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This article studies the finite-time (FT) convergence of a fast primal-dual gradient dynamics (PDGD), called FT-PDGD, for solving constrained optimization with general constraints and cost functions. Based on the nonsmooth analysis and augmented Lagrangian function, sufficient conditions are established for FT-PDGD to enable the realization of primal-dual optimization in FT. A specific class of nonsmooth sign-preserving functions is defined and analyzed for ensuring FT stability. Particularly, the matrix of linear equations is not required to have a full-row rank and the cost function is not necessary to be strictly convex. By introducing auxiliary variables for general linear inequality constraints, reduced sufficient conditions are further derived for the optimization with linear equality and inequality constraints after transformation. In addition, by the nonsmooth analysis, the switching dynamics evolved in both primal and dual variables are carefully investigated and the upper bound on the convergence time is explicitly provided. Moreover, as applications of FT-PDGD, several FT convergent distributed algorithms are designed to solve distributed optimization with separated and coupled linear equations, respectively. Finally, two case studies are conducted to show the performance of the proposed algorithms.

The usage of social media around the world is ever-increasing. Social media statistics from 2019 show that there are 3.5 billion social media users worldwide. However, the existence of community structure renders the network vulnerable to attacks and large-scale losses. How does one comprehensively consider the multiple information sources and effectively evaluate the vulnerability of the community? To answer this question, we design a gravity-based community vulnerability evaluation (GBCVE) model for multiple information considerations. Specifically, we construct the community network by the Jensen-Shannon divergence and log-sigmoid transition function to show the relationship between communities. The number of edges inside community and outside of each community, as well as the gravity index are the three important factors used in this model for evaluating the community vulnerability. These three factors correspond to the interior information of the community, small-scale interaction relationship, and large-scale interaction relationship, respectively. A fuzzy ranking algorithm is then used to describe the vulnerability relationship between different communities, and the sensitivity of different weighting parameters is then analyzed by Sobol' indices. We validate and demonstrate the applicability of our proposed community vulnerability evaluation method via three real-world complex network test examples. Our proposed model can be applied to find vulnerable components in a network to mitigate the influence of public opinions or natural disasters in real time. The community vulnerability evaluation results from our proposed model are expected to shed light on other properties of communities within social networks and have real-world applications across network science.

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the nx n network structure rather than 2ⁿ x 2ⁿ state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.

This article is concerned with the problem of the $H_{∞}$ output feedback control for a class of event-triggered networked systems subject to multiple cyber attacks. Two dynamic event-triggered generators are equipped at sensor and observer sides, respectively, to lower the frequency of unnecessary data transmission. The sensor-to-observer (STO) channel and observer-to-controller (OTC) channel are subject to deception attacks and Denial-of-Service (DoS) attacks, respectively. The aim of the addressed problem is to design an output feedback controller, with the consideration of the effects of dynamic event-triggered schemes (DETSs) and multiple cyber attacks. Sufficient condition is derived, which can guarantee that the resulted closed-loop system is asymptotically mean-square stable (AMSS) with a prescribed $H_{∞}$ performance. Moreover, we provide the desired output feedback controller design method. Finally, the effectiveness of the proposed method is demonstrated by an example.

This article focuses on the composite ${H}_{∞ }$ synchronization problem for jumping reaction-diffusion neural networks (NNs) with multiple kinds of disturbances. Due to the existence of disturbance effects, the performance of the aforementioned system would be degraded; therefore, improving the control performance of closed-loop NNs is the main goal of this article. Notably, for these disturbances, one of them can be described as a norm-bounded, and the other is generated by an exogenous model. In order to reject the above one kind of disturbance, a disturbance observer is developed. Furthermore, combining the disturbance observer approach and conventional state-feedback control scheme, a composite disturbance rejection controller is specifically designed to compensate for the influences of the disturbances. Then, some criteria are established based on the general Lyapunov stability theory, which can ensure that the synchronization error system is stochastically stable and satisfies a fixed $ {H}_{∞ } $ performance level. A simulation example is finally presented to verify the availability of our developed method.

