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The distributed online convex optimization problem with time-varying constraints for multi-agent networks is addressed in this article. The purpose is to optimize a sequence of time-varying global cost functions defined as the accumulated values of local cost functions, also attempt to meet the requirement of a sequence of time-varying coupled constraint functions which denote the sum of local constraint functions. Cost functions and constraint functions are unknown to agents beforehand. It is supposed that each agent in the network communicates with its neighbours through a uniformly strongly connected sequence of time-varying directed communication topologies. This paper proposes the bandit distributed primal-dual mirror descent push-sum (BDPDMDPS) algorithm constructed by bandit primal-dual, mirror descent and push-sum methods. Operational performance of the presented algorithm is measured by expected regret and expected constraint violation, both of which are proved to be sublinear with respect to the total iteration span T in this paper. Finally, a numerical simulation example is shown, which confirms the results for expected regret and expected constraint violation of BDPDMDPS algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of stochastic mixed impulsive control and stability for stochastic functional differential systems with semi-Markov jump. A new definition of average stochastic impulsive gain is formulated to estimate the stochastic mixed impulsive intensity. Functional systems states are referred to the historical system states in the past time interval rather than in the past time instant of the current time instant. The stability analysis is carried out based on the constructed appropriate Lyapunov functional, Dupire functional Itô's formula, stochastic analysis theory and graph theory techniques. Moreover, we provide some exponential stability criteria for the investigated systems, which have close relation to not only the topological structures and semi-Markov jump of the functional systems but also average stochastic impulsive gain and stochastic disturbance intensity. Further we put it into practice of a new class of stochastic oscillators systems with semi-Markov jump and the corresponding numerical simulations results are on show to demonstrate the validity of the derived theoretical results. [ABSTRACT FROM AUTHOR]

• Heterogeneous networks with both heterogeneous coefficients and heterogeneous nonlinear functions are investigated. • A generalized impulsive controller is designed. • Parameter uncertainties of both linear and nonlinear dynamics are considered. • The sufficient criteria of quasi-synchronization are derived for the heterogeneous networks. The target of this paper is studying the problem of quasi-synchronization of heterogeneous Lur'e networks with uncertain parameters and impulsive effect. Considering the heterogeneity of Lur'e networks, quasi-synchronization instead of synchronization is discussed. Noting that the uncertain factors exist extensively in reality, uncertain parameters are introduced to the system in this paper. By using the Schur complement lemma, stability theory and the principle of comparison, the sufficient criteria for the heterogeneous networks to achieve quasi-synchronization are derived, and the upper bound of exponential quasi-synchronization errors is calculated. In addition, two corollaries are presented in consideration of homogeneous systems and weighted undirected graphs. Finally, three numerical simulations are given to illustrate the effectiveness of the control protocol and theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the global stability of delayed genetic regulatory networks (DGRNs) with Hill-type activation (or inhibition) functions based on the mixing monotone semiflows approach, where Hill coefficients can be arbitrary positive real number. A new result on the global stability of DGRN is given in the case that all Hill coefficients are less than or equal to 1. In addition, for all Hill coefficients greater than 1, a new sufficient condition for global convergence of DGRN is given, which is less conservative than the condition of the existing correlation results. Finally, two numerical examples and simulations are given to explain the effect of obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study a projective multi-synchronization problem for fractional-order complex-valued coupled multi-stable neural networks (FCVCMNNs) with time-delays. Using a complex decomposition approach, FCVCMNNs are divided into their real and imaginary components. Our method uses certain conditions for each subnetwork to achieve the multiple local equilibrium points or stable periodic orbits that are exponentially stable, which, when combined with the Lyapunov functions method, result in FCVCMNNs that are projectively multi-synchronized. The FCVCMNNs, on the other hand, are examined directly through the use of the Lyapunov functional method and linear matrix inequality (LMI). Various new sufficient conditions in the form of complex-valued LMIs are presented for the projective multi-synchronization of the considered FCVCMNNs. As a final step, we provide two numerical simulations to verify the effectiveness of the main results derived in this paper. [ABSTRACT FROM AUTHOR]

A growing interest in applying Natural Language Processing (NLP) models to computer vision problems has recently emerged. This interest is motivated by the success of NLP models in tasks such as translation and text summarization. In this paper, we propose a new method for applying NLP to image classification problems. We aim to represent the visual patterns of objects by using a sequence of alphabet symbols and then train a Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), or Transformer using these sequences to classify objects. An extensive experimental evaluation using a limited number of images for training has been conducted to compare our method with the ResNet-50 deep learning architecture. The results obtained by the proposed method outperform ResNet-50 in all test scenarios. In one test, the method achieved an average accuracy of 95.3% compared to 89.9% of ResNet-50. The source code (http://git.inovisao.ucdb.br/inovisao/applying-npl-to-image-classification) and dataset (https://doi.org/10.6084/m9.figshare.20055602.v1) are publicly available. [ABSTRACT FROM AUTHOR]

