Fixed-time synchronization criteria for complex networks via quantized pinning control

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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Sampled-Data Exponential Synchronization of Complex Dynamical Networks with Saturating Actuators

This paper investigates the problem of exponential synchronization control for complex dynamical systems (CDNs) with input saturation. Considering the effects of transmission delay, a memory sampled-data controller is designed. A modified two-sided looped functional is constructed that takes into account the entire sampling period, which includes both current state information and delayed state information. This functional only needs to be positive definite at the sampling instants. Sufficient criteria and the controller design method are provided to ensure the exponential synchronization of CDNs with input saturation under the influence of transmission delay, as well as the estimation of the basin of attraction. Additionally, an optimization algorithm for enlarging the region of attraction is proposed. Finally, a numerical example is presented to verify the effectiveness of the conclusion.

Design of a Robust Synchronization-Based Topology Observer for Complex Delayed Networks with Fixed and Adaptive Coupling Strength

Network topology plays a key role in determining the characteristics and dynamical behaviors of a network. But in practice, network topology is sometimes hidden or uncertain ahead of time because of network complexity. In this paper, a robust-synchronization-based topology observer (STO) is proposed and applied to solve the problem of identifying the topology of complex delayed networks (TICDNs). In comparison to the existing literature, the proposed STO does not require any prior knowledge about the range of topological parameters and does not have strict limits on topology type. Furthermore, the proposed STO is suitable not only for networks with fixed coupling strength, but also for networks with adaptive coupling strength. Finally, a few comparison examples for TICDNs are used to verify the feasibility and efficiency of the proposed STO, and the results show that the proposed STO outperforms the other methods.

Optimal preview pinning control of Boolean networks

This paper investigates the problem of optimal preview pinning control for Boolean networks. The primary objective is to design efficient control strategies that leverage future reference information for improved control performance. We propose a policy iteration algorithm specifically for Boolean networks based on an augmented error system, constructed using the state augmentation technique in combination with the Exclusive-Or operator approach. The algorithm effectively optimizes control policies using future information. Finally, an example is presented to illustrate the effectiveness of the proposed algorithm.

Synchronization of discrete-time fractional fuzzy neural networks with delays via quantized control

In this paper, synchronization issue of discrete-time fractional fuzzy neural networks (DFFNNs) with delays is solved via quantized control, and is applied in image encryption. Firstly, a novel fractional-order h-difference inequality which makes Lyapunov method more flexible and practical is strictly proved based on the properties of convex functions and theory of discrete fractional calculus. Secondly, by using compression mapping theorem and mathematical induction, we obtain two sufficient conditions to ensure the existence and uniqueness of solutions for DFFNNs. Whereafter, we design a suitable quantized controller, which not only saves channel resources but also reduces control costs. By utilizing our inequality and some analytical techniques, several conservative synchronization criteria for DFFNNs are acquired. Finally, two examples are arranged to illustrate the validity and practicability of our results.

Aperiodically intermittent event-triggered pinning control on cluster synchronization of directed complex networks

This paper is dedicated to investigating the exponential cluster synchronization in a class of nonlinearly coupled complex networks with non-identical nodes and an asymmetrical coupling matrix. A novel aperiodically intermittent pinning control (APIPC) protocol is presented, which takes full account of the cluster-tree topology structure of the networks and pins only the nodes in the current cluster that have directional links to neighboring clusters. Since it is difficult to precisely determine the intermittent control instants and rest instants of APIPC in advance, the event-triggered mechanism (ETM) is thus proposed. Based on the concept of the minimal control ratio and the segmentation analysis method, sufficient requirements for realizing the exponential cluster synchronization are derived. Moreover, the Zeno behavior of ETM is excluded by rigorous analysis. Eventually, the effectiveness and advantages of the established theorems and control strategies are demonstrated by two numerical simulations.

Fixed/Preassigned-time stochastic synchronization of T-S fuzzy complex networks with partial or complete information communication

This paper is devoted to analyzing Fixed/Preassigned-time synchronization of T-S fuzzy complex networks (TSFCNs) with stochastic effects. Unlike the existing results, partial information communication and complete information communication are all considered according to a Bernoulli distribution. Furthermore, different controllers with quantization are structured to realize our synchronization goal, and one of control parameters can switch based on the error information. Besides, we derive sufficient conditions to guarantee Fixed-time(FDT) and Preassigned-time(PAT) synchronization of TSFCNs, and analyze the difference of FDT and PAT synchronization. Finally, numerical examples and comparisons show that our results are valid.

Fixed-Time Synchronization of Coupled Oscillator Networks with a Pacemaker

This paper investigates the fixed-time synchronization problem of a Kuramoto-oscillator network in the presence of a pacemaker. Based on the framework of the cyber-physical system (CPS), fixed-time synchronization criteria of such network are presented respectively for identical and non-identical oscillators. In virtue of Lyapunov stability analyses, sufficient conditions are deduced for achieving phase agreement and frequency synchronization for arbitrary initial phases and/or frequencies under distributed control strategies. Theoretical analysis shows that synchronization can be achieved in a fixed time, which is unrelated to initial phases/frequencies. Furthermore, the upper bounds of synchronization time are also obtained. Finally, the numerical simulations also verify the effectiveness of the derived results.

H∞ filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H_∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system's matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H_∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H_∞ filtering approach are demonstrated via a practical example.

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability

This article is concerned with the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks by improving FXT stability and developing simple control schemes. First, some more relaxed conditions for FXT stability are established and several more accurate estimates for the settling time (ST) are obtained by means of some special functions. Based on the improved FXT stability, FXT synchronization for discontinuous networks is discussed by designing a simple controller without a linear feedback term. Besides, the PAT synchronization is also explored by developing several nontrivial control protocols with finite control gains, where the synchronized time can be prespecified according to actual needs and is irrelevant with any initial value and any parameter. Finally, the improved FXT stability and the synchronization for complex networks are confirmed by two numerical examples.