Boundary dynamic feedback control for a class of semi‐linear distributed parameter systems

Zhou, Yanjiu; Cui, Baotong

doi:10.1049/iet-cta.2018.6159

Cited by 5 publications

(8 citation statements)

References 44 publications

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“…By the Definition 2.1, we can conclude that system (1)-( 3) with the boundary controller ( 9) is M-L stable if the control gain k 1 satisfies the LMI Ξ 1 < 0, namely, the closed-loop system (10)-( 12) is M-L stable. This proves that the controller ( 9) is effective for realizing system (1)-( 3 With the help of the description of domain-averaged measurement in Zhou and Cui [35], there may be one or more sensors to obtain the effective information of their respective measurements, and then, the domain-averaged measurement information is obtained by summarizing and averaging this information. In this paper, the boundary controller is designed based on this domain information.…”

Section: Boundary Control Design Based On Domain Average Measurementmentioning

confidence: 87%

Boundary Mittag–Leffler stabilization of a class of time fractional‐order nonlinear reaction–diffusion systems

Zhao

Lei

et al. 2023

Asian Journal of Control

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Boundary control design of a class of time fractional‐order nonlinear reaction–diffusion systems (FNRDSs) is considered in three cases: domain‐averaged measurement, collocated boundary point measurement, and anti‐collocated boundary point measurement. For domain‐averaged measurement and collocated boundary point measurement, boundary controllers are designed directly based on the measurements, respectively. For the anti‐collocated boundary point measurement, to overcome the difficulty that the measurement cannot be used for the controller design directly, an observer is constructed firstly, and then, an observer‐based boundary controller is designed. Sufficient conditions for Mittag–Leffler (M‐L) stability of the closed‐loop system are all provided in terms of linear matrix inequalities (LMIs). Numerical simulation results are provided to illustrate the feasibility and effectiveness of the proposed methods.

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Section: Boundary Control Design Based On Domain Average Measurementmentioning

confidence: 87%

Boundary Mittag–Leffler stabilization of a class of time fractional‐order nonlinear reaction–diffusion systems

Zhao

Lei

et al. 2023

Asian Journal of Control

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“…Combining with the bump-like function (28), we can get that ‖w(s, t )‖ L 2 → 0 as t → T . In virtue of Definition 1, the target system (7)-( 9) is fixed-time stable.…”

Section: Proof Consider a Lyapunov Functionmentioning

confidence: 96%

“…In addition, the economical and technical constraints, the sensor and actuator at the interior of spatial domain is not realisable in some applications such as viscous fluid, high temperature and chemical reactor. Therefore, the boundary control of parabolic distributed parameter systems has received an increased attention due to the more realistic problem in many applications [22][23][24][25][26][27][28]. It is worth noting that the backstepping technique has been become one of the popular research methods to the boundary feedback control of the parabolic distributed parameter systems [29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Fixed‐time stabilisation of boundary controlled linear parabolic distributed parameter systems with space‐dependent reactivity

Bao

Cui

Lou

et al. 2020

IET Control Theory & Appl

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The problems of state feedback and output feedback for fixed‐time stabilisation of a linear parabolic distributed parameter system with space‐dependent reactivity are considered by means of continuous backstepping approach and Lyapunov method. First, the invertible Volterra integral transformation with time dependent gain kernel is adopted to convert the original system into a fixed‐time stable target system with time‐dependent coefficient. The well‐posedness of the resulting kernel equations is proved by the method of successive approximation. Then a state feedback controller is designed to guarantee fixed‐time stabilisation of the closed‐loop system. Moreover, a fixed‐time observer is considered to estimate the state of the original system on the basis of the measurement signal at the boundary. Based on this observer, a observer‐based output feedback controller is established to fixed‐time stabilise the closed‐loop system in a prescribed time by using separation principle. Finally, a numerical simulation is provided to verify the feasibility of the proposed theoretical results by using the modified Ablowitz‐Kruskal‐Ladik scheme.

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“…The study of system stability has always been one of the most basic and important problems in distributed parameter systems. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] At present, several control methods have been proposed for various distributed parameter systems, such as robust control, 5 adaptive control, 6,7 sliding mode control, 8 pulse control, 9 boundary control, [11][12][13] and parallel control. 14 With the development of artificial intelligence, intermittent control 10,[19][20][21][22] has attracted more attention.…”

Section: Introductionmentioning

confidence: 99%

“…The study of system stability has always been one of the most basic and important problems in distributed parameter systems 1–18 . At present, several control methods have been proposed for various distributed parameter systems, such as robust control, 5 adaptive control, 6,7 sliding mode control, 8 pulse control, 9 boundary control, 11–13 and parallel control 14 .…”

Section: Introductionmentioning

confidence: 99%

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

Xia

Luo

Zhou³

2023

Math Methods in App Sciences

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A class of time-varying delay distributed parameter systems with input saturation is investigated in this paper. The periodic intermittent control method is adopted to make the system stable in finite time, improve the control performance of the system, and save on control cost. A periodic intermittent controller combined saturated input is designed to ensure the stability of the proposed system in finite time. Lyapunov-Krasoviskii stability theory and matrix inequality techniques are used to analyze the finite-time stability of the system, and sufficient conditions for the system to be stable in finite time are obtained. Finally, the correctness of the theorems is verified by simulation experiments.

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Boundary dynamic feedback control for a class of semi‐linear distributed parameter systems

Cited by 5 publications

References 44 publications

Boundary Mittag–Leffler stabilization of a class of time fractional‐order nonlinear reaction–diffusion systems

Boundary Mittag–Leffler stabilization of a class of time fractional‐order nonlinear reaction–diffusion systems

Fixed‐time stabilisation of boundary controlled linear parabolic distributed parameter systems with space‐dependent reactivity

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

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