Multi-weighted Complex Structure on Fractional Order Coupled Neural Networks with Linear Coupling Delay: A Robust Synchronization Problem

This sequel is concerned with the analysis of robust synchronization for a multi-weighted complex structure on fractional-order coupled neural networks (MWCFCNNs) with linear coupling delays via state feedback controller. Firstly, by means of fractional order comparison principle, suitable Lyapunov method, Kronecker product technique, some famous inequality techniques about fractional order calculus and the basis of interval parameter method, two improved robust asymptotical synchronization analysis, both algebraic method and LMI method, respectively are established via state feedback controller. Secondly, when the parameter uncertainties are ignored, several synchronization criterion are also given to ensure the global asymptotical synchronization of considered MWCFCNNs. Moreover, two type of special cases for global asymptotical synchronization MWCFCNNs with and without linear coupling delays, respectively are investigated. Ultimately, the accuracy and feasibility of obtained synchronization criteria are supported by the given two numerical computer simulations.

     

The Optimization of Control Parameters: Finite-time and Fixed-time Synchronization of Inertial Memristive Neural Networks with Proportional Delays and Switching Jumps Mismatch

This thesis’s object is inertial memristive neural networks (IMNNs) with proportional delays and switching jumps mismatch. Different from the traditional bounded delay, the proportional delay will be infinite as t → ∞. The finite-time synchronization (FN-TS) and fixed-time synchronization (FX-TS) can be realized with the devised controllers for the drive-response systems (D-RSs). Along with the Lyapunov function and some inequalities, the synchronization criteria of D-RSs are given. This paper presents an optimization model with minimum control energy and dynamic error as objective functions, aiming to obtain more accurate and optimized controller parameters. An intelligent algorithm: particle swarm optimization with stochastic inertia weight (SIWPSO) algorithm is introduced to solve the optimization model. Meanwhile, an integrated algorithm for selecting optimal control parameters is presented as well. In this method, the optimal control parameters and the setting time of synchronization can be obtained directly. At last, some simulations are presented to verify the theorems and the optimization model.

     

Adaptive Synchronization of Stochastic Memristor-Based Neural Networks with Mixed Delays

In this paper, adaptive synchronization of stochastic memristor-based neural networks with mixed delays is investigated. By using the differential inclusions theory, adaptive control technique and stochastic Lyapunov method, two adaptive updated laws are designed and two synchronization criteria are derived for stochastic memristor-based neural networks with mixed delays. The derived criteria complement and improve the previously known results since stochastic perturbations and mixed delays are considered. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical results.     

时延网络化控制系统中智能控制器的设计

网络化控制系统的出现,大大推动了控制系统的发展,正成为新的研究热点。针对网络化控制系统,建立了一种新型的状态变量模型,以此为基础设计了线行二次型最优控制器(LQR)。同时也给出了时钟同步估计网络延迟的方法。在LQR控制器的具体实施中,又给出了一种智能模糊逻辑设计的方法。实验控制结果表明,这种智能控制器能使时变延迟的网络化控制系统稳定。     

Pinning Synchronization for a General Complex Networks with Multiple Time-Varying Coupling Delays

This paper investigates the problem of pinning synchronization for a general complex networks with multiple time-varying coupling delays by using Lyapunov functional method. Firstly, we design a controller to keep the given system synchronized, and provide a simple approximate formula to estimate the detailed pinning synchronization states. Furthermore, by using the same method, an adaptive pinning control scheme is developed to achieve global synchronization, and the adaptive pinning controllers are simpler than some traditional controllers. Moreover, the presented results can also be applied to the system with single time delay, and the coupling-configuration matrices are not necessarily symmetric. Finally, numerical examples are given to show the effectiveness of the proposed methods.     

