scholarly journals Adaptive Backstepping Control of a Class of Incommensurate Fractional Order Nonlinear MIMO Systems With Unknown Disturbance

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 150949-150959 ◽  
Author(s):  
Changhui Wang ◽  
Mei Liang
Keyword(s):  
Fractional Order ◽  
Mimo Systems ◽  
Backstepping Control ◽  
Adaptive Backstepping ◽  
Adaptive Backstepping Control ◽  
Unknown Disturbance

scholarly journals Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Wang ◽  
Ling Liu ◽  
Chongxin Liu ◽  
Ziwei Zhu ◽  
Zhenquan Sun
Keyword(s):  
Fractional Order ◽  
Control Strategy ◽  
Reference Signal ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
Control Input ◽  
Fractional Order Systems ◽  
Adaptive Backstepping ◽  
Unknown Parameters ◽  
Adaptive Backstepping Control

In this paper, fractional calculus is applied to establish a novel fractional-order ferroresonance model with fractional-order magnetizing inductance and capacitance. Some basic dynamic behaviors of this fractional-order ferroresonance system are investigated. And then, considering noncommensurate orders of inductance and capacitance and unknown parameters in an actual ferroresonance system, this paper presents a novel fractional-order adaptive backstepping control strategy for a class of noncommensurate fractional-order systems with multiple unknown parameters. The virtual control laws and parameter update laws are designed in each step. Thereafter, a novel fractional-order adaptive controller is designed in terms of the fractional Lyapunov stability theorem. The proposed control strategy requires only one control input and can force the output of the chaotic system to track the reference signal asymptotically. Finally, the proposed method is applied to a noncommensurate fractional-order ferroresonance system with multiple unknown parameters. Numerical simulation confirms the effectiveness of the proposed method. In addition, the proposed control strategy also applies to commensurate fractional-order systems with unknown parameters.

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