Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control

In this paper, we concern the finite-time synchronization problem for delayed dynamical networks via aperiodically intermittent control. Compared with some correspondingly previous results, the intermittent control can be aperiodic which is more general. Moreover, by establishing a new differential inequality and constructing Lyapunov function, several useful criteria are derived analytically to realize finite-time synchronization for delay complex networks. Additionally, as a special case, some sufficient conditions ensuring the finite-time synchronization for a class of coupled neural network are obtained. It is worth noting that the convergence time is carefully discussed and does not depend on control widths or rest widths for the proposed aperiodically intermittent control. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.     

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.     

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.     

Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design

This paper is concerned with the finite-time and fixed-time synchronization of complex networks with discontinuous nodes dynamics. Firstly, under the framework of Filippov solution, a new theorem of finite-time and fixed-time stability is established for nonlinear systems with discontinuous right-hand sides by using mainly reduction to absurdity. Furthermore, for a class of discontinuous complex networks, a general control law is firstly designed. Under the unified control framework and the same conditions, the considered networks are ensured to achieve finite-time or fixed-time synchronization by only adjusting the value of a key control parameter. Based on the similar discussion, a unified control strategy is also provided to realize respectively asymptotical, exponential and finite-time synchronization of the addressed networks. Finally, the derived theoretical results are supported by an example with numerical simulations.     

Exponential synchronization for coupled complex networks with time-varying delays and stochastic perturbations via impulsive control

This paper is concerned with the problem of exponential synchronization of coupled complex networks with time-varying delays and stochastic perturbations (CCNTDSP). Different from previous works, both the internal time-varying delay and the coupling time-varying delay are taken into account in the network model. Meanwhile, an impulsive controller is designed to realize exponential synchronization in mean square of CCNTDSP. Combining the Lyapunov method with Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are obtained to guarantee exponential synchronization in mean square of CCNTDSP. Furthermore, we apply the theoretical results to study exponential synchronization of stochastic coupled oscillators with the internal time-varying delay and the coupling time-varying delay. And a synchronization criterion is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of our theoretical results and the superiority of impulsive control.     

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.     

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.     

Exponential synchronization of coupled neutral-type neural networks with mixed delays via quantized output control

In this paper, new control scheme is considered for exponential synchronization of coupled neutral-type neural networks (NTNNs) with both bounded discrete-time delay and unbounded distributed delay (mixed delays). It is assumed that only the measured output can be utilized to design the controller. Quantized output controllers (QOCs) are considered to save the bits rate of communication channels and the bandwidth. The main difficulty in solving this problem is to cope with the neutral terms, the delays, and the uncertainties induced by the quantization simultaneously. By designing new Lyapunov–Krasovskii functionals and proposing novel analytical techniques, sufficient conditions are derived to ensure the exponential synchronization of the interested NTNNs. The control gains are given by solving a set of linear matrix inequalities (LMIs), which are not necessarily to be negative-definite matrices. Numerical examples are provided to verify the effectiveness and merits of the proposed approach.     

A survey on global pinning synchronization of complex networks

In practice, it is almost impossible to directly add a controller on each node in a complex dynamical network due to the high control cost and the difficulty of practical implementation, especially for large-scale networks. In order to address this issue, a pinning control strategy is introduced as a feasible alternative. The objective of this paper is first to recall some recent advancements in global pinning synchronization of complex networks with general communication topologies. A systematic review is presented thoroughly from the following aspects, including modeling, network topologies, control methodologies, theoretical analysis methods, and pinned node selection and localization schemes (pinning strategies). Fully distributed adaptive laws are proposed subsequently for the coupling strength as well as pinning control gains, and sufficient conditions are obtained to synchronize and pin a general complex network to a preassigned trajectory. Moreover, some open problems and future works in the field are also discussed.     

A class of fast fixed-time synchronization control for the delayed neural network

This paper deals with the synchronization control of a class of delayed neural networks using a fast fixed-time control theory. By employing Lyapunov stability theory, a novel sufficient criterion is derived such that two neural networks can be synchronized within a fixed-time. Compared with some existing results, the proposed controller can render two neural networks faster synchronized. A numerical example is given to demonstrate the effectiveness of the criterion.     

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.     