Synchronization of Switched Neural Networks with Time‐varying Delays via Sampled‐data Control

This paper investigates sampled‐data synchronization control of switched neural networks with time‐varying delays under average dwell time. Based on the delay system method, the sampled‐data synchronization system is proposed with time‐varying delays and input delays in the unified framework for switched neural networks. By constructing a suitable Lyapunov‐Krasovskii functional and free‐weighting matrix, the relationship between the average dwell time and the maximum sampling interval is revealed to form delay‐dependent exponentially synchronization criteria. The desired mode‐dependent controller under the maximum sampling interval and decay rate is designed. Finally, two numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed techniques.     

Synchronization of Instantaneous Coupled Harmonic Oscillators With Communication and Input Delays

This paper investigates the synchronization issue of instantaneous coupled harmonic oscillators with communication and input delays. A distributed synchronization algorithm is proposed for such oscillator systems, and some general algebraic criteria on exponential convergence are established for the algorithm. The main contributions of the present investigations include: (i) the directed network topology is first considered in the case of instantaneous interaction; (ii) both the time‐varying communication and input delays are simultaneously addressed; (iii) the effects of communication and input delays on synchronization performance of coupled harmonic oscillators are discussed. It is shown the communication delays have a more important impact than the input delays on determining synchronization dynamics of coupled harmonic oscillators. Explicitly, in absence of communication delays, coupled harmonic oscillators can achieve synchronization oscillatory motion, whereas, so long as communication delays are nonzero at infinite multiple impulsive times, its synchronization (or consensus) state is zero. Finally, numerical examples demonstrate the obtained theoretical results.     

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

This paper is concerned with the problem of synchronization of complex dynamical networks with state and coupling time‐delays. Therefore, larger class and more complicated complex dynamical networks could be considered for the synchronization problem. Based on the Lyapunov‐Krasovskii functional, some delay‐independent and delay‐dependent criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the synchronization between each node of the complex dynamical network. The effectiveness of the proposed method is illustrated using some numerical simulations.     

Stability Criteria of Linear Neutral Systems With Multiple Delays

In the present note, stability of linear neutral systems with multiple delays is investigated. By principle of the argument, stability criteria are derived which are necessary and sufficient for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function and the argument on the boundary of a certain rectangular region. Several numerical examples are given to illustrate the results     

Finite-time Synchronization of a Class of Coupled Memristor-based Recurrent Neural Networks: Static State Control and Dynamic Control Approach

This paper investigates the problem of the finite-time synchronization of a class of coupled memristor-based recurrent neural networks (MRNNs) with time delays. Based on the drive-response concept and differential inclusions theory, several sufficient assumptions are given to ensure the finite-time synchronization of MRNNs. In order to realize the finite-time synchronization between the drive system and the response system, we design three classes of novel control rules such as static state controller, static output controller, dynamic state controller. Using the theory of differential inclusion, a generalized finite-time convergence theorem and Lyapunov method, the conditions herein are easy to be verified. Moreover, the upper bounds of the settling time of synchronization are estimated and the designed dynamic state controllers have good anti-interference capacity. Finally, two numerical examples are presented to illustrate the effectiveness and the validity of theoretical results.

     

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

In this paper, finite‐time stabilization of coupled systems on networks with time‐varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self‐delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite‐time stabilization of coupled oscillators with time‐varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.     

Exponential Synchronization of Dynamical Network with Distributed Delays Via Intermittent Control

In this paper, the exponential synchronization of dynamical network with distributed time delays is investigated. The intermittent controllers are designed to achieve the exponential synchronization. Based on the Lyapunov function method and the mathematical analysis technique, some synchronization criteria with respect to the system parameters, control gain and control rate are presented. From the criteria, for any given dynamical network, the needed values of control gains and rate can be easily estimated. Finally, two numerical simulations are performed to verify the derived theoretical results.     

Finite-Time Synchronization of Complex-Valued Neural Networks with Multiple Time-Varying Delays and Infinite Distributed Delays

Neural Processing Letters - This paper investigates finite-time synchronization of complexed-valued neural networks with multiple time-varying delays and infinite distributed delays. By separating...     