This article identifies a new upper bound norm for the intervalized interconnection matrices pertaining to delayed dynamical neural networks under the parameter uncertainties. By formulating the appropriate Lyapunov functional and slope-bounded activation functions, the derived new upper bound norms provide new sufficient conditions corresponding to the equilibrium point of the globally asymptotic robust stability with respect to the delayed neural networks. The new upper bound norm also yields the optimized minimum results as compared with some existing methods. Numerical examples are given to demonstrate the effectiveness of the proposed results obtained through the new upper bound norm method.

In this article, we study the finite-time stabilization and the asymptotic stabilization with probability one of Markovian jump Boolean control networks (MJBCNs) by sampled-data state feedback controls (SDSFCs). Based on the semi-tensor product (STP), we introduce an augmented variable multiplied by the vector form of the switching signal and the state of MJBCN. We find that under SDSFC, the sequence of the states of the augmented variable at sampling instants satisfies the Markov property. Based on the convergences of the switching signal and the augmented variable, we obtain the sufficient and necessary criteria for the finite-time stabilization and the asymptotic stabilization of MJBCNs by SDSFCs, respectively. Moreover, for the two kinds of stabilization, the feedback matrices of SDSFCs are constructed, respectively. Finally, the obtained results are applied to an apoptosis network and a model of the lactose operon in the Escherichia Coli.

A large number of experiments have proved that the ring structure is a common phenomenon in neural networks. Nevertheless, a few works have been devoted to studying the neurodynamics of networks with only one ring. Little is known about the dynamics of neural networks with multiple rings. Consequently, the study of neural networks with multiring structure is of more practical significance. In this article, a class of high-dimensional neural networks with three rings and multiple delays is proposed. Such network has an asymmetric structure, which entails that each ring has a different number of neurons. Simultaneously, three rings share a common node. Selecting the time delay as the bifurcation parameter, the stability switches are ascertained and the sufficient condition of Hopf bifurcation is derived. It is further revealed that both the number of neurons in the ring and the total number of neurons have obvious influences on the stability and bifurcation of the neural network. Ultimately, some numerical simulations are given to illustrate our qualitative results and to underpin the discussion.

In nature and human society, successive lag synchronization (SLS) is an important synchronization phenomenon. Compared with other synchronization patterns, the control theory of SLS is very lacking. To this end, we first introduce a complex dynamical network model with distributed delayed couplings, and design both the linear feedback pinning control and adaptive feedback pinning control to push SLS to the desired trajectories. Second, we obtain a series of sufficient conditions to achieve SLS to a desired trajectory with global stability. What is more, the control flow of SLS is given to show how to pick the pinned nodes accurately and set the feedback gains as well. Finally, since time-varying delay is common, we extend the constant time delay in SLS to be time varying. We find that the proposed pinning control schemes are still feasible if the coupling terms are appropriately adjusted. The theoretical results are verified on a neural network and the coupled Chua's circuits.

In this article, a periodic self-triggered impulsive (PSTI) control scheme is proposed to achieve synchronization of neural networks (NNs). Two kinds of impulsive gains with constant and random values are considered, and the corresponding synchronization criteria are obtained based on tools from impulsive control, event-driven control theory, and stability analysis. The designed triggering protocol is simpler, easier to implement, and more flexible compared with some previously reported algorithms as the protocol combines the advantages of the periodic sampling and event-driven control. In addition, the chaotic synchronization of NNs via the presented PSTI sampling is further applied to encrypt images. Several examples are also utilized to illustrate the validity of the presented synchronization algorithm of NNs based on PSTI control and its potential applications in image processing.

This article concentrates on the synchronization of discrete-time persistent dwell-time (PDT) switched bidirectional associative memory inertial neural networks with time-varying delays. Through the use of the switched system theory related to the PDT, the convex optimization technique together with some straightforward decoupling methods, an appropriate mode-dependent controller with nonfragility is developed to acclimatize itself to some practical circumstances. Simultaneously, sufficient conditions of ensuring the performance and exponential stability for the resulting switched synchronization error system are derived. Finally, a numerical example is utilized to show the validity of the model constructed and the influence of the PDT on the performance. In addition, an image encryption example is employed to show the potential application prospect of the investigated system.

