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This article deals with the fully distributed dual-terminal dynamic event-triggered bipartite output containment control of heterogeneous linear multiagent systems (HLMASs) subject to actuator faults. First, a class of fully distributed dynamic event-triggered observers is proposed over the directed signed communication network for each follower to estimate the leaders’ system matrices and (symmetric) combination states, which are merely available to a small fraction of followers. Then, based on the estimations of leaders’ system matrices, adaptive algorithms are employed to solve the regulator equations. Furthermore, the fully distributed observer-based dynamic event-triggered controllers are proposed by integrating the adaptive gains to compensate for actuator faults. Dual-terminal dynamic event-triggered mechanisms (ETMs) are addressed to exclude not only continuous control updates but also continuous communication among agents. Correspondingly, some mild criteria and the rigorous proofs are established to ensure the implementation of bipartite output containment through the Lyapunov stability theory. Moreover, the strictly positive lower bounds of intervals between two adjacent event-triggered time instants are derived, which indicates that Zeno behavior is ruled out in the dual-terminal dynamic ETMs. Finally, numerical simulations are performed to demonstrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

The fully distributed consensus tracking of stochastic nonlinear multiagent systems (MASs) is investigated with Markovian switching topologies and intermittent control strategy, where the dynamics of agents are depicted by Itô differential equations and the leader’s information is just known for a fraction of followers. The switching mechanism of interaction topologies is modeled as a Markov process. A novel class of fully distributed control protocols is proposed via intermittent control method, which is only associated with the relative state measurements of neighbors and does not involve any global information. Meanwhile, the control gains are designed to be intermittently adaptive, which can effectively reduce energy consumption and avoid the gains being larger than those needed in practice. Several sufficient conditions and corresponding proofs are provided by using the Lyapunov stability theory. Finally, numerical simulation is presented to state the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive secure output consensus tracking (ASOCT) problem for general linear multi-agent systems (MASs) with denial-of-service (DoS) attacks via novel dynamic event-triggered impulsive control (DETIC) protocols is considered. An observer-based distributed impulsive control scheme is proposed, where the designed control protocols and event-triggered mechanisms (ETMs) use the estimated value of the observer instead of the sampled information. The DoS attack considered in this paper appears aperiodically with an unknown attack strategy, which interrupts all communication links between agents, and further damages the controllers of agents. To handle the ASOCT under the DoS attack, some sufficient conditions for attack duration and attack frequency are derived. Moreover, the ETM considered in this paper is pull-based dynamic event-triggered mechanism (DETM), that is, the controllers of each agent merely are updated at its own triggering time while its neighbors will not be affected, as well each agent dynamically regulates its event-triggering threshold with the help of auxiliary parameters, which can effectively reduce controllers updates and allow larger triggering intervals. Furthermore, rigorous mathematical proofs are given, and some sufficient conditions are obtained to guarantee ASOCT of the linear MASs. The Zeno behavior is also proved theoretically to be precluded. Finally, the validity of the proffered control schemes is demonstrated by provided simulations. [ABSTRACT FROM AUTHOR]

In this article, the containment control problem of multiagent systems (MASs) with active leaders under a directed communication graph is addressed. A novel pull-based event-triggered protocol combined with aperiodic sampled-data mechanism is first presented, where each agent merely updates controller at its own triggering instants. Under the proposed control protocols, the information is only exchanged and calculated at the aperiodic sampling instants, therefore, it can reduce communication congestion and save computing resources. Furthermore, the Zeno behavior is naturally excluded because the trigger instants are in the set of aperiodic sampled instants. By virtue of the algebraic graph theory and Lyapunov stability analysis, it is shown that the active leaders can reach their desired states predefined arbitrarily and all followers are driven to the convex hull formed by the leaders. Finally, an illustrative example is given to validate the theoretical results and emphasize the advantages of the proposed protocols. [ABSTRACT FROM AUTHOR]

