Control and Synchronization Of A Class Of Uncertain Fractional Order Chaotic Systems Via Adaptive Backstepping Control

Summary An observer‐based adaptive fuzzy backstepping approach is proposed for nonlinear systems with respect to fractional‐order differential equations, unmatched uncertainties, unmeasured states, and actuator faults. The approximation capability of fuzzy logic system and minimal learning parameter approaches are applied to identify uncertain functions in a simultaneous manner. For estimating the unavailable conditions, a fuzzy fractional‐order state‐observer is extended. Applying fault‐tolerant approach in a backstepping design methodology would provide a new fault‐tolerant adaptive fuzzy output‐feedback approach for fractional‐order strict‐feedback systems. This control structure would assure the considered system stability through selection of the appropriate Lyapunov candidate function. Two numerical simulations are run to exhibit the validity herein.

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“…The nonlinear chaotic Chua system is expressed as:

\{\begin{matrix} left \\ D^{α} x_{1} = x_{2} + \frac{10}{7} (x_{1} - x_{1}^{3}), \\ D^{α} x_{2} = x_{3} + 10 x_{1} - x_{2}, \\ D^{α} x_{3} = - \frac{100}{7} x_{2} + ρ italicu, \\ y = x_{1} . \end{matrix}

…”

Section: Simulation Resultsmentioning

confidence: 99%

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

Naderolasli

Hashemi

Shojaei

2020

Adaptive Control & Signal

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“…Where, p i 'sand z i 's stand for poles and zeroes, respectively. For an unstable fractional order system, there exists some unstable poles in the equivalent transfer function of equation (9), that is, ∃i; arg p i ð Þ j j< απ 2 . The approximated model is a high order model so, using a model order reduction method, the high order system could be reduced to a lower order one.…”

Section: Oustaloup Approximation Methodsmentioning

confidence: 99%

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

Sanatizadeh

Bigdeli

2018

Asian Journal of Control

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In this paper, a new approach, called coprime‐factorized predictive functional control method (CFPFC‐F) is proposed to control unstable fractional order linear time invariant systems. To design the controller, first, a prediction model should be synthesized. For this purpose, coprime‐factorized representation is extended for unstable fractional order systems via a reduced approximated model of unstable fractional order (FO) system. That is, an approximated integer model of fractional order system is derived via the well‐known Oustaloup method. Then, the high order approximated model is reduced to a lower one via a balanced truncation model order reduction method. Next, the equivalent coprime‐factorized model of the unstable fractional‐order plant is employed to predict the output of the system. Then, a predictive functional controller (PFC) is designed to control the unstable plant. Finally, the robust stability of the closed‐loop system is analyzed via small gain theorem. The performance of the proposed control is investigated via simulations for the control of an unstable non‐laminated electromagnetic suspension system as our simulation test system.

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“…Strict feedback system [22] can be used to express different real world systems, which can be described as follows…”

Section: Preliminaries and System Descriptionmentioning

confidence: 99%

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

Tian

Yang

2019

Symmetry

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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.

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Control and Synchronization Of A Class Of Uncertain Fractional Order Chaotic Systems Via Adaptive Backstepping Control

Cited by 42 publications

References 49 publications

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

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

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