In this article, the problem of passivity and dissipativity analysis is investigated for a class of fractional-order quaternion-valued fuzzy memristive neural networks. Based on the famous nonlinear scalarizing function, a nonlinear scalarization method is developed, which can be employed to compare the ``size'' of two different quaternions. In this way, the convex closure proposed by the quaternion-valued connection weights is meaningful. By constructing proper Lyapunov functional, several improved passivity criteria and dissipativity conclusions are established, which can be checked efficiently by utilizing some standard mathematical calculations. Finally, the obtained results are validated by simulation examples.

This study investigates an outlier-resistant state estimation problem for singularly perturbed complex networks (SPCNs) with sojourn probabilities and randomly occurring coupling strengths. Aiming at better describing the dynamic behavior of the network topology for SPCNs, a novel switching law associated with the time-varying sojourn probabilities is developed, and the variation of sojourn probabilities is arranged by a high-level deterministic switching signal. Meanwhile, a sequence of mode-dependent variables is employed to describe the randomly occurring coupling strength. Subsequently, to alleviate the side effects from possible measurement outliers, a dynamic saturation function-based state estimator is designed, whose saturation level is adaptively varying based on previous estimation errors. In virtue of Lyapunov theory and mode-dependent average dwell-time strategy, it can be verified that the resulting dynamics is stochastic H

The distributed stabilization problem is studied in this article for a group of heterogeneous second-order agents in the strong-weak competition network containing three kinds of relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. The entire network satisfies the structural balance condition which can be partitioned into two subnetworks, while the strong and weak competitions are alternate actions on the agents from different subnetworks. To stabilize such heterogeneous networked systems in a distributed way, the switched system approach is developed and utilized in this article, where it is revealed that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. As an extension, a periodical switching law is taken into account to simplify the design process, where the periodical competition function is introduced correspondingly and several effective sufficient conditions are attained. Finally, the derived analytical results are demonstrated by performing numerical simulations.

This article is concerned with the bipartite synchronization problem of coupled switching neural networks with cooperative-competitive interactions and reaction-diffusion terms. Different from the existing literature, the networked systems under investigation possess the relationship of cooperation and competition among nodes. Notably, the switching topology is described by a signed graph subject to the Markov jump process with the coexistence of positive and negative interaction weights. Specifically, a positive weight indicates an alliance relationship between two nodes and a negative one shows an adversary relationship. This article aims to design a bipartite synchronization controller for the aforementioned networks with the switching topology such that a prescribed H

A neural-network model of fractional order with impulsive perturbations, time-varying delays, and reaction-diffusion terms is investigated in this article. The focus is on investigating qualitative properties of the states and developing new almost periodicity and stability criteria. The uncertain case is also considered. Examples are established and the effectiveness of the obtained criteria is demonstrated. © 2013 IEEE.

This paper studies the fixed-time anti-synchronization (FTAS) of discontinuous reaction-diffusion neural networks (DRDNNs) with both time-varying coefficients and time delay. First, differential inclusion theory is used to deal with the influence caused by discontinuous activations. In addition, a new fixed-time convergence theorem is used to handle the time-varying coefficients. Second, a novel state-feedback control algorithm and integral state-feedback control algorithm are proposed to realize FTAS of DRDNNs. During the generalized (adaptive) pinning control strategy, a guideline is proposed to select neurons to pin the designed controller. Furthermore, we present several criteria on FTAS by using the generalized Lyapunov function method. Different from the traditional Lyapunov function with negative definite derivative, the derivative of the Lyapunov function can be positive in this paper. Finally, we give two numerical simulations to substantiate the merits of the obtained results.

This paper focuses on the state estimator design problem for a switched neural network (SNN) with probabilistic quantized outputs, where the switching process is governed by a sojourn probability. It is assumed that both packet dropouts and signal quantization exist in communication channels. Asynchronous estimator and quantification function are described by two different hidden Markov model between the SNNs and its estimator. To deal with the small uncertain of estimators in a random way, a probabilistic nonfragile state estimator is introduced, where uncertain information is described by the interval type of gain variation. A sufficient condition on mean square stable of the estimation error system is obtained and then the desired estimator is designed. Finally, a simulation result is provided to verify the effectiveness of the proposed design method.