As a special type of neurodynamic methodology dedicated to finding zeros of equations, zeroing neurodynamics has shown a powerful ability in solving challenging online time-varying problems. Multi-linear systems, on the other hand, are a type of tensor equations with a wide range of applications. In this paper, a zeroing neurodynamics approach for solving multi-linear systems with M -tensors is proposed along with three specific accelerated finite-time convergent zeroing neurodynamics models, which breaks the limitations of a recently presented neural network approach termed continuous time neural network. Activation functions available in constructing zeroing neurodynamics models for solving multi-linear systems with M -tensors are also investigated in the rest of the paper. Theoretical analyses prove that the proposed zeroing neurodynamics approach is stable in the sense of Lyapunov stability theory and the proposed models converge to the theoretical solution in finite time. Finally, computer simulations are provided to substantiate the efficacy and superiority of the proposed zeroing neurodynamics models for solving multi-linear systems with M -tensors. [ABSTRACT FROM AUTHOR]

From the perspective of large-scale system, a directed complex dynamic network (DCDN) may be considered as a coupling system of the node subsystem (NS) and the link subsystem (LS). In this paper, by using the outgoing link vector and incoming link vector for DCDN, the dynamics of LS is described by employing the vector differential equation instead of the matrix differential equation. Since the outgoing and incoming link vectors have the stronger geometric intuition, the results in this paper show that this kind model of links can not only reflect the direction of links but also find the dynamic tracking goal of links more easily when the state synchronization of NS emerges. Furthermore, by employing the simple mathematical conditions, the nonlinear controller of NS and the coupling term of LS are proposed to ensure achieving the asymptotical state synchronization for DCDN. Finally, the numerical simulations are given to demonstrate the validity of the results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the multiple asymptotic stability is investigated for fractional-order quaternion-valued neural networks (FQVNNs) with time-varying delays. The activation function is a nonmonotonic piecewise nonlinear activation function. By applying the Hamilton rules, the FQVNNs are transformed into real-valued systems. Then, according to the Brouwer's fixed point theorem, three new conditions are proposed to ensure that there exist 3 4 n equilibrium points. Moreover, by virtue of fractional-order Razumikhin theorem and Lyapunov function, a new condition is derived to guarantee the FQVNNs have 2 4 n locally asymptotic stable equilibrium points. For the first time, the multiple asymptotic stability of delayed FQVNNs is investigated. Contrast to multistability analysis of integer-order quaternion-valued neural networks, this paper present different conclusions. Finally, two numerical simulations demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

Time-varying linear complementarity problem (TLCP) has received a great deal of attention due to its broad variety of scientific and engineering applications. Several efficient Zhang neural networks are introduced for solving TLCP in this paper. Theoretical analysis shows that the related error function of the model proposed in this paper eventually tends to zero. The state convergence time periods of those Zhang neural networks with three types of activation functions are proved to be finite and can be quantitatively estimated by using some given parameters. Further, it is shown that the proposed neural network is of noise-tolerance, which means the neural network is more appropriate for a wider application. Moreover, in order to implement neural network numerically, a related discrete-time version is also studied. Finally, numerical simulations confirm the analysis of the proposed models concretely. [ABSTRACT FROM AUTHOR]

This paper is concerned with the issue of fixed-time (FT) and preassigned-time (PT) synchronization of impulsive complex networks (ICNs) with mismatched parameters. Firstly, several more succinct conditions are established to achieve FT stability of impulsive systems and an improved estimation for the stable time is given. Subsequently, based on the improved FT stability results, the FT synchronization criteria for ICNs with mismatched parameters are proposed by designing fixed-time controllers without the linear part. Correspondingly, the PT synchronization problem is also considered by developing several innovative control protocols, where the synchronized time can be arbitrary predefined according to task demands and the control gains are bounded. Ultimately, the presented synchronization criteria are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper deals with the state estimate problem for a class of discrete-time complex networks. The target plant involves Markovian jumping parameters and mode-dependent distributed time-delays. It is assumed that the measurements for the estimate purpose are just from a portion of network nodes, and corrupted by a certain stochastic noise. A unified framework is developed to cope with the state estimation issue based on the outputs from the fraction of nodes for the discrete-time complex networks with distributed time delay and measurement noise. By employing the Lyapunov stability theory and some new techniques, the sufficient conditions are established to ensure the state estimation error is exponentially ultimately mean-square bounded. As the special case when the measurement is noise-free, the resulting criteria are to guarantee that the dynamics of state estimation error is exponentially stable. In addition, the estimator gain matrices are given in the explicit formula. Finally, numerical simulations are presented to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with global exponential stabilization (GES) and exponential lag synchronization (ELS) for impulsive complex-valued inertial neural networks (ICVINNs) with proportional delays, without employing the standard order-reduction transformation and the general separation approach of the real and imaginary part of the ICVINNs. Several algebraic criteria involving multi-parameters for examining the GES and ELS of the ICVINNs are built, via establishing an appropriate Lyapunov functional, and utilizing inequality techniques, which can be achieved by the novel design of the adaptive controller. Numerical simulations are shown to sustain the availability and efficiency of the proposed criteria. [ABSTRACT FROM AUTHOR]

