Finite‐time stability and stabilisation of distributed parameter systems

Li, Xueyang; Mao, Weijie

doi:10.1049/iet-cta.2016.1087

Cited by 24 publications

(26 citation statements)

References 27 publications

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“…When the fractional order α = 1, the fractional order distributed parameter System (1) is reduced to an integral order one, which has been widely investigated in [11,[16][17][18][19].…”

Section: Remarkmentioning

confidence: 99%

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ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Lan

Cui

2018

Algorithms

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This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

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“…When the fractional order α = 1, the fractional order distributed parameter System (1) is reduced to an integral order one, which has been widely investigated in [11,[16][17][18][19].…”

Section: Remarkmentioning

confidence: 99%

“…Distributed parameter systems are a class of complicated infinite-dimensional systems, whose states depend on both spatial position and time [8][9][10][11]. In recent years, the application of ILC to distributed parameter systems has become a new topic [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Lan

Cui

2018

Algorithms

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“…It should be noted that few results related to the finite‐time stability of PDE‐based systems have been achieved. In [29], the definitions of finite‐time stability and stabilisation have been extended to distributed parameter systems, and sufficient conditions in terms of LMIs are obtained to achieve

L^{2}

finite‐time stability and

W^{1, 2}

finite‐time stability using distributed state‐feedback controllers. For distributed control, the actuation penetrates inside the domain of PDE systems or is evenly distributed everywhere in the domain.…”

Section: Introductionmentioning

confidence: 99%

DC‐boundary finite‐time stabilisation for distributed parameter systems

Mao

2020

IET Control Theory & Appl

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“…Accordingly, various finite time theorems and lemmas have been introduced of which some have been presented in [20,37]. The finite time stability has been very much considered in the recent literature to speed up the convergence rate and improve the concept of stability [11,18,37]. In [2], Finite time concept has been considered to incorporate with optimal robust control for Photovoltaic system using the VSC model in Smart Grid.…”

Section: Introductionmentioning

confidence: 99%

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

Abadi

Hosseinabadi

Mekhilef

2018

Technol Econ Smart Grids Sustain Energy

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The presence of uncertainties and external disturbances is one of the unavoidable problems with various practical systems which might be unavailable in real-time. Sliding Mode Control (SMC) is one of the effective robust control methods to deal with these uncertainties and external disturbances. In this paper, two novel controllers are designed by using Nonsingular Terminal SMC (NTSMC) and Adaptive Nonsingular Terminal SMC (ANTSMC) methods for synchronization of dual smart grid chaotic systems with various uncertainties and external disturbances. Indeed, both adaptive and non-adaptive controllers based on NTSMC are proposed to provide two alternatives which can adjust by changing operating conditions and dynamics. The concept of SMC method guarantees controller robustness against various uncertainties and external disturbances. Elimination of the undesirable chattering phenomenon is addressed in this study which is one of the common deficiencies with conventional SMC method. Additionally, finite time concept is used to speed up the convergence rate. Finite time stability proof is performed by using Lyapunov stability theory. The numerical simulation is carried out in Simulink/MATLAB to reveal the validity of the proposed controllers for the smart grid chaotic system. A comprehensive comparison is made by performing simulation for the Fractional Order Adaptive Sliding Mode Control (FOASMC) controller and defining three performance criteria, among the proposed controllers in this study and FOASMC controller.

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Finite‐time stability and stabilisation of distributed parameter systems

Cited by 24 publications

References 27 publications

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

DC‐boundary finite‐time stabilisation for distributed parameter systems

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

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