Boundary state and output feedbacks for underactuated systems of coupled time-fractional PDEs with different space-dependent diffusivity

Chen, Juan; Tepljakov, Aleksei; Petlenkov, Eduard; Zhuang, Bo

doi:10.1080/00207721.2020.1803442

Cited by 12 publications

(7 citation statements)

References 39 publications

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“…Obviously, the results in this article are more general than those obtained by the backstepping method. [15][16][17][18]21,37 Remark 6. The widespread application of distributed control has aroused the attention of more and more scholars.…”

Section: Design Of Feedback Control Based On Piecewise Measurementmentioning

confidence: 99%

Distributed robust output feedback control of uncertain fractional-order reaction-diffusion systems

Zhao

Lei

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article focuses on the problem of distributed robust stabilization for a class of uncertain fractional-order reaction–diffusion systems (FRDS) by using two distributed output feedback control strategies: pointwise control based on collocated pointwise measurements and piecewise control based on collocated piecewise measurements. First, the corresponding distributed robust feedback controllers are designed based on the two measurement methods. Then, based on the Lyapunov direct method, Mittag-Leffler (M-L) function, and linear matrix inequality technique (LMI), sufficient conditions for the Mittag-Leffler stability of the closed-loop system are obtained in terms of linear matrix inequalities, respectively. Finally, numerical studies are given to verify the effectiveness of the robust distributed controllers designed in this article.

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Section: Design Of Feedback Control Based On Piecewise Measurementmentioning

confidence: 99%

Distributed robust output feedback control of uncertain fractional-order reaction-diffusion systems

Zhao

Lei

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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“…Remark 5. For the disturbance-free control problem of FRD system with distinct diffusivity in [10], the kernel equation is simplified by assuming a diagonal structure of the kernel matrix. There, the last term in the diagonal matrix is zero for designing underactuated controllers.…”

Section: Deviation Of Kernel Pde and Design Of Sliding Mode Controlmentioning

confidence: 99%

“…Subsequently, a fair amount of literatures (see e.g. [8,10]) on the counterparts of the case of spatially varying coefficients have emerged.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances

Chen

Zhuang

Chen

et al. 2021

Preprint

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In this paper we develop backstepping-based boundary sliding mode controllers for coupled time fractional reaction diffusion (FRD) systems governed by time fractional partial differential equations (PDEs) with time varying delay and input disturbances. Here, the diffusion coefficients are spatially varying (nonconstant) and can be same or different. To asymptotically stabilize the system, we first use a backstepping transformation to convert the original dynamics into a target dynamics with a new manipulable input and the perturbation. Then, the sliding mode algorithm is employed to design this discontinuous controller to suppress disturbances. In this case, we obtain the combined backstepping/sliding mode controller of the original dynamics, with which the closed-loop asymptotic stability is proved by the fractional Halanay's inequality. Fractional numerical examples are given to demonstrate the efficiency of the proposed synthesis.

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“…A lot of fractional-order models can be described by time-fractional PDEs, such as fractional differential model for anomalous diffusion phenomenon [7], fractional combustion models [8], fractional diffusion model of head conduction [9], fractional Schrödinger systems [10] in quantum mechanics, etc. Time-fractional PDE systems play more and more important roles in control theory/ engineering and have been an active research area [11][12][13]. For the fractional-order systems, the stabilisation problem is a fundamental one and important.…”

Section: Introductionmentioning

confidence: 99%

Observation and stabilisation of coupled time‐fractional reaction–advection–diffusion systems with spatially‐varying coefficients

Chen

Tepljakov

Petlenkov

et al. 2020

IET Control Theory & Appl

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This study solves the problem of observer-based output feedback stabilisation of a coupled time-fractional reactionadvection-diffusion system with space-dependent coefficients. In light of the backstepping approach, the Mittag-Leffler convergent observer is derived to enable stabilisation by output feedback. By the fractional Lyapunov method, the Mittag-Leffler stability of the estimation error system is then established. Using the separation principle yields a stabilising output feedback controller, with which the closed-loop stability is proved. Finally, the feasibility of the proposed approach is tested by fractional numerical examples when the kernel matrix equation has not the explicit solution.

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Boundary state and output feedbacks for underactuated systems of coupled time-fractional PDEs with different space-dependent diffusivity

Cited by 12 publications

References 39 publications

Distributed robust output feedback control of uncertain fractional-order reaction-diffusion systems

Distributed robust output feedback control of uncertain fractional-order reaction-diffusion systems

Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances

Observation and stabilisation of coupled time‐fractional reaction–advection–diffusion systems with spatially‐varying coefficients

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