Lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks with nonidentical characteristics via quantized control: A vector fractional Halanay inequality approach

This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker.     

Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control

This paper addresses the synchronization of stochastic complex networks with time-varying delay via aperiodically intermittent control (AIC). By proposing the concepts of average control ratio and average control frequency for AIC, some new synchronization conditions are obtained, which relax the constraints of the lower bound of control widths and the upper bound of control periods. And the proportion of rest widths can be any value in (0,1). So the constraints on AIC are loosened and thus the conservativeness is reduced compared with the existing related results. Two types of time delay are investigated: (i) the upper bound of time-varying delay should be smaller than the average control width but can be larger than the lower bound of control widths; (ii) the upper bound of time-varying delay has no relationship with control and rest widths. An example of coupled stochastic oscillators systems is presented to show the effectiveness and superiority of our results.     

Fixed-time synchronization of multiplex networks by sliding mode control

Multiplex networks involve different types of synchronization due to their complex spatial structure. How to control multiplex networks to achieve different types of synchronization is an interesting topic. This paper considers the fixed-time synchronization of multiplex networks under sliding mode control (SMC). Firstly, for realizing three types of synchronization of multiplex networks in a fixed time, a unified sliding mode surface (SMS) is established. After that, based on the theory of SMC, a sliding mode controller (SMCr) which is more intelligent and has a simpler form than those in the existing literature is put forward for multiplex networks. It can not only guarantee the emergence of sliding mode motion, but also can realize three different kinds of synchronization by adjusting some parameters or even one parameter of the controller. Based on some theories of fixed-time stability, this paper deduces several sufficient conditions for the trajectories of the system to reach the preset SMS in a fixed time, and derives some sufficient conditions for multiplex networks to realize three different types of fixed-time synchronization. At the same time, the settling time which can reveal what factors determine the fixed-time synchronization in multiplex networks is obtained. Finally, in numerical simulations, different chaotic systems are set for each layer of multiplex networks to represent the nodes of different layers, which can prove that the theoretical results are practical and effective.     

Finite-time synchronization of coupled Cohen–Grossberg neural networks with and without coupling delays

This paper analyzes synchronization in finite time for two types of coupled delayed Cohen–Grossberg neural networks (CDCGNNs). In the first type, linearly coupled Cohen–Grossberg neural networks with and without coupling delays are considered, respectively. In the second type, nonlinearly coupled Cohen–Grossberg neural networks both with and without coupling delays are discussed. By designing suitable controllers and using some inequality techniques, several criteria ensuring finite-time synchronization of the CDCGNNs with linear coupling and nonlinear coupling are derived, respectively. Moreover, the settling times of synchronization in finite time for the considered networks are also predicted. In the end, the availability for the acquired finite-time synchronization conditions is confirmed by two selected numerical examples.     

Fixed-time outer synchronization of hybrid-coupled delayed complex networks via periodically semi-intermittent control

In this paper, the fixed-time synchronization between two delayed complex networks with hybrid couplings is investigated. The internal delay, transmission coupling delay and self-feedback coupling delay are all included in the network model. By introducing and proving a new and important differential equality, and utilizing periodically semi-intermittent control, some fixed-time synchronization criteria are derived in which the settling time function is bounded for any initial values. It is shown that the control rate, network size and node dimension heavily influence the estimating for the upper bound of the convergence time of synchronization state. Finally, numerical simulations are performed to show the feasibility and effectiveness of the control methodology by comparing with the corresponding finite-time synchronization problem.     

Finite/fixed-time synchronization control of coupled memristive neural networks

Finite-time and fixed-time synchronization (FAFS) of coupled memristive neural networks (CMNNs) with discontinuous feedback functions are explored in this paper. Firstly, a more comprehensive stability theory is systematically established. Secondly, by designing adaptive feedback controller and discontinuous feedback controller, both finite-time and fixed-time synchronization can be realized through regulating the main control parameter. Thirdly, 1-norm and quadratic-norm Lyapunov functions are considered simultaneously in this article, while in estimating the settling time, the former one is more accurate than the latter one under the same synchronization criteria. Finally, in numerical simulation, the analysis and comparison of the proposed controllers are given to show the effectiveness of the corresponding results.     