On-orbit configuration estimation is one of the most important tasks for large-scale distributed spacecraft systems, yet incomplete measurement topologies limit the acquisition of partial inter-satellite relative navigation information. In this article, an on-orbit configuration estimation algorithm based on augmented sensing is proposed, which enables each spacecraft to extend the estimation range beyond the observation range without any communication overhead. Referring to the Bayesian inference process, the cooperative behavior of the large-scale distributed spacecraft system is applied to infer relative motion states of unobservable spacecrafts. Under the framework of scaled unscented transformations (SUT), we achieve high-accuracy configuration estimation for the large-scale distributed spacecraft system. Finally, the proposed algorithm is verified in a high-orbiting gravitational wave detector constellation with inter-satellite laser interferometers. [ABSTRACT FROM AUTHOR]

This paper investigates the cluster consensus of multi-agent systems (MASs) with general linear and nonlinear dynamics via intermittent adaptive pinning control, where each cluster has a virtual leader whose state can be sensed by only a small part of followers on some disconnected time intervals because of communication constraints. The communication topology is considered to be weakly connected, that is, it is not necessary to be in-degree balanced, strongly connected or contain a directed spanning tree. To realise the cluster consensus, a class of intermittent adaptive pinning control protocols is proposed according to difference that the agents receive information source. The pinning gains are designed to be intermittent adaptive and with an exponential convergence rate, which will effectively reduce communication costs, avoid the pinning gains being larger than those needed in practice. Meanwhile, it guarantees that the pinning gains quickly converge to steady value. Correspondingly, some sufficient consensus criteria are derived to guarantee that the agents in the same cluster asymptotically can reach consensus while the agents in different clusters can reach different consensus. Rigorous proofs are given by the aid of Lyapunov stability theory and matrix theory. Finally, a numerical simulation example is presented to validate the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered consensus of linear multiagent systems with periodic data sampling mechanisms, where random packet losses are taken into account. The random packet losses occur in communication links based on a certain probability, and it is subject to the Bernoulli distribution. A novel distributed control protocol is designed based on the combined measurement to achieve the mean square consensus. By using the Riccati inequalities and linear matrix inequalities, an event-triggered condition with fewer parameters is also designed to reduce the information updating number. The interaction among the control gain matrix, sampling interval, and packet losses probability is used to describe the consensus conditions. The maximum sampling interval is presented explicitly. It is shown that the advantages of the proposed event-triggered strategy with the data sampling mechanism can avoid the Zeno behavior of the systems and continuous monitoring of the states. The simulations are provided to verify the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the observer-based output consensus of leader-following fractional-order heterogeneous nonlinear multi-agent systems with potentially different state dimensions and different dynamics are investigated. Considering the agents' states may be not available in practice, the distributed state observer is designed for each agent. Then corresponding distributed control protocols based a proposed virtual exosystem are proposed to convert the output consensus problem into the stabilisation problem. By employing matrix theory, algebraic graph theory and the stability theory of fractional system, the state consensus of the virtual exosystem and the output consensus of heterogenous fractional nonlinear MAS is achieved. Moreover, the sufficient conditions are also obtained. Simulation examples are presented to verify the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, group multiple lags consensus of fractional-order leader-following multi-agent systems with nonlinear dynamics are investigated, in which two kinds of lag consensus are considered. One is said to be outergroup lag consensus, which means that different group leaders reach lag consensus. The other one is called innergroup lag consensus, that is to say, the followers will reach lag consensus with their own group leader. Based on Mittag–Leffler stability for fractional-order systems, algebraic graph theory, a class of novel control protocols is designed and the corresponding sufficient conditions are derived to guarantee the achievement of group multiple lags consensus. Furthermore, considering parametric uncertainties, an adaptive control technology is employed to solve the group multiple lags consensus for fractional order multi-agent systems, and the corresponding adaptive control protocols and sufficient conditions are proposed. Finally, numerical simulations are given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems’ convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems’ stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results. [ABSTRACT FROM AUTHOR]