Different from the conventional calculation method, the discrete-time noise-suppression zeroing neural dynamic (DTNSZND) model is developed and investigated for online solving the time-varying/time-invariant scalar cube root problem with different disturbances (bounded/unbounded disturbances) from a control perspective in this paper. The solving precision and robustness of different DTNSZND models are generated via various difference rules are discussed and analyzed, and numerical simulations verify that the convergence property of the developed models are closely related to the accuracy of difference rules. The zero-stable, consistent and convergent of different DTNSZND models are demonstrated via theoretical analyses. Furthermore, numerical simulation and comparative results prove that the convergence, robustness and superiority of the presented different DTNSZND models for online solving time-varying/time-invariant cube root problems with different interferences in real domain or complex domain. Finally, different fractals are generated by utilizing the developed DTNSZND model to solve the cube root problem with different noises in complex domain, which are quite different from Newton fractals produced by Newton–Raphson iteration. Therefore, the proposed different DTNSZND models can be considered as a novel iterative algorithm to generate new fractal. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization analysis problem of a class of incommensurate fractional-order memristor-based neural networks with multiple time-varying delays (IFOMNNs-MTDs). In previously published studies of IFOMNNs-MTDs, the controller is usually designed as a general delay-independent feedback controller. Due to the simple form of the feedback controller, less system information is used and less adjustable parameters are considered, which limits the flexibility and control effect of controller. Specially, the use of delay information is insufficient in the existing results, which will make the controller insensitive to the influence of delay factors and affect the control performance. Thereby, the accurate analysis of the dynamic characteristics of IFOMNNs-MTDs by designing appropriate controller needs further study. This paper aims to propose a new delay-dependent controller to improve the stabilization analysis of IFOMNNs-MTDs. Firstly, a delay-dependent distributed controller with distributed control gain and time-delay state summation term is proposed, which accords with the transmission law of activation function weights and is helpful to consider the historical information (i.e., time delay factors) of system. Thereby, the flexibility and control effect of controller are improved by adding control parameters and improving the use of system information. Secondly, a new less-conservatism stabilization criterion of IFOMNNs-MTDs is established by using the designed controller. Moreover, the controller gain can be searched in a large range by using the established criterion. Finally, a numerical simulation is provided to verify the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the practical fixed-time event-triggered consensus problem of multi-agent nonholonomic systems with dynamic disturbances. The continuous communications can be avoided in the update of controller. By converting the nonholonomic chained systems into two subsystems, a switching control algorithm was proposed to deal with the coupling problem in systems. Compared with the event-triggered fixed-time consensus problem of first-order or second-order linear systems, the research of nonholonomic chained systems is more challenging due to the inherent nonlinearity of these systems. Moreover, the convergence time of fixed-time consensus problem is independent of initial states, which is more practical than finite-time consensus problem. Furthermore, it is proved that there is no Zeno behavior under the fixed-time event-triggered consensus control strategies. The effectiveness of the proposed control algorithms is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper considers the leader-following bipartite consensus for a class of nonlinear multi-agent systems (MASs) subject to exogenous disturbances under directed fixed and switching topologies, respectively. Firstly, two new output feedback control protocols involving signs of link weights are introduced based on relative output measurements of neighboring agents. In order to estimate the disturbances produced by an exogenous system, a disturbance observer-based approach is developed. Then, sufficient conditions for leader-following bipartite consensus with directed fixed topologies are derived. Furthermore, by assuming that each switching topology contains a directed spanning tree, it is proved that the leader-following bipartite consensus can be realized with the designed output feedback control protocol if the dwell time is larger than a non-negative threshold. Finally, numerical simulations inspired by a real-world DC motors are provided to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

A continuous-time distributed algorithm based on multi-agent systems is proposed to solve the convex nonsmooth optimization with globally coupled constraints in this paper. Firstly, the relationship of equivalence between the equilibrium and the optimal solution of the system is proved by using the properties of projection operator and saddle point. In addition, the stability of the algorithm is analyzed by means of Lie derivative and set-valued LaSalle's invariance principle. In particular, the trajectory of the proposed algorithm from any initial point can converge to the global optimal solution. Finally, the effectiveness of the designed algorithm is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, without dividing the fractional-order complex-valued coupled neural networks (FCVCNNs) into two real-valued systems, the problem of synchronization is investigated for FCVCNNs with time-varying coupling strength. To achieve synchronization, by updating coupling strength, two feasible adaptive protocols are designed, 1) a fractional-order adaptive strategy depending on global information; 2) a fractional-order adaptive law relying on the local information based on the connected dominating set theory. Additionally, instead of making the weighted average technique or the solution of the isolated node equation as synchronization reference value, direct error method is adopted to realize synchronization, which offers a flexible way in analysis of FCVCNNs. At last, a numerical simulation is provided to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