Synchronization of switched logical control networks via event-triggered control

This paper investigates the event-triggered control design for state/output synchronization of switched k-valued logical control networks (SKVLCNs). Firstly, based on the algebraic form of SKVLCNs, some necessary and sufficient conditions are presented for the event-triggered state/output synchronization of SKVLCNs. Secondly, using the partitioning technique of matrix, a constructive procedure is proposed to design state feedback event-triggered controllers for the synchronization of SKVLCNs. Finally, an illustrative example is worked out to show the effectiveness of the obtained new results.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Finite-time robust control of a class of nonlinear time-delay systems via Lyapunov functional method

This paper investigates the finite-time robust control problem of a class of nonlinear time-delay systems with general form, and proposes some new delay-independent and delay-dependent conditions on the issue. First, by developing an equivalent form, the paper studies finite-time stabilization problem, and presents some delay-dependent stabilization results by constructing suitable Lyapunov functionals. Then, based on the stabilization results, we study the finite-time robust control problem for the systems, and give a robust control design procedure. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the finite-time stabilization and robust stabilization for the systems. It is shown that, by using the method in the paper, the obtained results do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden. Moreover, different from existing finite-time results, the paper also presents delay-dependent sufficient conditions on the finite-time control problem for the systems.     

Stabilization of dynamic-algebraic Boolean control networks via state feedback control

In this paper, we study the state feedback stabilization of dynamic-algebraic Boolean control networks (DABCNs). Using a novel normalization approach, we present necessary and sufficient conditions for the feedback stabilization of DABCNs, and a construction method for the corresponding feedback controllers is proposed. Reduced order feedback stabilization is also studied in this paper. Two examples are given to illustrate the obtained results.     

Synchronization of IT2 stochastic fuzzy complex dynamical networks with time-varying delay via fuzzy pinning control

In this paper, the problem of synchronization on interval type-2 (IT2) stochastic fuzzy complex dynamical networks (CDNs) with time-varying delay via fuzzy pinning control is fully studied. Firstly, a more general complex network model is considered, which involves the time-varying delay, IT2 fuzzy and stochastic effects. More specifically, IT2 fuzzy model, as a meaningful fuzzy scheme, is investigated for the first time in CDNs. Then, with the aid of Lyapunov stability theory and stochastic analysis technique, some new sufficient criteria are established to ensure synchronization of the addressed systems. Moreover, on basis of the parallel-distributed compensation (PDC) scheme, two effective fuzzy pinning control protocols are proposed to achieve the synchronization. Finally, a numerical example is performed to illustrate the effectiveness and superiority of the derived theoretical results.     

Stop and Go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights

Although the drive-response synchronization problem of memristive recurrent neural networks (MRNNs) has been widely investigated, all the existing results are based on the assumption that the parameters of the drive system are known in prior, which are difficult to implement in real-life applications. In the present paper, a Stop and Go adaptive strategy is proposed to investigate the synchronization control of chaotic delayed MRNNs with unknown memristive synaptic weights. Firstly, by defining a series of measurable logical switching signals, a switched response system is constructed. Subsequently, by utilizing the logical switching signals, several suitable parameter update laws are proposed, then some different adaptive controllers are devised to guarantee the synchronization of unknown MRNNs. Since the parameter update laws are weighted by the logical switching signals, they will work or stop automatically with the switch of the unknown weights of drive system. Finally, two numerical examples with their computer simulations are provided to illustrate the effectiveness of the proposed adaptive synchronization schemes.     

Lag projective synchronization of fractional-order delayed chaotic systems

This paper considers the lag projective synchronization of fractional-order delayed chaotic systems. The lag projective synchronization is achieved through the use of comparison principle of linear fractional equation at the presence of time delay. Some sufficient conditions are obtained via a suitable controller. The results show that the slave system can synchronize the past state of the driver up to a scaling factor. Finally, two different structural fractional order delayed chaotic systems are considered in order to examine the effectiveness of the lag projective synchronization. Feasibility of the proposed method is validated through numerical simulations.     

Lag synchronization for fractional-order memristive neural networks with time delay via switching jumps mismatch

This paper studies drive-response synchronization in fractional-order memristive neural networks (FMNNs) with switching jumps mismatch. A comparison theorem for fractional-order systems with variable order is provided first. Theories of fractional order Filippov differential inclusions are used to treat FMNNs because the parameters of FMNNs are state dependent and the FMNNs has discontinuous right hand sides. Based on Laplace transform and linear feedback control, some lag quasi-synchronization conditions are obtained with variable order α: 0?<?α?<?1 and 1?<?α?<?2. The error level is estimated and the larger synchronization regain is discussed. Finally, two numerical examples are presented to illustrate the effectiveness of our proposed theorems.