding Surface ◽  
Mode Control ◽  
Necessary And Sufficient

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.

Sign in / Sign up

Export Citation Format

Share Document