scholarly journals Adaptive Stabilization of a Fractional-Order System with Unknown Disturbance and Nonlinear Input via a Backstepping Control Technique

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 55
Author(s):  
Xiaomin Tian ◽  
Zhong Yang
Keyword(s):  
Fractional Order ◽  
Dead Zone ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Fractional Order System ◽  
Control Technique ◽  
Order System ◽  
Distributed Model ◽  
Adaptive Stabilization ◽  
Unknown Parameters

In this paper, a new backstepping-based adaptive stabilization of a fractional-order system with unknown parameters is investigated. We assume that the controlled system is perturbed by external disturbance, the bound of external disturbance to be unknown in advance. Moreover, the effects of sector and dead-zone nonlinear inputs both are taken into account. A fractional-order auxiliary system is established to generate the necessary signals for compensation the nonlinear inputs. Meantime, in order to deal with these unknown parameters, some fractional-order adaption laws are given. The frequency-distributed model is used so that the indirect Lyapunov theory is available in designing controllers. Finally, simulation results are presented to verify the effectiveness and robustness of the proposed control strategy.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

Synchronization of a Fractional-Order System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 796-799
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Stability

In this paper, synchronization of a fractional-order system with unknown parameters is studied. The chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, suitable synchronization controllers and parameter identification rules for the unknown parameters are designed. Numerical simulations are used to demonstrate the effectiveness of the controllers.

Adaptive Control for Fractional-Order Micro-Electro-Mechanical Resonator With Nonsymmetric Dead-Zone Input

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Xiaomin Tian ◽  
Shumin Fei
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Dead Zone ◽  
Lyapunov Stability Theory ◽  
Distributed Model ◽  
Mechanical Resonator ◽  
Unknown Parameters ◽  
The Dead ◽  
Resonator System ◽  
The Stability

This paper deals with the adaptive control of fractional-order micro-electro-mechanical resonator system (FOMEMRS) with nonsymmetric dead-zone nonlinear input. The slope parameters of the dead-zone nonlinearity are unmeasured and the parameters of the controlled systems are assumed to be unknown in advance. To deal with these unknown parameters, some fractional versions of parametric update laws are proposed. On the basis of the frequency distributed model of fractional integrator and Lyapunov stability theory, a robust control law is designed to prove the stability of the closed-loop system. The proposed adaptive approach requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. Finally, simulation examples are given to verify the robustness and effectiveness of the proposed control scheme.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

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