Adaptive backstepping output feedback control for a class of nonlinear fractional order systems

Wei, Yiheng; Tse, Peter W.; Zhao, Yixuan; Wang, Yong

doi:10.1007/s11071-016-2945-4

Cited by 144 publications

(65 citation statements)

References 23 publications

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“…Moreover, at larger γ i , the control action may become aggressive. Smaller values of the σ ‐modification parameter, that is, σ i , lead to a smaller ultimate bound in the adaptive laws, while it may result in a parametric drift. Remark The backstepping control approaches that are proposed in References for then nonlinear fractional‐order systems cannot meet the fault compensation and are only beneficial in uncertain fractional‐order systems. The adaptive controls are assessed with respect to a category of strict‐feedback systems containing fault compensation design in Reference , which cannot be applied in fractional‐order systems.…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, the employment of the fractional‐order controllers increases the degree of freedom and enhances the system performance in dynamical systems . Some available strategies, such as adaptive, optimal, and proportional integral derivative (PID) controllers, are exploited to control the systems' fractional order . The stability of these systems is very essential in control systems and also is discussed in some recent works.…”

Section: Introductionmentioning

confidence: 99%

“…29 Some available strategies, such as adaptive, optimal, and proportional integral derivative (PID) controllers, are exploited to control the systems' fractional order. [30][31][32][33][34][35] The stability of these systems is very essential in control systems and also is discussed in some recent works. In this context, the unknown external disturbances are of concern for a category of these systems in Reference 36.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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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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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Fractional‐order calculus is the generalization of the classical integer‐order calculus, and it has been widely used in system description and control to obtain better performances. () It does also provide another effective way to design a reaching law whose reaching time is robust to initial conditions. The fractional‐order integral is defined as

_{0} ℐ_{t}^{α} f false(t false) = \frac{1}{normalΓ false(α false)} \int_{0}^{t} {((), t - τ)}^{α - 1} f false(τ false) normald τ,

where α >0,

normalΓ false(α false) = \int_{0}^{\infty} x^{α - 1} e^{- x} normald x

is the Gamma function.…”

Section: Resultsmentioning

confidence: 99%

On 2 types of robust reaching laws

Chen

Wei

Wang

2018

Intl J Robust & Nonlinear

Self Cite

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Summary The reaching law is an important part of a sliding‐mode controller, which guarantees the existence of sliding motion in finite time. Fast access to sliding motion with a weak chattering phenomenon in control input is always desired. In this paper, 2 different types of reaching laws are proposed, which guarantee finite‐time convergence to the sliding manifold. Moreover, the reaching time is robust to initial conditions and can be designed by the user. Some useful discussions on the design of parameters are also presented to weaken the chattering phenomenon. A careful simulation study is finally provided to verify the effectiveness and efficiency of the proposed methods.

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“…The overparametrization and partial overparametrization problems were soon eliminated by elegantly introducing the tuning functions [33,35]. On the other hand, with the aids of this frequency distribute model and the indirect Lyapunov method, the adaptive backstepping control of fractional-order systems were established [37][38][39]. As far as we know, there are few results on the generalization of backstepping into fractional-order systems.…”

Section: Introductionmentioning

confidence: 99%

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Wang

2018

Adv Differ Equ

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In this paper, we consider the problem of Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. With the help of backstepping design method, the stabilizing functions and tuning functions are constructed. The controller is designed to ensure that the pseudo-state of the fractional-order nonlinear system converges to the equilibrium. The effectiveness of the proposed method has been verified by some simulation examples.

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Adaptive backstepping output feedback control for a class of nonlinear fractional order systems

Cited by 144 publications

References 23 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

On 2 types of robust reaching laws

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

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