Uniformly continuous differintegral sliding mode control of nonlinear systems subject to Hölder disturbances

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

doi:10.1016/j.automatica.2016.01.011

Cited by 26 publications

(19 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Secondly, recent results in [26][27][28] are adopted to design a fractional-order sliding mode control that rejects exactly (not just equivalently) the matched Hölder disturbances in finite-time, by invoking the topological properties of differintegral operators [17]. Finally, a nominal controller is designed to enforce finite-time convergence of the whole (pseudo)state [10].…”

Section: Proposed Solution and Contributionmentioning

confidence: 99%

“…The interested reader is referred to [14,17,18,[26][27][28], and for completeness, in this section, the differintegral operators and some properties of Hölder functions are introduced. Consider ∈ (0, 1] and the following differintegral operators:…”

Section: Fractional Differintegral Operators Fractional Calculus Is mentioning

confidence: 99%

“…Fractional-order operators provide tools to study nonlocal topological properties of continuous functions, such as their regularity degree in connection with the Hölder condition [17,26]. 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%

“…where the continuous nominal control 0 stabilizes the ideal system without disturbance [10], and the differintegral sliding mode control compensates the matched Hölder disturbance [26][27][28]. Let be a penalization variable that measures the deviation from the ideal system (without disturbances) to the real system defined by (7).…”

Section: Disturbance Observer Based On Fractional Differintegralmentioning

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Proposed Solution and Contributionmentioning

confidence: 99%

Section: Fractional Differintegral Operators Fractional Calculus Is mentioning

confidence: 99%

Section: Hölder Functions and Fractional-order Differentiabilitymentioning

confidence: 99%

Section: Disturbance Observer Based On Fractional Differintegralmentioning

confidence: 99%

See 2 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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Definition 1 [42] The Hölder space H ϑ ( ) is the set of all functions f (t) that comply with (7) over .…”

Section: On Hölder Spacementioning

confidence: 99%

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, attempts are made to design a novel time-varying switching surface in sliding mode control which enables us to synchronize two fractional chaotic systems precisely at any arbitrary pre-specified time. For both Caputo (C) and Riemann-Liuville (RL) derivatives, control laws based on Lyapunov stability theorem are derived. The proposed method is completely robust against existence of uncertainties and exogenous disturbances due to eliminating the reaching phase. Since the sign function is replaced by fractional RL integral of the sign function, the chattering is removed. The simulation results in different scenarios are reported to show the effectiveness of the proposed method.

show abstract

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

Muñoz‐Vázquez

Parra-Vega

Sánchez‐Orta

2016

Asian Journal of Control

View full text Add to dashboard Cite

Aiming at designing a robust controller to withstand a class of continuous, but not necessarily differentiable, disturbances, such as Hölder type, a continuous and chattering‐free sliding mode control is proposed. The key idea is a judicious synthesis of a resetting memory principle for the differintegral operators to show that a sliding mode is induced, and sustained, in finite‐time, to guarantee asymptotic tracking. The closed‐loop system achieves exact rejection of Hölder disturbances even in case of uncertain flow, but assuming certain knowledge of the input matrix. Furthermore, it is shown that our methodology generalizes continuous high‐oder sliding mode schemes by using an integral action of fractional‐order. A representative simulation study is discussed to show the feasibility of the proposal.

show abstract

Uniformly continuous differintegral sliding mode control of nonlinear systems subject to Hölder disturbances

Cited by 26 publications

References 15 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

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

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

Contact Info

Product

Resources

About