Enhancing the settling time estimation of fixed-time stability and applying it to the predefined-time synchronization of delayed memristive neural networks with external unknown disturbance

Lin, Lixiong; Wu, Peixin; Chen, Yanjie; He, Bingwei

doi:10.1063/5.0010145

Cited by 20 publications

(6 citation statements)

References 43 publications

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“…Lemma [34]. Suppose that the continuous radially unbounded function

V : {double-struckR}^{n} \to {double-struckR}_{+} \cup false{0 false}

satisfies (1)

V (x) = 0

where

x = 0

; (2)For any

V (x) > 0

, there exist

b_{1}, b_{2}, T_{c 1}, T_{c 2} > 0, c_{1}, c_{2} \geq 0

p > 0

and

q > 1

such that:

\dot{V} \leq \{\begin{matrix} true \\ left - \frac{C_{v 1}}{T_{c 1}} (b_{1} V^{p} + c_{1}), w h e n 0 < V \leq 1 \\ left - \frac{C_{v 2}}{T_{c 2}} (b_{2} V^{q} + c_{2}), w h e n V > 1 \end{matrix},

where

T_{c 1}

and

T_{c 2}

are user defined parameters and

C_{v 1} = \{\begin{matrix} true \\ left \frac{1}{b_{1}^{\frac{1}{p}} (1 - p)} \cdot [(b_{1}^{\frac{1}{p}} + c_{1}^{...} \end{matrix}

…”

Section: Preliminariesmentioning

confidence: 99%

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The sliding mode control approach design for nonholonomic mobile robots based on non‐negative piecewise predefined‐time control law

Lin

et al. 2021

IET Control Theory & Appl

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In this paper, a novel trajectory tracking control method of nonholonomic mobile robots based on the non-negative piecewise predefined-time theorem is proposed. The idea of cascade control is used to divide the posture error system of the mobile robot into two subsystems. Firstly, for the first-order subsystem, an active predefined-time controller is designed to realize that the angle error system converges and stabilizes to zero within a given time, which is preset in advance. Secondly, a novel predefined-time sliding mode controller is designed for the second-order subsystem, which adds a constant to compensate for the influence of singularity. Moreover, compared with the existing fixed-time control algorithm, the control scheme proposed in this paper provides a more accurate upper bound of the settling time estimation. For convenience, the complex expression of the settling time estimation is transformed into an adjustable parameter. Furthermore, the stability of the two developed controllers is analyzed and some conditions for selecting parameters are given. Finally, the simulation results show the feasibility and correctness of the proposed control algorithm. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…Lemma [34]. Suppose that the continuous radially unbounded function

V : {double-struckR}^{n} \to {double-struckR}_{+} \cup false{0 false}

satisfies (1)

V (x) = 0

where

x = 0

; (2)For any

V (x) > 0

, there exist

b_{1}, b_{2}, T_{c 1}, T_{c 2} > 0, c_{1}, c_{2} \geq 0

p > 0

and

q > 1

such that:

\dot{V} \leq \{\begin{matrix} true \\ left - \frac{C_{v 1}}{T_{c 1}} (b_{1} V^{p} + c_{1}), w h e n 0 < V \leq 1 \\ left - \frac{C_{v 2}}{T_{c 2}} (b_{2} V^{q} + c_{2}), w h e n V > 1 \end{matrix},

where

T_{c 1}

and

T_{c 2}

are user defined parameters and

C_{v 1} = \{\begin{matrix} true \\ left \frac{1}{b_{1}^{\frac{1}{p}} (1 - p)} \cdot [(b_{1}^{\frac{1}{p}} + c_{1}^{...} \end{matrix}

…”

Section: Preliminariesmentioning

confidence: 99%

“…Sanchez-Torres [32] proposed a new theorem named predefined-time stability to overcome these difficulties. However, the predefined time control of mobile robots has rarely been investigated [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

The sliding mode control approach design for nonholonomic mobile robots based on non‐negative piecewise predefined‐time control law

Lin

et al. 2021

IET Control Theory & Appl

Self Cite

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“…Recently, Anguiano-Gijon et al (2019), Lin (2021b), Assali (2021), Lin et al (2021), andMuoz-Vazquez et al (2021) went further and discussed the predefined-time synchronization of two chaotic systems, one of them obtained the projective synchronization criterion about predefined-time (Lin et al, 2021), and another two of them considered chaotic systems of fractional-order forms (Lin et al, 2021;Muoz-Vazquez et al, 2021). In 2020, Lin defined the novel criterion of predefined-time synchronization in different kinds of neural networks, including a chaos neural network and memristive neural network (Lin et al, 2020;Lin, 2021a).…”

Section: Introductionmentioning

confidence: 99%

Predefined-Time Stability/Synchronization of Coupled Memristive Neural Networks With Multi-Links and Application in Secure Communication

et al. 2021

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This paper explores the realization of a predefined-time synchronization problem for coupled memristive neural networks with multi-links (MCMNN) via nonlinear control. Several effective conditions are obtained to achieve the predefined-time synchronization of MCMNN based on the controller and Lyapunov function. Moreover, the settling time can be tunable based on a parameter designed by the controller, which is more flexible than fixed-time synchronization. Then based on the predefined-time stability criterion and the tunable settling time, we propose a secure communication scheme. This scheme can determine security of communication in the aspect of encrypting the plaintext signal with the participation of multi-links topology and coupled form. Meanwhile, the plaintext signals can be recovered well according to the given new predefined-time stability theorem. Finally, numerical simulations are given to verify the effectiveness of the obtained theoretical results and the feasibility of the secure communication scheme.

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“…with 0 < q < 1. The predefined-time stability theorem proposed in this paper is more general than (Aldana-Lopez et al, 2019;Anguiano-Gijon et al, 2019;Lin et al, 2020). Synchronization has important applications in many fields, such as secure communication, nonlinear control systems, pattern recognition, and information processing (Alimi et al, 2019;Ouyang et al, 2020).…”

mentioning

confidence: 98%

“…At present, there are some research results on predefined-time synchronization. Lin et al (2020) proposed a predefined-time stability theorem based on a piecewise Lyapunov function, in which the Lyapunov function should satisfy the inequality: (αV p (t) + βV q (t)) with α, β > 0, p > 1 and 0 < q < 1. Anguiano-Gijon et al (2019) introduced…”

mentioning

confidence: 99%

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

Liu

Zhao²,

Wang³

et al. 2022

Front. Neurorobot.

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This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

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Enhancing the settling time estimation of fixed-time stability and applying it to the predefined-time synchronization of delayed memristive neural networks with external unknown disturbance

Cited by 20 publications

References 43 publications

The sliding mode control approach design for nonholonomic mobile robots based on non‐negative piecewise predefined‐time control law

The sliding mode control approach design for nonholonomic mobile robots based on non‐negative piecewise predefined‐time control law

Predefined-Time Stability/Synchronization of Coupled Memristive Neural Networks With Multi-Links and Application in Secure Communication

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

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