Continuous Fractional‐Order Sliding PI Control for Nonlinear Systems Subject to Non‐Differentiable Disturbances

Muñoz‐Vázquez, Aldo Jonathan; Parra-Vega, Vicente; Sánchez‐Orta, Anand

doi:10.1002/asjc.1370

Cited by 23 publications

(22 citation statements)

References 24 publications

(49 reference statements)

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“…In addition, it has been shown that the fractionalorder integral of the discontinuous signum function preserves the main features required to design sliding mode control [29], including finite-time convergence and exact rejection of Hölder disturbances by means of a continuous signal of control.…”

Section: Hölder Functions and Fractional-order Differentiabilitymentioning

confidence: 99%

“…, }, with Ω the timeinterval at which the system is studied, output = 1 stands for the measured variable, is the control input, and : Ω → R represents matched disturbances and uncertainties. Examples of Hölder effects in physical systems modeled throughout , are given in [27][28][29][30][31].…”

Section: System Description and Control Statementmentioning

confidence: 99%

“…The proof is built upon [34] and our previous proposals [28][29][30] in conjunction with the finite-time state estimator. Consider the fractional-order differintegral dynamics resulting from applying control (18) into (17):…”

Section: Theorem 9 Consider System (20) For Feedback Gain > ((3+mentioning

confidence: 99%

“…whose existence of solutions has been studied in [28,29,34]. In accordance with the dynamic resetting memory principle [28][29][30], { } ∞ =0 can be considered as an increasing sequence of time instants when ( ) crosses the zero value, that is, when ( ) = 0.…”

Section: Theorem 9 Consider System (20) For Feedback Gain > ((3+mentioning

confidence: 99%

“…In accordance with the dynamic resetting memory principle [28][29][30], { } ∞ =0 can be considered as an increasing sequence of time instants when ( ) crosses the zero value, that is, when ( ) = 0. In addition, by virtue of the continuity of ( ), the value ( ) can be approximated by its preceding value ( − ), where is the sampling time, during real-time digital implementation [28].…”

Section: Theorem 9 Consider System (20) For Feedback Gain > ((3+mentioning

confidence: 99%

See 4 more Smart Citations

Output Feedback Finite‐Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

Muñoz‐Vázquez

Parra-Vega²,

Sánchez‐Orta³

et al. 2017

Mathematical Problems in Engineering

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The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

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Section: Hölder Functions and Fractional-order Differentiabilitymentioning

confidence: 99%

Section: System Description and Control Statementmentioning

confidence: 99%

Section: Theorem 9 Consider System (20) For Feedback Gain > ((3+mentioning

confidence: 99%

Section: Theorem 9 Consider System (20) For Feedback Gain > ((3+mentioning

confidence: 99%

Section: Theorem 9 Consider System (20) For Feedback Gain > ((3+mentioning

confidence: 99%

See 3 more Smart Citations

Output Feedback Finite‐Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

Muñoz‐Vázquez

Parra-Vega²,

Sánchez‐Orta³

et al. 2017

Mathematical Problems in Engineering

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Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

Chen

et al. 2017

Asian Journal of Control

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The extended state observer (ESO) based controller has been used successfully with integer-order systems involving large uncertainties. In this paper, the robust control of uncertain multi-order fractional-order (FO) systems based on ESO is investigated. First, we transform the multi-order FO system into an equivalent system in the form of a same-order state-space equation. Then, the ESO for the new system is established for estimating both the state and the total disturbance. Sufficient conditions for bounded-input and bounded-output stability are derived, and the asymptotic stability of the closed loop system is analyzed, based on whether the states are available or not. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed methodology.

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Algebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem Approach

Taghavian

Tavazoei

2018

Asian Journal of Control

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Continuous Fractional‐Order Sliding PI Control for Nonlinear Systems Subject to Non‐Differentiable Disturbances

Cited by 23 publications

References 24 publications

Output Feedback Finite‐Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

Output Feedback Finite‐Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

Algebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem Approach

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