This paper mainly studies the periodicity and exponential stability for a class of inertial neural networks (INNs) with time-varying delays. Without utilizing standard reduced-order transformation, by using the continuation theorem and Cauchy–Schwarz inequality, delay-dependent criteria shown by some algebraic inequalities are derived to ensure the existence of periodic solutions. Furthermore, by means of the fundamental inequality and constructing a modified delay-dependent Lyapunov functional, global exponential stability analysis is obtained based on the derived delay-dependent criteria. In comparison with the reduced order approach applied to the INNs and delay-independent criteria provided for the INNs in the existed literatures, the results obtained in this paper are new. Finally, numerical simulations are carried out to verify the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the fault-tolerant tracking control issue for a class of discrete-time systems with sensor fault. A novel model-free adaptive fault-tolerant tracking control scheme is proposed by utilizing the dynamic linearization approach, in which only input/output (I/O) data of controlled plant are required. Moreover, due to the characteristics of simple structure and powerful approximation ability, RBF neural network (RBFNN) is introduced to approximate the fault dynamics after the sensor fault is detected. The approximated fault dynamic is utilized to reconstruct the controller. The major feature of this paper is that the whole fault-tolerant tracking controller structure is derived from the dynamic linearization of the ideal controller, rather than the criterion function. Finally, the proposed model-free adaptive fault-tolerant tracking controller is verified to be effective by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we address a pursuit-evasion game involving multiple players by utilizing tools and techniques from reinforcement learning and matrix game theory. In particular, we consider the problem of steering an evader to a goal destination while avoiding capture by multiple pursuers, which is a high-dimensional and computationally intractable problem in general. In our proposed approach, we first formulate the multi-agent pursuit-evasion game as a sequence of discrete matrix games. Next, in order to simplify the solution process, we transform the high-dimensional state space into a low-dimensional manifold and the continuous action space into a feature-based space, which is a discrete abstraction of the original space. Based on these transformed state and action spaces, we subsequently employ min–max Q-learning, to generate the entries of the payoff matrix of the game, and subsequently obtain the optimal action for the evader at each stage. Finally, we present extensive numerical simulations to evaluate the performance of the proposed learning-based evading strategy in terms of the evader's ability to reach the desired target location without being captured, as well as computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the cooperative output regulation problem for a class of heterogeneous linear multi-agent systems under undirected communication topological graph. First, an adaptive event-triggered protocol is introduced to achieve the consensus problem for leader-following system. Then, two fully distributed event-triggered adaptive control protocols are designed. That is, the state feedback and dynamic output feedback controllers, which does not need global information about network topology of system. Under the proposed two control protocols, the cooperative output regulation problem can be solved and no Zeno behavior happens for each agent. Finally, a numerical simulation is used to corroborate the validity of the conclusions under two control laws. Moreover, a comparative experiment is carried out to highlight the advantages of the control protocol designed in this paper. [ABSTRACT FROM AUTHOR]

