Fixed-Time Stabilization of Discontinuous Neutral Neural Networks With Proportional Delays via New Fixed-Time Stability Lemmas

Fixed-time synchronization of proportional delay memristive complex-valued competitive neural networks

The fixed-time synchronization (FXS) is considered for memristive complex-valued competitive neural networks (MCVCNNs) with proportional delays. Two less conservative criteria supporting the FXS of MCVCNNs are founded by involving Lyapunov method and inequality techniques. Suitable switch controllers are designed by defining different norms of complex numbers instead of treating complex-valued neural networks as two real-valued systems. Furthermore, the settling time (ST) has been approximated. Finally, two simulations are shown to confirm the effectiveness of criteria in this paper and the outcomes of practical application in image protection.

Stability Analysis of Fractional Bidirectional Associative Memory Neural Networks With Multiple Proportional Delays and Distributed Delays

This article investigates the finite-time stability of a class of fractional-order bidirectional associative memory neural networks (FOBAMNNs) with multiple proportional and distributed delays. Different from the existing Gronwall integral inequality with single proportional delay ( ), we establish the Gronwall integral inequality with multiple proportional delays for the first time in the case of . Since the existing fractional-order single-constant delay Gronwall inequality with two different orders cannot be directly applied to the stability analysis of the aforementioned system, initially, we skillfully develop a novel one with generalized fractional multiproportional delays' Gronwall inequalities of different orders. Furthermore, combined with the newly constructed generalized inequality, the stability criteria of FOBAMNNs with fractional orders and under weaker conditions, i.e., at most linear growth and linear growth conditions rather than the global Lipschitz condition, are given respectively. Finally, numerical experiments verify the effectiveness of the proposed method.

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0 Collapse

Key Words

• Cellular neural networks
• Complex-valued neural networks
• Fixed-time synchronization
• Fuzzy neural networks
• Non-separation approach

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MESH Headings

• Neural Networks, Computer
• Fuzzy Logic
• Computer Simulation
• Algorithms
• Time Factors

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Grants Collapse

Affiliation(s)

Jingsha Zhang Hebei Provincial Innovation Center for Wireless Sensor Network Data Application Technology, Hebei Provincial Key Laboratory of Information Fusion and Intelligent Control, Hebei Normal University, Shijiazhuang 050024, China.
Jing Yang Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050003, China.
Qintao Gan Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050003, China.
Huaiqin Wu School of Science, Yanshan University, Qinhuangdao 066001, China.
Jinde Cao School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea.

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Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper's method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

Fast synchronization control and application for encryption-decryption of coupled neural networks with intermittent random disturbance

In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied.

Tradeoff analysis between time cost and energy cost for fixed-time synchronization of discontinuous neural networks

This article focuses on the tradeoff analysis between time and energy costs for fixed-time synchronization (FXTS) of discontinuous neural networks (DNNs) with time-varying delays and mismatched parameters. First, a more comprehensive lemma is systematically established to study fixed-time stability, which is less conservative than those in most current results. Besides, theoretical proof has proven that the upper bounds of the settling time (ST) in this article are more accurate compared to existing results. Second, on the grounds of the new fixed-time stability lemma, fixed-time synchronization problem for discontinuous neural networks with time-varying delays and mismatched parameters is explored, and sufficient conditions for fixed-time synchronization are obtained. Further, the upper bounds of energy cost during the synchronization process are estimated. Third, in order to achieve a balance between time cost and energy cost, the genetic algorithm is utilized to find the satisfactory control parameter. Finally, a numerical example is provided to verify the theoretical analysis's correctness and the control mechanism's feasibility.

Fixed-time stabilization of fuzzy neutral-type inertial neural networks with proportional delays

The issue of fixed-time stabilization (FTS) for a class of fuzzy neutral-type inertial neural networks (FNTINNs) with proportional delays (PDs) is discussed in this research. Two feedback controllers were constructed utilizing the fixed-time stability theorem. Two criteria for figuring out the FTS of FNTINNs with PDs were acquired by building suitable Lyapunov functions (LFs). The theoretical conclusions offered could potentially contribute to a more precise calculation of the upper settling-time (ST) when compared to previously conducted research. Two simulation examples are provided to demonstrate the applicability of the stated theoretical conclusions.

Comprehensive analysis of fixed-time stability and energy cost for delay neural networks

This paper focuses on comprehensive analysis of fixed-time stability and energy consumed by controller in nonlinear neural networks with time-varying delays. A sufficient condition is provided to assure fixed-time stability by developing a global composite switched controller and employing inequality techniques. Then the specific expression of the upper of energy required for achieving control is deduced. Moreover, the comprehensive analysis of the energy cost and fixed-time stability is investigated utilizing a dual-objective optimization function. It illustrates that adjusting the control parameters can make the system converge to the equilibrium point under better control state. Finally, one numerical example is presented to verify the effectiveness of the provided control scheme.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

Finite-Time Projective Synchronization and Parameter Identification of Fractional-Order Complex Networks with Unknown External Disturbances

This paper is devoted to exploring the finite-time projective synchronization (FTPS) of fractional-order complex dynamical networks (FOCDNs) with unknown parameters and external disturbances. Based on the stability theory of fractional-order differential systems, synchronization criteria between drive-response networks were obtained and both the uncertain parameters and external disturbances were identified or conquered simultaneously. Moreover, the upper limit of the settling-time function was obtained. Finally, a numerical example was given to verify the effectiveness of the results.