Generalized matrix projective synchronization of general colored networks with different-dimensional node dynamics

This paper investigates the generalized matrix projective synchronization problem of general colored networks with different-dimensional node dynamics. A general colored network consists of colored nodes and edges, where the dimensions of colored node dynamics can be different in addition to the difference of the inner coupling matrices between any pair of nodes. For synchronizing a colored network onto a desired orbit with respect to the given matrices, open-plus-closed-loop controllers are designed. The closed-loop controllers are chosen as adaptive feedback and intermittent controllers, respectively. Based on the Lyapunov stability theory and mathematical induction, corresponding synchronization criteria are derived. Noticeably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulations are provided to verify the theoretical results.     

Fixed-time pinning synchronization for delayed complex networks under completely intermittent control

The present study investigates the fixed-time synchronization issue for delayed complex networks under intermittent pinning control. Different from some existing semi-intermittent controllers for finite/fixed-time synchronization, our pinning controller is designed in a complete intermittent way. In order to address the encountered theoretical analysis difficulties, a new differential inequality lemma is developed, which is suitable for the fixed-time synchronization studies under periodic or aperiodic complete intermittent control. Then, by using Lyapunov theory and pinning control approach, sufficient conditions are proposed which can guarantee the aperiodically completely intermittent-controlled delayed complex networks realizing fixed-time pinning synchronization. Moreover, the settling time is explicitly estimated, which is irrelevant to the initial values of our network systems. Additionally, as a special case, the scenario of periodic complete intermittent control is also discussed. At last, some simulation examples are utilized to confirm our theoretical outcomes.     

Robust quantized consensus of discrete multi-agent systems under input saturation

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from input saturation. As agents transmit state information through communication networks with limited bandwidth, the states of agents have to be quantized into a finite number of bits before transmission. To handle this quantized consensus problem, we introduce an internal time-varying saturation function into the controllers of all agents and ensure that the range of the state of each agent can be known in advance by its neighboring agents. Based on such shared state range information, we construct a quantized consensus protocol which implements a finite-bit quantization strategy to all states of agents and can guarantee the achievement of the asymptotic consensus under any given input saturation threshold. Such desired consensus can be guaranteed at as low bit rate as 1 bit per time step for each agent. Moreover, we can place an upper bound on the convergence rate of the consensus error of agents. We further improve that quantized consensus protocol to a robust version whose parameters are determined with only an upper bound on the number of agents and does not require any more global information of the inter-agent network. Simulations are done to confirm the effectiveness of our quantized consensus protocols.     

Fixed-time consensus for stochastic multi-agent systems with discontinuous dynamics via quantized control

In this study, the fixed-time consensus (FDTC) for stochastic multi-agent systems (MASs) with discontinuous inherent dynamics is investigated via quantized control. Firstly, an improved lemma for fixed-time (FDT) stability is derived and several more precise estimations for settling time (SLT) are gained by using certain special functions. Secondly, a more general MAS containing discontinuous inherent dynamics and stochastic perturbations is considered, which is closer to practical life. Thirdly, to overcome the limitation of communication, two kinds of quantized control protocols are designed. Besides, in the light of the graph theory, non-smooth analysis, fixed-time (FDT) stability and stochastic analysis theory, some sufficient conditions are put forward to achieve FDTC of MASs. Finally, the validity of the derived theoretical results is testified by two numerical examples.     

时滞动态网络自适应同步的研究

研究了节点带有时滞且节点之间的通信也带有时滞的复杂动态网络的自适应同步问题。基于稳定性理论,设计了复杂网络同步的自适应控制器。该控制器结构简单,易于应用。最后,以环状耦合的时滞Lorenz系统为例进行数值仿真,检验了结果的正确性和设计方法的有效性。     

Fixed-time synchronization of memristor-based fuzzy cellular neural network with time-varying delay

This paper mainly investigates the fixed-time synchronization of memristor-based fuzzy cellular neural network (MFCNN) with time-varying delay. By utilizing differential inclusion, set-valued map theory, the definitions of finite-time and fixed-time stability, we convert the fixed-time synchronization control of the drive-response MFCNN into the equivalent fixed-time stability problem of the error system between the drive-response systems. Some novel sufficient conditions are derived to guarantee the fixed-time synchronization of the drive-response MFCNN based on a simple Lyapunov function and a nonlinear feedback controller. Meanwhile, the settling time can be estimated by simple calculations. Furthermore, these fixed-time synchronization criteria here are easy to validate and extend to the MFCNN without time-varying delay and general memristor-based neural networks. Finally, three numerical examples are given to illustrate the correctness of the main results.     

Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching

This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.     

Cluster synchronization in community networks with nonidentical nodes via edge-based adaptive pinning control

This paper investigates cluster synchronization in community networks with nonidentical nodes. Several effective strategies to enhance the coupling weights are designed. For the first time, adaptive enhancing factor method combined with edge-based pinning control is adopted to achieve synchronization. Furthermore, distributed adaptive pinning control scheme is adopted based on the local information of node dynamics. Noticeably, only the coupling weights of spanning trees in each community are tuned, which are low-cost and more practicable. Based on Lyapunov stability theory, some sufficient conditions for cluster synchronization are derived. Numerical simulations are provided to verify the effectiveness of the theoretical results.     

Bounded controls for discrete-time linear systems subject to input time delay

This paper investigates the global stabilization of discrete-time linear systems with input time delay by bounded controls. Based on some special canonical forms containing time delays both in its input and state, two special discrete-time linear systems---multiple integrators and oscillators are first considered. The global stabilizing controllers are respectively established, and moreover, explicit conditions are established to guarantee the stability of the closed-loop systems. Subsequently, a concise design method is proposed for globally stabilizing general discrete-time linear system by combining the design methods for multiple integrators and oscillators. The designed controller is in the explicit form with explicit stability conditions being given, and thus is easier to use than the existing results. Finally, numerical simulations illustrate the effectiveness of the proposed approaches.     

Projective synchronization in fixed time for complex dynamical networks with nonidentical nodes via second-order sliding mode control strategy

This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.     

Graph theory-based finite-time synchronization of fractional-order complex dynamical networks

This paper considers the finite-time synchronization problem for a class of fractional-order complex dynamical networks (FOCDNs). By utilizing the properties of fractional calculus and fractional-order comparison principle, we propose a new lemma. Base on the new lemma, some analysis techniques and algebraic graph theory method, some novel criteria are given to ensure finite-time synchronization of FOCDNs, and the upper bound of the setting time for synchronization is estimated. At last, numerical simulations are given to verify the effectiveness of the obtained results.     

On the existence of constant-ratio trajectories in nominally time- optimal control systems subject to parameter variation

In a previous paper it was found that certain control systems with nominally time-optimal feedback controllers are highly sensitive to changes of plant parameter. When the plant consists of several pure integrators, changes of plant parameter can cause what are termed constant-ratio trajectories. Such trajectories yield slow settling, or even instability. The previous paper used, in part, computational methods to show the existence of constant-ratio trajectories. In the present paper some simple conditions are shown to be sufficient for existence of the constant-ratio trajectories.     

On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays

This paper investigates the problem of designing decentralized impulsive controllers for synchronization of a class of complex dynamical networks (CDNs) about some prescribed goal function. The CDNs are allowed to possess nonidentical nodes and coupling delays. Two cases of time-varying coupling delays are considered: the case where the coupling delays are uniformly bounded, and the case where the derivatives of the coupling delays are not greater than 1. The synchronization analysis for the first case is performed by applying a time-varying Lyapunov function based method combined with Razumikhin-type technique, while the synchronization analysis for the second case is conducted based on a time-varying Lyapunov functional based method. For each case, by utilizing a convex combination technique, the resulting synchronization criterion is formulated as the feasibility problem of a set of linear matrix inequalities (LMIs). Then, sufficient conditions on the existence of a decentralized impulsive controller are presented by employing these newly obtained synchronization criteria. The local impulse gain matrices can be designed by solving a set of LMIs. Finally, two representative examples are given to illustrate the correctness of the theoretical results.