This paper discusses the finite-time synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. By using nonlinear transformation, an equivalent system is obtained from the discussed neural network. By investigating the finite-time synchronization of the alternative system, some finite-time synchronization criteria of the considered memristor-based Cohen–Grossberg neural network can be obtained. In the whole process, the error state | e (t)| are divided into two procedures: | e (t)| moving from initial value to 1, next, | e (t)| from 1 to 0. Especially, the error state variables e (t) move to 1 in a finite time, and move to 0 in a fixed time. Compared to the classical Lyapunov asymptotic convergence, the finite-time convergence of this paper is a new way to study the synchronization problems. Finally, numerical simulations are presented to display the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on synchronization issue of coupled multistable memristive neural networks (CMMNNs) with time delay under multiple stable equilibrium states. First, we build delayed CMMNNs consisting of one master subnetwork without controller and N − 1 identical slave subnetworks with controllers, and every subnetwork has n nodes. Moreover, this paper investigates multistability of delayed CMMNNs with continuous nonmonotonic piecewise linear activation function (PLAF) owning 2 r + 2 corner points. By using the theorems of differential inclusion and fixed point, sufficient conditions are derived such that master subnetwork of CMMNNs can acquire (r + 2) n exponentially stable equilibrium points, stable periodic orbits or hybrid stable equilibrium states. Then, this paper proposes hybrid multisynchronization of delayed CMMNNs related with various external inputs under multiple stable equilibrium states for the first time. There exist (r + 2) n hybrid multisynchronization manifolds in CMMNNs with different initial conditions and external inputs. Finally, two numerical simulations are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the flocking control issue of multi-agent systems, where each agent utilizes the broadcasting communication manner and takes the Cucker–Smale style dynamic model. In the setting of broadcasting scenario, each agent broadcasts the state information only at certain moments determined by its own clock, and recalculates the control input only when its clock ticks or it receives information from the neighbors. In the Cucker–Smale model, a nonlinear weight function about the communication distance is set to portray the mutual influence degree between agents. With the help of the properties of sub-stochastic matrix, a comprehensive analysis of the asymptotic convergence of the model is performed and the algebraic conditions for achieving flocking control are established. In addition, the obtained theoretical results are further extended to the bipartite flocking control issue for multi-agent systems with both cooperative and competitive interactions. At last, numerical simulations are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the differential privacy-preserving problem for multi-agent systems (MASs) in the presence of antagonistic information over signed digraph. As for the structurally balanced case, an ε -differential privacy algorithm is proposed, upon which some sufficient conditions guaranteeing almost sure bipartite consensus are given. Based on the above scheme, the tradeoff between the system performance and the privacy guarantee is elaborated, and the optimal noise is also devised. Moreover, the proposed privacy preserving scheme is further applied to the scenario of structurally unbalanced graph, where a criterion with respect to almost sure stability of the considered system is derived, as well as the privacy preserving condition. This extends the balanced interaction scenario, and consequently the cooperative multi-agent systems. Finally, numerical simulations are presented to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, the stability for a class fractional-order inertial neural networks with time-delay are investigated. Moreover, some sufficient conditions for the Mittag-Leffler stability and the asymptotical ω -periodicity are obtained, by the appropriate transformation, using the property of the Riemann-Liouville fractional integral and derivative. In the end, results of the theoretical derivation are verified by virtue of two numerical simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, the intermittent dynamic event-based state estimation problem is investigated for a class of delayed complex dynamic networks (CDNs). The estimate is implemented based on the measurements from a fraction of network nodes. In the framework of aperiodic intermittent measurement outputs, a dynamic event-triggered mechanism is introduced to save communication resources and reduce actuation burden. The aim of this work is to design a dynamic event-based state estimator by adopting intermittent dynamic event-triggered (IDET) strategy, such that the dynamics of estimation error system is exponentially stable. By resorting to Halanay inequality and switched system method, the sufficient conditions are derived for ensuring the existence of the desired state estimator, and are characterized by the ratio of the average working time to the average rest time. In the meanwhile, the estimator gains for partial nodes are explicitly obtained by solving some matrix inequalities. Furthermore, it is also proven that Zeno behavior can be excluded under the proposed IDET strategy. Finally, a numerical simulation is provided to verify the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This paper respectively discusses the passivity of fractional-order coupled neural networks with multiple state couplings (FOCNNMSCs) or multiple derivative couplings (FOCNNMDCs). In light of fractional-order system theory, several sufficient conditions for ensuring the passivity of the FOCNNMSCs are established. Moreover, a synchronization criterion for the FOCNNMSCs is obtained under the condition that the FOCNNMSCs is output-strictly passive. Similarly, we also investigate the passivity of the FOCNNMDCs by resorting to the Lyapunov functional method, and the output-strict passivity is used to deal with the synchronization for the FOCNNMDCs. Finally, the effectiveness of the obtained criteria is verified by two numerical examples with simulations. [ABSTRACT FROM AUTHOR]

Bipartite networks, which comprise two classes of nonoverlapping nodes with links existing only between nodes in different classes, are natural models for many practical systems. Currently, most researches on network synchronization have been focusing on unipartite networks, and relatively few works have been done on bipartite networks. This paper aims to investigate the impulsive pinning control problem for synchronization of directed delayed bipartite networks with node delays and hybrid coupling. By using the methods of average impulsive interval and mathematical induction, some sufficient conditions ensuring global exponential synchronization of the addressed networks are derived. Here, a more flexible impulsive pinning scheme is proposed, which allows the set of pinned nodes as well as the corresponding number of pinned nodes to be different at distinct impulsive instants. Furthermore, an index called impulse pinned proportion is introduced, and the lower bound of impulse pinned proportions is determined, based on which a simple guide to picking what kind of nodes as pinned candidates is given. Some numerical simulations are finally presented to verify the correctness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