Consensus for the fractional‐order double‐integrator multi‐agent systems is mainly studied in this study. First, a control law based on the sliding mode estimator is proposed to achieve consensus for the multi‐agent systems, where the linear systems and the non‐linear systems are discussed, respectively. Second, a distributed control law based on the sliding mode estimator is given to accomplish distributed consensus for the multi‐agent systems, the linear systems and the non‐linear systems are also considered, respectively. The validity of the designed control laws is proved by choosing the adaptive Lyapunov candidate functions. Finally, several examples are presented to demonstrate the obtained results and show the advantage of the proposed control laws in the convergence speed. [ABSTRACT FROM AUTHOR]

• The finite-time and fixed-time bipartite consensus of MASs over signed graph while considering both leaderless and leader-following MASs are investigated. • In contrast to the existing methods to address FNTBC and FXTBC, the impulsive control was employed, which has a better performance in convergence speed and less state information transmission. • Some sufficient criteria and the settling time which are based on the proposed impulsive control protocols are derived. This paper studies the finite-/fixed-time bipartite consensus (FNTBC and FXTBC) of multi-agent systems (MASs) over signed graph via discontinuous impulsive control while considering both leaderless and leader-following MASs. In contrast to the existing methods of FNTBC and FXTBC, the impulsive control has a better performance in convergence speed and less state information transmission, which is more practical and flexible in real applications. To realize FNTBC and FXTBC for leaderless and leader-following MASs, a class of distributed impulsive control protocols is proposed. Then by utilizing impulsive control theory and finite-/fixed-time stability theory, some sufficient criteria and the settling time which are based on the proposed impulsive control protocols for FNTBC and FXTBC for leaderless and leader-following MASs are derived. It has been shown that the settling time for FNTBC depends on initial conditions of systems, while this limitation is removed for FXTBC. Finally, the proposed impulsive protocols are validated by some simulations, separately. [ABSTRACT FROM AUTHOR]

Distributed consensus tracking for the fractional-order multi-agent systems is mainly studied in this paper. Firstly, the simple Lyapunov candidate function is discussed to judge the validity of the proposed controller. Secondly, according to the sliding mode control method, a controller is designed to achieve the consensus tracking problem when the followers are described by the fractional-order linear dynamics. Thirdly, the case when the dynamics of followers own the intrinsic nonlinear function is discussed, it proves that the designed sliding mode controller is still valid for this case under the certain conditions. For the above two parts, the systems stabilities are judged based on the result of the first part. Finally, several simulations are presented to verify the obtained results. [ABSTRACT FROM AUTHOR]

In this study, the authors consider the consensus tracking problem for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state. The dynamics of each agent consists of nonlinear inherent dynamics. In order to reach consensus tracking, a class of nonsmooth control protocols is proposed which only depends on the agent's own information and its neighbours’ information. With the aid of algebraic graph theory, matrix theory, and Lyapunov theory, some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived. Finally, the numerical simulations are given to illustrate the effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates group consensus of a class of heterogeneous multi-agent systems with input saturation via pinning scheme, in where the heterogeneous multi-agent system is composed of first-order agents and second-order agents. Firstly, based on the fact that the control input of partial first-order integrator agents could be bounded due to the limitation of actuators, a class of control protocols including partial first-order integrator agents with input saturation is proposed to solve the group consensus problem of heterogeneous multi-agent systems. Secondly, to guarantee the states of agents in the same group can converge to one specified consensus state, the group consensus problem of heterogeneous multi-agent systems with some pinned agents who can be first-order or second-order agents is discussed. Then a class of new control protocols with pinning scheme is proposed. By using LaSalle Invariance Principle, matrix theory, algebraic graph theory and Lyapunov stability theory, the rigorous proofs are given and the corresponding sufficient group conditions are also obtained. Finally, simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics group consensus problem of heterogenous multi-agent systems with time delays, in which agents’ dynamics are modeled by single integrators and double integrators. To achieve group consensus, a class of dynamics group consensus protocols is proposed for heterogenous multi-agent systems with input time delays, which can also be used to solve group consensus for heterogenous multi-agent systems without input time delays. By using frequency-domain analysis method and matrix theory, some sufficient group consensus conditions, which are dependent on the input delays and the control parameters, are obtained for heterogenous multi-agent systems under directed and undirected communication topologies with and without input time delays, respectively. Simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The distributed formation control of fractional-order multi-agent systems is mainly studied under directed interaction topology in this paper. First, the control algorithm with absolute damping and communication delay is proposed to achieve the formation control. Then, some sufficient conditions are derived by using the matrix theory, graph theory and the frequency-domain analysis method. Finally, based on the numerical method of predictor–corrector, several simulations are presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM PUBLISHER]