The consensus tracking problem means that a group of followers tracks the desired trajectory with local communication. In this article, partial components of cluster consensus have been considered. In this scenario, the p components of the followers in different clusters track the leader at different lag times, while p components of each agent in the same cluster reach a consensus, which is called p components of cluster-lag (PCCL) consensus. By using a seminorm $||x_{i}||_{2,p}$ and a Lyapunov-Krasovskii functional, PCCL consensus for second-order multiagent systems with homogeneous nonlinear systems on cooperative-competitive networks has been considered. For the case that the communication network graph is undirected, a decentralized adaptive controller, which is based on the exchanged neighbors' information from the same cluster, is designed such that all the agents reach PCCL consensus. For the directed graph case, an adaptive protocol based on the intracoupling strength is constructed for each cluster to achieve PCCL consensus. Finally, two simulation examples are illustrated to show the effectiveness of the proposed control protocols.

This article concentrates on the synchronization of discrete-time persistent dwell-time (PDT) switched bidirectional associative memory inertial neural networks with time-varying delays. Through the use of the switched system theory related to the PDT, the convex optimization technique together with some straightforward decoupling methods, an appropriate mode-dependent controller with nonfragility is developed to acclimatize itself to some practical circumstances. Simultaneously, sufficient conditions of ensuring the H

This article focuses on the composite H

This article focuses on a distributed optimization problem subject to partial-impact cost functions that relates to two decision variable vectors. To this end, two algorithms are presented with the aim of solving the considered optimization problem in a structure fashion and in a gradient fashion, respectively. Furthermore, a connection between the equilibrium of the induced algorithm and the involved optimization problem is established, with the aid of the tools from nonsmooth analysis and change of coordinate theorem. Two numerical examples with practical significance are given to demonstrate the efficiency of the designed algorithm.

In this paper, some efficient criteria for finite-time consensus of a class of nonsmooth opinion dynamics over a digraph are established. The lower and upper bounds on the finite settling time are obtained based respectively on the maximal and minimal cut capacity of the digraph. By using tools of the nonsmooth theory and algebraic graph theory, the Carathéodory and Filippov solutions of nonsmooth opinion dynamics are analyzed and compared in detail. In the sense of Filippov solutions, the dynamic consensus is demonstrated without a leader and the finite-time bipartite consensus is also investigated in a signed digraph correspondingly. To achieve a predetermined consensus, a leader agent is introduced to the considered agent networks. As an application, the nonsmooth compartmental dynamics in the presence of a leader is embedded in the proposed continuous-time protocol to solve the distributed optimization problems over an unbalanced digraph. The convergence to the optimal solution by using the proposed distributed algorithm is guaranteed with appropriately selected parameters. To verify the effectiveness of the proposed protocols, three numerical examples are performed.

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

This article studies the constrained optimization problems in the quaternion regime via a distributed fashion. We begin with presenting some differences for the generalized gradient between the real and quaternion domains. Then, an algorithm for the considered optimization problem is given, by which the desired optimization problem is transformed into an unconstrained setup. Using the tools from the Lyapunov-based technique and nonsmooth analysis, the convergence property associated with the devised algorithm is further guaranteed. In addition, the designed algorithm has the potential for solving distributed neurodynamic optimization problems as a recurrent neural network. Finally, a numerical example involving machine learning is given to illustrate the efficiency of the obtained results.

This article is concerned with the global Mittag-Leffler group consensus and group consensus in finite time for fractional multiagent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to the local Holder nonlinear growth in a neighborhood of continuous points. First, a fractional differential inequality on convex functions and a global convergence principle in finite time for absolutely continuous functions are developed, respectively. Second, two new distributed control protocols are designed to realize the consensus between the follower agents in each subgroup and respective leaders. In addition, under the fractional Filippov differential inclusion framework, by applying the Lur'e Postnikov-type convex Lyapunov functional approach and Clarke's nonsmooth analysis technique, some sufficient conditions with respect to the global Mittag-Leffler group consensus and group consensus in finite time are addressed in terms of linear matrix inequalities (LMIs), respectively. Moreover, the settling time for the group consensus in finite time is estimated accurately. Finally, two simulation examples are provided to illustrate the validity of the proposed scheme and theoretical results.