• A duplex network model with different intralayer coupling delay and interlayer transmission delay has been constructed. • The intralayer network topologies are independent each other, and the nodal dynamics in different layers are different as well. • A few pinning impulsive strategies guaranteeing interlayer synchronization are obtained. • The relatively small intralayer coupling delay and interlayer transmission delay can enlarge the stable region. This paper mainly focuses on interlayer synchronization in a duplex network setting with the intralayer coupling delay and the interlayer transmission delay via pinning impulsive control. Firstly, based on Lyapunov stability theory, a general pinning impulsive strategy guaranteeing interlayer synchronization is obtained. Then, the minimum number of pinned nodes and the maximum impulse interval needed theoretically for interlayer synchronization are obtained. Moreover, when some parameters, including the impulse strengths, the ratio of pinned nodes and the impulse interval, are fixed certain values, their influences on the stable region are further discussed. It is found that the stable region becomes smaller as the ratio of pinned nodes decreases, and gets larger as the impulse strength with no delay is closer to −1 and that with delay is closer to 0. At the same time, the small intralayer coupling delay and interlayer transmission delay can enlarge the stable region. Finally, numerical simulations are provided to verify the effectiveness and correctness of our results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of p th moment exponential stability for multi-links stochastic delayed complex networks with semi-Markov jump under hybrid multi-delay impulsive control. Different from the previous literature on multi-links systems, we take semi-Markov jump into account. The hybrid multi-delay impulses we addressed are composed of unstable delay-free impulses, stable delay-free impulses, unstable multi-delay impulses and stable multi-delay impulses. Average multi-delay impulsive gain is proposed to quantify the strength of the impulses. Serving as an extension of Halanay inequality, a novel multi-delay impulsive differential inequality is constructed. Combining the multi-delay impulsive differential inequality with Lyapunov method and graph theory, the sufficient criteria for p th moment exponential stability of the considered systems are given, which are closely related to average multi-delay impulsive gain, topological structure, stochastic disturbance strength and semi-Markov jump. Furthermore, the obtained theoretical results are applied to a class of stochastic delayed coupled oscillator systems. Finally, a corresponding numerical simulation is provided to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Distinguished from the stationary group consensus problem, in this paper, the dynamic group consensus for a class of heterogeneous multi-agent systems under the influence of input time delays is investigated. A novel dynamic group consensus protocol is designed, where the coexisted cooperation and competition interaction relationships among the agents are considered. Two cases including identical and diverse input time delays are discussed, respectively. Based on matrix theory, system stability theory and pinning control strategy, some sufficient conditions for the heterogeneous systems are established to achieve dynamic group consensus asymptotically. The obtained results reveal that the achievement of systems' dynamic group consensus is related to systems control parameters, the in-degree and input time delays of the agents. Finally, the effectiveness of our theoretical results is verified by some numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the problem of synchronization for a class of fractional-order delayed spatio-temporal neural networks with Dirichlet boundary conditions is investigated. Firstly, based on the L'Hopital law, a Caputo fractional partial differential inequality with p -norm is established to improve the previous results. Besides, a generalized fractional-order Halanay inequality is introduced by rigorous theoretical deduction. Additionally, to realize synchronization, two different control schemes are designed for the networks, respectively, and several criteria are derived based on the developed fractional inequalities. Finally, numerical examples and simulations are provided to verify the correctness of the results. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on studying the distributed leader-following consensus problem of heterogeneous second-order time-varying nonlinear multi-agent systems (HSTN_MASs) under directed switching topology. Firstly, based on the relative position and relative velocity measurements among neighborhood agents, a class of distributed tracking protocols are proposed. Then the state transformations are provided to solve the time-varying nonlinearity and translate the leader-following problem into the stabilization control problem. By constructing the topology-dependent Lyapunov function and choosing appropriate time-varying regulation factor and coupling strength, it is shown that the exponential tracking of HSTN_MASs can be achieved. Moreover, this paper discusses the distributed leaderless consensus problem of HSTN_MASs. Finally, several simulation examples are given to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

Highlights This paper studies the consensus problems for the two types of double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays: the DIFOMAS with symmetric time delays over undirected topology, and the DIFOMAS with asymmetric time delays over directed topology. The main contributions of this paper are as follows: • Consider the double-integrator fractional-order dynamics. • Consider the nonuniform time-delays, which contain up to n(n-1) different values when the DIFOMAS consists of n agents. • Consider the dynamics of each agent containing two state-variable with different fractional orders. • Obtain the two kinds of the upper bound of time-delays about Theorems 1 and 2 and the corollaries of Theorems 1 and 2. Abstract This paper addresses the distributed consensus control for a double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays. A general model of the DIFOMAS is introduced by such case: the dynamic model of each agent contains two state variables with different fractional orders. The consensus conditions on the two kinds of network topology and the nonuniform time-delays can be obtained by using the generic model: the DIFOMAS with symmetric time-delays over undirected topology, and the DIFOMAS with asymmetric time-delays over directed topology. With the help of matrix theory, Laplace transform and graph theory, two kinds of upper bounds of time-delays are derived to ensure the DIFOMAS with nonuniform time-delays can reach consensus. Finally, some numerical simulations with different parameters are offered to illustrate the feasibility and effectivity of the results derived. [ABSTRACT FROM AUTHOR]