In this paper, the distributed formation control problem for multiple nonholonomic mobile robots using consensus-based approach is considered. A transformation is given to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem. Distributed control laws are developed for achieving the formation control objectives: a group of nonholonomic mobile robots at least exponentially converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. Rigorous proofs are provided by using graph, matrix , and Lyapunov theories. Simulations are also given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, a distributed time‐varying optimization problem for multirobot systems with collision avoidance is studied. A hierarchical control framework is employed to simplify the complex problem into two subproblems in two layers. One is the network layer where a novel distributed time‐varying finite‐time optimal control protocol as a signal generator is proposed for each robot. The signal generator ignores the model constraint and uncertainty. The other is the real‐time layer, which mainly contains a sampling module and a robust nonlinear model predictive control (NMPC) module. The former samples the optimal signal from the signal generator as a series of sampling tracking points with proper distance to improve tracking performance, and the latter searches for the optimal control protocol for the robot system to track these sampling tracking points in sequence with the model constraint and uncertainty. Furthermore, considering the collision between each robot, a give‐way strategy is designed that the robot with a low priority has to stop to wait for the other with a high priority to move first. And a primary‐secondary judgment technology determines the priorities of robots adaptively according to the current state of the robots. If the way forward of the moving robot is blocked by the stopping one, an auxiliary point is introduced as a temporary transfer station to avoid collision further. Finally, the effectiveness of the proposed methods is verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

Abstract: This paper investigates the leader–follower formation control problem for nonholonomic mobile robots based on a bioinspired neurodynamics based approach. The trajectory tracking control for a single nonholonomic mobile robot is extended to the formation control for multiple nonholonomic mobile robots based on the backstepping technique, in which the follower can track its real-time leader by the proposed kinematic controller. An auxiliary angular velocity control law is proposed to guarantee the global asymptotic stability of the followers and to further guarantee the local asymptotic stability of the entire formation. Also a bioinspired neurodynamics based approach is further developed to solve the impractical velocity jumps problem. The rigorous proofs are given by using Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results. [Copyright &y& Elsevier]

This paper investigates the observer-based bipartite consensus tracking of nonlinear fractional-order multi-agent systems (FOMASs) by employing a pull-based dynamic event-triggered mechanism (DETM). First, considering that the relevant state information of each agent is not always measurable, a class of distributed observers is considered for each agent to estimate its state information. Then, a pull-based DETM for FOMASs is proposed to avoid continuous controller updates, in which the dynamic threshold is modulated according to the preset conditions. The pull-based DETM constructed in this paper enables each agent to update the controller only based on its own trigger instants. Furthermore, an observer-based dynamic event-triggered control protocol is designed to guarantee the bipartite consensus tracking of FOMASs. Correspondingly, sufficient conditions are obtained by using graph theory and choosing suitable Lyapunov candidate functions. Moreover, the Zeno behavior is precluded. Finally, two simulation examples are presented to illustrate the theoretical results efficiently. [ABSTRACT FROM AUTHOR]