The problem of secure adaptive-event-triggered filter design with input constraint and hybrid cyber attack is investigated in this article. First, a new model of hybrid cyber attack, which considers a deception attack, a replay attack, and a denial-of-service (DoS) attack, is established for filter design. Second, an adaptive event-triggered scheme is applied to the filter design to save the limited communication resource. In addition, a novel adaptive-event-triggered filtering error model is established with the consideration of hybrid cyber attack and input constraint. Moreover, based on the Lyapunov stability theory and linear matrix inequality technique, sufficient conditions are obtained to guarantee the augmented system stability, and the parameters of the designed filter are presented with explicit forms. Finally, the proposed method is validated by simulation examples.

The time-triggered impulsive control of complex homogeneous dynamical networks has received wide attention due to its occasional occupation of the communication channels. This article is devoted to quasisynchronization of heterogeneous dynamical networks via event-triggered impulsive controls with less channel occupation. Two kinds of triggered mechanisms, that is, the centralized event-triggered mechanism in which the control is updated based upon the state information of all nodes, and the distributed event-triggered mechanism where the control is updated according to the state information of each node and its neighboring node, are proposed, respectively, such that the synchronization error between the heterogeneous dynamical networks and a virtual target is not more than a nonzero bound. What is more, the Zeno behavior is shown to be excluded. It is found that the combination method of the event-triggered control and the impulsive control, that is, the distributed event-triggered impulsive control has the advantage of low-energy consumption and takes up many fewer communication channels over the time-triggered impulsive control. Two numerical examples are conducted to illustrate the effectiveness of the proposed event-triggered impulsive controls.

This article concentrates on event-based secure leader-following consensus control for multiagent systems (MASs) with multiple cyber attacks, which contain replay attacks and denial-of-service (DoS) attacks. A new multiple cyber-attacks model is first built by considering replay attacks and DoS attacks simultaneously. Different from the existing researches on MASs with a fixed topological graph, the changes of communication topologies caused by DoS attacks are considered for MASs. Besides, an event-triggered mechanism is adopted for mitigating a load of network bandwidth by scheduling the transmission of sampled data. Then, an event-based consensus control protocol is first developed for MASs subjected to multiple cyber attacks. In view of this, by using the Lyapunov stability theory, sufficient conditions are obtained to ensure the mean-square exponential consensus of MASs. Furthermore, the event-based controller gain is derived by solving a set of linear matrix inequalities. Finally, an example is simulated for confirming the effectiveness of the theoretical results.

This article investigates the reliable output feedback control problem for networked nonlinear semi-Markov jump systems, in which a control strategy with redundant channels is established to reduce the adverse effect caused by packet dropouts. The actuator faults are fully considered in the setup. On the basis of stochastic analysis theory and fuzzy-model-based method, some criteria are established to guarantee the $\sigma $ -error mean-square stability for the considered systems. As a consequence, the reliable output feedback controller design method is proposed, which can be utilized to deal with the actuator failures problem effectively. Finally, two illustrative examples are employed to explain the availability of the presented design approach, where the single-link robot arm system model is contained.

This paper is concerned with the distributed consensus tracking problem of uncertain multiagent systems with directed communication topology and a single high-dimensional leader. Compared with existing related works, the dynamics of each follower in the present framework are subject to unmodeled dynamics and unknown external disturbances, which is more practical in various applications. Furthermore, the dimensions of leader's dynamics may be different with those of the followers' dynamics. Under the mild assumption that each follower can directly or indirectly sense the output information of the leader, a distributed robust adaptive neural network controller together with a local observer are designed to each follower to ensure that the states of each follower ultimately synchronize to the leader's output with bounded residual errors under a fixed topology. By appropriately constructing some multiple Lyapunov functions, the derived results are further extended to consensus tracking with switching directed communication topologies. The effectiveness of the analytical results is demonstrated via numerical simulations.