Differential-Difference Games of Approach with Multiple Delays

Cybernetics and Systems Analysis - Differential-difference games of approach with multiple delays are considered. The schemes of the method of resolving functions and the first direct...     

Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations

This paper concerns the problem of finite-time synchronization for a class of complex-valued neural networks (CVNNs) with both time-varying and infinite-time distributed delays (mixed delays). Both the driving and response CVNNs are disturbed by external uncertain perturbations, which may be nonidentical. A simple state-feedback controller is designed such that the response CVNNs can be synchronized with the driving system in a settling time. By using inequality techniques and constructing some new Lyapunov–Krasovskii functionals, several sufficient conditions are derived to ensure the synchronization. It is discovered that the settling time cannot be estimated when the interested CVNNs exhibit infinite-time distributed delays, while it can be explicitly estimated for the CVNNs with bounded delays. The settling time is dependent on both the delays and the initial value of the error system. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.     

State Feedback Control of Uncertain Networked Control Systems With Random Time Delays

This note investigates the stabilization problem for a class of linear uncertain networked control systems with random communication time delays. Both sensor-to-controller and controller-to-actuator random-network-induced delays are considered. Markov processes are used to model these random-network-induced delays. Based on the Lyapunov-Razumikhin method a mode-dependent state feedback controller is proposed to stabilize this class of systems. The existence of such a controller is given in terms of the solvability of bilinear matrix inequalities, which are to be solved by a newly proposed algorithm. A numerical example is used to illustrate the validity of the design methodology.     

时延复杂网络的自适应周期间歇同步控制

研究同时具有耦合时延和节点时延复杂网络的自适应周期间歇同步控制问题.运用 Lyapunov 稳定性理论,自适应控制、牵制控制和间歇控制方法,给出保证该时延复杂网络全局指数同步、且保守性更小的判定准则,并给出相应的自适应和牵制自适应间歇同步控制器设计,该控制策略对节点间的耦合强度和网络的拓扑结构等具有较强的鲁棒性.最后以时延非线性动力系统为节点对复杂网络进行数值仿真,验证了结论的正确性和有效性.     

不确定多状态滞后系统时滞相关鲁棒稳定与镇定

针对具有范数有界参数不稳定性的多态性滞后系统,本文提出了与系统时滞相关的鲁棒稳定性判据,并给出了一种无记忆的时滞相关的鲁棒稳定控制率的设计方法,本文的结果与系统的时滞大小有关,并采用ＬＭＩ描述。     

变时滞随机忆阻器神经网络的同步控制

在实现实际的复杂人工神经网络模型以及大规模集成电路时,随机噪声是不可避免的.因此,随机忆阻器神经网络具有重要的现实研究意义.针对变时滞随机忆阻器神经网络的同步控制问题,基于非光滑分析以及集值映射、随机微分包含的理论,利用Lyapunov函数和基本不等式的方法,设计了一个线性反馈控制器.通过恰当选择控制器增益,实现了随机忆阻器神经网络驱动系统与相应的响应系统之间的指数同步,所得到的结果保守性更小.最后,给出数值例子验证了理论结果的有效性.     

Synchronization of complex switched networks with two types of delays

In this paper, a general switched model of complex network with two types of delays is presented. The complex switched network (CSN) contains switching behaviors on both its nodes and topology configuration. Different from those CSNs studied in the existing literatures, the two switching signals dominating the nodes and topology are desynchronized. The two types of delays are the time-varying system delay in nodes and the time-varying coupling delay between nodes and they have different values. The inherent synchronization properties of the CSN have been studied not subject to any controllers. By defining a piecewise Lyapunov-Krasovskii function and by using the improved free-weighting matrix method, global exponential synchronizations are obtained. Illustrated example is presented to show the effectiveness of the proposed result.