This paper addresses the time-varying formation-containment (FC) problem for general linear multi-agent systems based on an observer viewpoint under the directed communication graph which contains a spanning tree. A new format of time-varying formation shapes with the properties of translation, scalability and rotation is proposed. Then the time-varying formation tracking problem where the real leader's input is unknown to all other agents is solved independently. After that, the time-varying FC problem where the challenge is how to deal with the formation-achieving agents' unknown nonzero inputs for containment-achieving agents, is firstly addressed. All the designed controllers, which need no eigenvalue information of the whole graph, are fully distributed and so can be applied to large-scale systems. The influence of communication graph structure to the control convergence rate is further analysed. The above theoretical results are verified by multiple nonholonomic vehicles in simulations. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed formation tracking control problem for multi-vehicle systems with nonholonomic constraints, by the aid of event-triggered and sampled-data control methods. Two classes of event-triggered communication and control strategies with fixed sampling period are considered. By designing different event conditions, the communications amongst neighbouring vehicles are allowed at each sampling time instant in the first strategy, whereas the control input of each vehicle is updated only when its own or neighbours' event conditions are violated. Furthermore, both communication and control update are allowed only when the events of itself or neighbours are triggered in another strategy. To this end, an unified event-triggered and distributed observer-based controller with globally asymptotic convergence rate is proposed. And corresponding sufficient conditions are derived regarding to two types of event conditions, based on Lyapunov technique, matrix analysis and algebraic graph theory. It is worth noting that the Zeno-behaviour of systems with the presented controllers and event conditions is naturally avoided for all the vehicles due to the advantageous property of sampled-data control. Finally, simulations are provided to verify the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the fixed-time formation tracking problem of multi-robot systems with nonholonomic constraints. A new type of distributed nonlinear controller for each robot is designed. Some corresponding sufficient conditions are derived by using algebraic graph theory, matrix analysis and fixed-time stability theory. In addition, an upper bound of the settling time for the multi-robot systems is also explicitly given. It is shown that the obtained upper bound of settling time is regardless of initial errors of systems, which implies that it can facilitate the pre-design of the convergence time off-line. Numerical example is provided to illustrate the effectiveness of the present theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed formation tracking problem of multi-robot systems with nonholonomic constraint via event-triggered approach. A variable transformation is firstly given to convert the formation tracking problem into the consensus-like issue. Then a novel type of distributed event-triggered control strategy is proposed under fixed topology and switching topology, which can guarantee multi-robot systems to produce desired geometric configuration from arbitrary initial positions and orientations for each robot, while the centroid of formation can follow one dynamic reference trajectory. Moreover, the novel event-triggering conditions under fixed topology and switching topology, which only need intermittent interaction between neighboring robots, are designed to assist the execution of distributed controllers. Based on the designed event-triggering conditions, the robot systems can effectively reduce the communication cost, energy consumption and mechanical wear, especially when the quantity of robots is huge. Finally, the effectiveness of theoretical results is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

This study investigates the robust fixed‐time consensus tracking problem of second‐order multi‐agent systems under fixed topology. A novel type of non‐linear protocol and the corresponding sufficient conditions for achieving robust fixed‐time consensus tracking are proposed with the aid of sliding mode technique and Lyapunov theory. Compared to finite‐time consensus tracking, the convergence time of the tracking errors is globally bounded for any initial conditions of the agents, which is also the global information for each agent. Furthermore, the results obtained for second‐order multi‐agent systems are also extended to deal with the fixed‐time formation tracking problem for unicycle‐type robots. Extensive numerical experiments are performed to illustrate the effectiveness of the present theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange. A class of general state and input transform is introduced to convert the formation-tracking issue of multi-robot systems into the consensus-like problem with time-varying reference. The distributed observer-based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system, which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory. The finite-time stability of observer and control law is analysed rigorously by using the Lyapunov direct method, algebraic graph theory and matrix analysis. Numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive distributed formation control problem for multiple nonholonomic wheeled mobile robots. First, the formation control problem is converted into a state consensus problem by the aid of a variable transformation. Then, distributed kinematic controllers and adaptive dynamic controllers are developed for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers. Also the followers are assumed to have only local interaction. Some sufficient conditions are derived for accomplishing the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