This paper investigates the leader-following consensus for multiagent systems with general linear dynamics by means of event-triggered scheme (ETS). We propose three types of schemes, namely, distributed ETS (distributed-ETS), centralized ETS (centralized-ETS), and clustered ETS (clustered-ETS) for different network topologies. All these schemes guarantee that all followers can track the leader eventually. It should be emphasized that all event-triggered protocols in this paper depend on local information and their executions are distributed. Moreover, it is shown that such event-triggered mechanism can significantly reduce the frequency of control's update. Further, positive inner-event time intervals are assured for those cases of distributed-ETS, centralized-ETS, and clustered-ETS. In addition, two methods are proposed to avoid continuous communication between agents for event detection. Finally, numerical examples are provided to illustrate the effectiveness of the ETSs.

This article addresses the issue of asynchronous partially mode-dependent filtering for networked Markov switching repeated scalar nonlinear systems (MSRSNSs) subject to quantized measurements (QMs). Especially, a novel partially mode-dependent filter (PMDF) is constructed, where the signal transmission of a filter mode occurred randomly and is modeled by a Bernoulli distributed sequence. The designed PMDF is different from state mode, which is governed by an asynchronous switching rule. By utilizing a diagonally dominant-type Lyapunov functional (DDTLF), sufficient conditions ensure that the existence of the PMDF and the $l_{2}-l_{\infty }$ performance index are derived. Finally, an economic example is adopted to substantiate the applicability of the developed theoretical results.

This paper investigates a distributed static and dynamic self-triggered impulsive control for nonlinear multiagent systems (MASs) where the impulsive gains follow a normal distribution, respectively. By integrating the distributed self-triggered control scheme with the impulsive control approach, a novel distributed impulsive controller is developed. The goal of the consensus of MASs can be realized using the proposed methods and several consensus criteria are obtained. Our schemes have some distinct superiorities, including the impulsive gains obeying a normal distribution, avoiding the continuous communication, and reducing the sampling frequency. Hence, compared with the existing literature, the conservativeness coming from the limitation of impulse gain and the sampling frequency is degraded, and it effectively extends the generality of the method in the practical application. Finally, the effectiveness of the theoretical results is demonstrated by two simulations.

This paper focuses on the exponential $ {\mathcal {H}}_ {\infty }$ filtering issue for a class of continuous-time switched neural networks (NNs). Our aim is to design a mode-dependent filter acquiring the state of the investigated system, and ensuring the global uniform exponential stability of the resulting filtering error system. The persistent dwell-time (PDT) switching strategy is employed to represent the switching among NNs. By utilizing a suitable Lyapunov function and the switched system theory, some criteria for the solvability of the addressed problem are presented under the full consideration of switching frequency. Finally, the filter gains are derived by a straightforward decoupling method, and with the aid of the algorithm of the continuous-time PDT switching regularity, the availability of the filter is expounded through a numerical example.

In this paper, the finite-time coordination behavior of multiple Euler–Lagrange systems in cooperation-competition networks is investigated, where the coupling weights can be either positive or negative. Then, two auxiliary variables about the information exchange among agents are designed, and the finite-time distributed protocol is proposed based on the auxiliary variables and the property of the Euler–Lagrange system. By combining the approach of adding a power integrator with the homogeneous domination method, it is shown that finite-time bipartite consensus can be achieved if the cooperation-competition network is structurally balanced and the parameters of the distributed protocol are chosen appropriately; otherwise, finite-time distributed stabilization can be achieved. Furthermore, from the perspective of network decomposition, the finite-time coordination behavior is further considered, and some sufficient conditions about the cooperation subnetwork and the competition subnetwork are obtained. As an extension, finite-time coordination behavior only with partial state information of the neighbors is discussed, and some similar results are obtained. Finally, four numerical examples are shown for illustration.

This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

This paper investigates the leader-following consensus problem of multiagent systems using a distributed event-triggered impulsive control method. For each agent, the controller is updated only when some state-dependent errors exceed a tolerable bound. The control inputs will be carried out by actor only at event triggering impulsive instants. According to the Lyapunov stability theory and impulsive method, several sufficient criteria for leader-following consensus are derived. Also, it is shown that continuous communication of neighboring agents can be avoided, and Zeno-behavior can be excluded in our schema. The results are illustrated through several numerical simulation examples.