Abstract Dealing with high-dimensional dataset has always been an important problem and feature selection is one of useful tools. In this paper, we develop a new filter based supervised feature selection method by combining Trace Ratio Criterion of Linear Discriminant Analysis (TRC-LDA) and group sparsity regularization. The filter based supervised feature selection method is a classifier-independent method while the TRC-LDA criterion is a recently developed criterion for dimensionality reduction that can well preserve discriminative information of dataset. However, there are seldom methods by utilizing TRC-LDA criterion for feature selection. On the other hand, imposing the l2,0-norm to the projection matrix of TRC-LDA will force some rows in it to be zero while keep other rows nonzero making the index of nonzero rows to be the selected features, however, l 2,0 -nom minimizing problem is NP-hard and intractable. To solve the above problem, in this paper, we develop a new method, namely, Trace Ratio Criterion Discriminative Feature Selection (TRC-DFS), for feature selection. The proposed TRC-DFS has imposed l 2,1 -norm, i.e. an approximation of l 2,0 -norm, to the projection matrix W of TRC-LDA to achieve feature selection. As a result, the proposed TRC-DFS can both achieve feature selection as well as capture the discriminative structure of data. We also extend the proposed method with l 2, p -norm (0 < p < 1) regularization to grasp more sparse property and develop an iterative approach to calculate the optimal solution, which is rigorously proved to be converged. Extensive simulations based on several real-world datasets verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract Twin extreme learning machine (TELM) is an efficient and effective method for pattern classification, based on widely known extreme learning machine (ELM). However, TELM is mainly used to deal with supervised learning problems. In this paper, we extend TELM to handle semi-supervised learning problems and propose a novel Laplacian twin extreme learning machine (LapTELM), which simultaneously trains two related and paired semi-supervised ELMs with two nonparallel separating planes for the final classification. The proposed method exploits the geometry structure property of the unlabeled samples and incorporates it as a manifold regularization term. This allows LapTELM to reap the benefits of fully exploring the plentiful unlabeled samples while retaining the learning ability and efficiency of TELM. Moreover, the paper shows that semi-supervised and supervised TELM can form an unified learning framework. Compared with several mainstream semi-supervised learning methods, the experimental results on the synthetic and several real-world data sets verify the effectiveness and efficiency of LapTELM. [ABSTRACT FROM AUTHOR]

Opinion dynamics on social networks describe the time evolution of the opinions within the leader–follower coopetitive (cooperative-competitive) interactions. When does opinion formation result in opinion separation with the single leader? This paper investigates a continuous-time model of such opinion separation problems with signed networks. Our model combines the positive/negative weighting rule of Degroot to describe the impact of their neighbors and the reflected leader–follower mechanism of Jadbabaie to describe trust/distrust relationships from followers to the leader. When the leader is stationary, we establish a necessary and sufficient condition, which ensure all opinions finally converge to bipartite consensus as long as the network topology is structurally balanced. When the leader is dynamic, a sufficient condition is proposed to ensure the opinions of followers move with the opinion of leader or the opposite value in the same velocity. Subsequently, we introduce Laplacian schemes, the framework of signed networks and matrix analysis to develop the stability of networked systems. Numerical simulation examples are given to illustrate the performance of the proposed leader–follower coopetitive systems. [ABSTRACT FROM AUTHOR]

Bayesian estimation of finite Gamma mixture model (GaMM) has attracted considerable attention recently due to its capability of modeling positive data. With conventional variational inference (VI) frameworks, we cannot derive an analytically tractable solution for the variational posterior, since the expectation of the joint distribution of all the random variables cannot be estimated in a closed form. Therefore, numerical techniques are commonly utilized to simulate the posterior distribution. However, the optimization process of these methods can be prohibitively slow for practical applications. In order to obtain closed-form solutions, some lower-bound approximations are then introduced into the evidence lower bound (ELBO), following the recently proposed extended variational inference (EVI) framework. The problem in numerical simulation can be overcome. In this paper, we address the Bayesian estimation of the finite Gamma mixture model (GaMM) under the EVI framework in a flexible way. Moreover, the optimal mixture component number can be automatically determined based on the observed data and the over-fitting problem related to the conventional expectation–maximization (EM) is overcome. We demonstrate the excellent performance of the proposed method with synthesized data and real data evaluations. In the real data evaluation, we compare the proposed method on object detection and image categorization tasks with referred methods and find statistically significant improvement on accuracies and runtime. [ABSTRACT FROM AUTHOR]

In this paper, periodic dynamics and periodic synchronization of a class of delayed neural networks with discontinuous neuron activations and impulsive perturbations are investigated. Firstly, based on Filippov's functional differential inclusion and impulsive differential inclusions theory, the existence of solutions of the considered neural network system is studied. Secondly, according to Krasnoselskii's fixed point theorem on cones of set-valued analysis, sufficient conditions are provided for the existence of at least one periodic solution and at least two periodic solutions for the neural network systems. Furthermore, we also use Kakutani's fixed point theorem to give sufficient criteria for the existence of at least one periodic solution of the neural network systems. These results shown that there are still one or more periodic solutions for the neural networks with discontinuous activations under the impulsive effects. Moreover, sufficient criteria are given to the exponential periodic synchronization under the switching state-feedback control strategy with or without delay. Finally, two numerical simulation examples are presented to verify the correctness and validity of our main conclusions. [ABSTRACT FROM AUTHOR]