The lag-generalized synchronization of coupled time-delay chaotic systems with unknown parameters and stochastic perturbation is investigated. Based on the LaSalle-type invariance principle of stochastic differential equation, the synchronization is realized by analyzing stochastic stability of the error system. In order to achieve the synchronization, the unknown parameter update laws and the control laws are proposed. At last, two numerical examples are presented to show the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the global stability analysis of fractional-order Hopfield neural networks with time delay is investigated. A stability theorem for linear fractional-order systems with time delay is presented. And, a comparison theorem for a class of fractional-order systems with time delay is shown. The existence and uniqueness of the equilibrium point for fractional-order Hopfield neural networks with time delay are proved. Furthermore, the global asymptotic stability conditions of fractional-order neural networks with time delay are obtained. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. [Copyright &y& Elsevier]

This paper investigates the distributed fixed-time consensus-based formation tracking problems for multiple nonholonomic wheeled mobile robots under a directed interaction topology. The distributed fixed-time consensus-based controllers under the directed interaction topology are proposed for the multiple wheeled mobile robots with nonholonomic constraints, which can guarantee the group of robots converge to a predefined formation pattern with its centroid moving along the predefined reference trajectory in a fixed time. The fixed-time formation tracking can be achieved within a fixed settling time, which is independent of the initial states of the whole system. Moreover, the conditions of formation stability control are analysed by utilising graph and Lyapunov stability theories. Finally, the feasibility of the proposed distributed controllers is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

• The containment control of fractional order multi-agent systems with nonlinearity is considered. • A control protocol with time delay for fractional order multi-agent systems is designed. • A pull-based event-triggered control law combined time delay is designed. • Mittag-Leffler function based method is adopted instead of Lyapunov method. • Zeno behavior is precluded by the strict proof. The containment control for fractional order multi-agent systems with nonlinearity and time delay is investigated in this article. Firstly, a distributed control protocol with fixed time delay is proposed for the purpose of achieving containment control for nonlinear fractional order multi-agent systems. Secondly, by using the pull-based event-triggered mechanism, a distributed event-based control law with time delay is further given to accomplish containment control for fractional order multi-agent systems with nonlinearity. In this way, the controller of each agent is merely updated at its own trigger moments. Hence, it can decrease network correspondence congestion and lower computational cost. Thanks to the stability theory of fractional order calculus, matrix theory, and properties of Mittag-Leffler function, the feasibility of the designed control protocols is confirmed. Furthermore, the Zeno behavior is precluded by the strict proof. Ultimately, two simulation examples are used to illustrate the availability of above theoretical analysis respectively. [ABSTRACT FROM AUTHOR]

Abstract The problem of disturbance rejection/attenuation for constant-input delayed linear multi-agent systems (MASs) with the directed communication topology is tackled in this paper, where a classic model reduction technique is introduced to transform the delayed MAS into the delay-free one. First, when the leader has no control input, a novel adaptive predictive extended state observer (ESO) using only relative state information of neighboring agents is designed to achieve disturbance-rejected consensus tracking. The stabilization analysis is presented via the Lyapunov function and sufficient conditions are derived in terms of linear matrix inequalities. Then the result is extended to disturbance-attenuated case where the leader has bounded control input which is only known by a portion of followers. Finally, two numerical examples are presented to illustrate the effectiveness of proposed strategies. The main contribution focuses on the design of adaptive predictive ESO protocols with the fully distributed property. [ABSTRACT FROM AUTHOR]

In this paper, RBF neural network consensus-based distributed control scheme is proposed for nonholonomic autonomous vehicles in a pre-defined formation along the specified reference trajectory. A variable transformation is first designed to convert the formation control problem into a state consensus problem. Then, the complete dynamics of the vehicles including inertia, Coriolis, friction model and unmodeled bounded disturbances are considered, which lead to the formation unstable when the distributed kinematic controllers are proposed based on the kinematics. RBF neural network torque controllers are derived to compensate for them. Some sufficient conditions are derived to accomplish the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov theory. Finally, simulation examples illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]