This paper studies the stability and Hopf bifurcation in a class of high-dimension neural network involving the discrete and distributed delays under a new framework. By introducing some virtual neurons to the original system, the impact of distributed delay can be described in a simplified way via an equivalent new model. This paper extends the existing works on neural networks to high-dimension cases, which is much closer to complex and real neural networks. Here, we first analyze the Hopf bifurcation in this special class of high dimensional model with weak delay kernel from two aspects: one is induced by the time delay, the other is induced by a rate parameter, to reveal the roles of discrete and distributed delays on stability and bifurcation. Sufficient conditions for keeping the original system to be stable, and undergoing the Hopf bifurcation are obtained. Besides, this new framework can also apply to deal with the case of the strong delay kernel and corresponding analysis for different dynamical behaviors is provided. Finally, the simulation results are presented to justify the validity of our theoretical analysis.

In this paper, we study a special class of distributed convex optimization problems—distributed parametric consensus optimization problem (DPCOP), for which a two-stage optimization method including primal decomposition and distributed consensus is provided. Different from traditional distributed optimization problems driving all the local states to a common value, DPCOP aims to solve a system-wide problem with partial common parameters shared amongst local agents in a distributed way. To relax the restriction on the topology, a distributed projected subgradient method is applied in distributed consensus stage to achieve the consensus of local estimated parameters, while the subgradients can be obtained by solving a multiparametric problem locally. For a special class of DPCOPs, a discrete-time distributed algorithm with exponential rate of convergence is provided. Furthermore, the proposed two-stage optimization method is applied to a distributed model predictive consensus problem in order to reach an optimal output consensus at equilibrium points for all agents. The stability analysis for the proposed algorithm is further given. Two case studies on a heterogenous multiagent system with high-order integrator dynamics are provided to verify the effectiveness of proposed methods.

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger’s inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

This paper considers the leader-following consensus problem for multiagent systems with inherent nonlinear dynamics. Some M-matrix strategies are developed to address several challenging issues in the pinning control of multiagent systems by using algebraic graph theory and the properties of nonnegative matrices. It is shown that second-order leader-following consensus in a nonlinear multiagent system can be reached if the virtual leader has a directed path to every follower and a derived quantity is greater than a positive threshold. In particular, this paper analytically proves that leader-following consensus may be easier to be achieved by pinning more agents or increasing the pinning feedback gains. A selective pinning scheme is then proposed for nonlinear multiagent systems with directed network topologies. Numerical results are given to verify the theoretical analysis.

This paper is concerned with the finite-time synchronization (FTS) issue of switched coupled neural networks with discontinuous or continuous activations. Based on the framework of nonsmooth analysis, some discontinuous or continuous controllers are designed to force the coupled networks to synchronize to an isolated neural network. Some sufficient conditions are derived to ensure the FTS by utilizing the well-known finite-time stability theorem for nonlinear systems. Compared with the previous literatures, such synchronization objective will be realized when the activations and the controllers are both discontinuous. The obtained results in this paper include and extend the earlier works on the synchronization issue of coupled networks with Lipschitz continuous conditions. Moreover, an upper bound of the settling time for synchronization is estimated. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

In this paper, the distributed exponential consensus of stochastic delayed multi-agent systems with nonlinear dynamics is investigated under asynchronous switching. The asynchronous switching considered here is to account for the time of identifying the active modes of multi-agent systems. After receipt of confirmation of mode’s switching, the matched controller can be applied, which means that the switching time of the matched controller in each node usually lags behind that of system switching. In order to handle the coexistence of switched signals and stochastic disturbances, a comparison principle of stochastic switched delayed systems is first proved. By means of this extended comparison principle, several easy to verified conditions for the existence of an asynchronously switched distributed controller are derived such that stochastic delayed multi-agent systems with asynchronous switching and nonlinear dynamics can achieve global exponential consensus. Two examples are given to illustrate the effectiveness of the proposed method.

This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.