This paper focuses on the control of spherical formation for multi-agent systems with double-integrator dynamics in three-dimensional space. To achieve the desired formation pattern on a spherical surface, N agents must be distributed evenly around a target. Based on the information gathered about the target and its immediate neighbors, all agents can either remain stationary or rotate around the target at the same velocity on a spherical surface while the target moves in three-dimensional space. A decoupled control method with limit cycle oscillator characteristics is explored to achieve the desired formation geometric pattern. Accordingly, three subproblems are proposed to achieve the spherical formation more effectively. The first subproblem, target-spherical-surface , requires the agents to converge on a specified spherical surface with the target as its center. The second subproblem, target-circling , requires the agents to follow three prescribed orthometric circular orbits on the spherical surface to avoid collisions while moving. The final subproblem is distributed-adjustment , which involves agents to maintaining a prescribed angular distance from their immediate neighbors while remaining relatively stationary or rotating around the target. By addressing the first two sub-problems simultaneously, the agents can be guided to the desired position. The properties of the limit-cycle-based spherical formation controller are analyzed theoretically, and its effectiveness is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a parallel extended state observer (PESO) is proposed by merging a series of different order linear tracking differentiators and first-order nonlinear differentiators. Both measurement noises and system uncertainties are taken into account in design procedures. A distinct feature of the parallel structure is that the observed information of each part is independent of each other, which effectively avoids the accumulation of the observation error of each part. The PESO is utilized to estimate the total disturbance, which reflects the combined impacts of internal uncertainties and external disturbances. Based on the observation results generated by the PESO, a composite controller is developed for output feedback control of uncertain nonlinear systems. The convergence performance of the proposed PESO and PESO-based controller is rigorously verified. Finally, some numerical simulation results are provided to verify the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper researches the adaptive bipartite output containment problem, for a signed graph of heterogeneous multi-agent systems (HMASs). The dynamics of leaders are subject to unknown but bounded inputs, which cannot be measured by followers. Therefore, an containment control protocol based on distributed observer is proposed. An adaptive state and an output feedback algorithm are designed to ensure that cooperative and antagonistic agents enter different convex hull. Then, based on the output regulation approach, Lyapunov stability analysis and some other methods, the bipartite output containment control is realized. Finally, we validate the analytical results by numerical simulations. [ABSTRACT FROM AUTHOR]

• A robust approximation-based model predictive control scheme for constrained networked nonlinear systems is proposed. • A novel constraint tightening approach for the formulation of the FHOCP is proposed. • Both model error and inter-sampling behavior are considered. • The state and control input constraints are satisfied in continuous-time sense. • A guideline to determine the allowable sampling period is provided. In this paper, a robust approximation-based model predictive control (RAMPC) scheme for the constrained networked control systems (NCSs) subject to external disturbances is proposed. At each sampling instant, the approximate discrete-time model (DTM) is utilized for solving the optimal control problem online, and the control input applied to continuous-time systems can then be determined. Such RAMPC scheme enables to implement MPC for the continuous-time systems in the digital environment, and meanwhile, achieves the state and control input constraints satisfaction in continuous-time sense. Furthermore, we also provide a guideline to determine the allowable sampling period. Sufficient conditions for the feasibility of the RAMPC scheme as well as the associated stability are developed. Finally, the effectiveness of the RAMPC scheme is shown through a numerical simulation. [ABSTRACT FROM AUTHOR]

This paper analyzes the stability and passivity problems for a class of memristor-based fractional-order competitive neural networks (MBFOCNNs) by using Caputo's fractional derivation. Firstly, impulsive effects are taken well into account and effective analysis techniques are used to reflect the system's practically dynamic behavior. Secondly, by using the Lyapunov technique, some sufficient conditions are obtained by linear matrix inequalities (LMIs) to ensure the stability and passivity of the MBFOCNNs, which can be effectively solved by the LMI computational tool in MATLAB. Finally, two numerical models and their simulation results are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the distributed cooperative control problem of heterogeneous nonlinear multi-agent systems (HNMASs) which are of pure-feedback forms coupled with nonaffine dynamics is considered with momentous emphasis on finite-time convergence. Multiple kinds of input constraints are also considered and can be completely unknown. To achieve the dynamic tracking for the heterogeneous followers with unknown input constrains, there are two consensus theorems are proposed, one of which can be utilized to achieve finite-time convergence. Meanwhile, it is the blend of fraction power feedback method and neural network (NN) technique that let the controlled systems have the finite-time characteristic. In the proposed tracking control protocols, only the local position information from neighbors or leader is required. In the end, the effectiveness of two proposed consensus algorithms is confirmed and compared by numerical simulation. [ABSTRACT FROM AUTHOR]

The natural residual (NR) function is a mapping often used to solve nonlinear complementarity problems (NCPs). Recently, three discrete-type families of complementarity functions with parameter p ⩾ 3 (where p is odd) based on the NR function were proposed. Using a neural network approach based on these families, it was observed from some preliminary numerical experiments that lower values of p provide better convergence rates. Moreover, higher values of p require larger computational time for the test problems considered. Hence, the value p = 3 is recommended for numerical simulations, which is rather unfortunate since we cannot exploit the wide range of values for the parameter p of the family of NCP functions. This paper is a follow-up study on the aforementioned results. Motivated by previously reported numerical results, we formulate a continuous-type generalization of the NR function and two corresponding symmetrizations. The new families admit a continuous parameter p > 0 , giving us a wider range of choices for p and smooth NCP functions when p > 1. Moreover, the generalization subsumes the discrete-type generalization initially proposed. The numerical simulations show that in general, increased stability and better numerical performance can be achieved by taking values of p in the interval (1 , 3). This is indeed a significant improvement of preceding studies. [ABSTRACT FROM AUTHOR]