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This paper applies a terminal learning strategy to study distributed quadratic optimization problems. Since the optimal state is unknown in advance, the tracking error information is generally unavailable. To achieve the optimal state without the tracking error information, the terminal consensus iterative learning scheme is used to solve the problem. And the terminal consensus state is obtained without the global information of network. On this basis, the optimal target is also achieved by choosing the proper initial state and learning parameters. And the optimization problem is studied with the constraints of state and control input. Results show that our approach is effective. Compared with existing distributed optimization methods, the learning strategy in this paper provides another effective analysis scheme. Last, a numerical example is presented to show the effective aspects of the method. [ABSTRACT FROM AUTHOR]

In this paper we explore the observer-based event-triggered tracking control problem for nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. To overcome the difficulty introduced by the nonlinear term, an observer based on neural networks (NNs-observer) is introduced to estimate unavailable system states. Besides, this paper designs a new secure distributed controller which can achieve the tracking control objective while maintaining the tolerance to DoS attacks. Furthermore, in order to save network resources, a new event-triggered mechanism is introduced which is mathematically proved to be free of the Zeno phenomenon. Finally, an example is provided to support the effectiveness of the proposed NNs-observer-based event-triggered resilient tracking control scheme. [ABSTRACT FROM AUTHOR]

The predefined-time cooperative output regulation of second-order nonlinear multiagent systems with an unknown exosystem is investigated in this paper. Existing similar work is almost limited to exactly known exosystems, and the upper bound of convergence time for closed-loop systems is difficult to adjust and predict, which may not meet practical needs. In this paper, we first propose a new dynamic compensator called predefined-time distributed observer, which guarantees that each agent estimates the state and parameters about the linear exosystem with unknown system matrix through the general directed communication network within the time set by an explicit parameter. Subsequently, combining the improved dynamic gain control method and the proposed predefined-time distributed observer, a novel distributed dynamic predefined-time control scheme is proposed, which solves the problem of this paper by simplifying the tedious arithmetic process caused by the traditional backstepping method. The final simulation experiments verify the effectiveness of the proposed control scheme. • We extended similar articles to more general leader and controlled objects. • The settling time of our controller can be set directly and structure is simple. • We present a new distributed observer for unknown leader and general digraph. • The designed observer can work for an arbitrarily set period of time. • We transform an unknown leader into a known one in a predefined time. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem of a new multi-agent system via multi-task, multi-control mechanism and multi-consensus strategy. Firstly, two multi-task algorithms are proposed, which can reasonably select some agent nodes with better performance to form the multi-agent system according to different tasks. Secondly, a multi-control protocol designed in this paper integrates continuous control mechanism, impulsive control mechanism and hybrid control mechanism, which has strong applicability and efficiency. Thirdly, a multi-consensus strategy is designed, and it can be converted into "average consensus strategy", "leader-following consensus strategy" and "hybrid consensus strategy" through different parameter settings, which greatly broadens the application field of the multi-agent system. We construct a dynamic model for the proposed multi-agent system, analyze it by using matrix measure and Lyapunov stability theory, and obtain the theorems that enable it to achieve multiple consensus. Finally, the efficiency and practicability of our theories are verified through several simulation experiments. We further carry out some comparative analysis with some relevant papers, and obtain the superiority of our theories in multiple indicators. [ABSTRACT FROM AUTHOR]

In this paper, we propose a distributed finite-time optimization protocol for single-integrator continuous-time multi-agent systems, which utilizes a modified Newton–Raphson method. The inverse of Hessian matrix, sign function and the gradient are adopted for the design of the algorithms. The proposed algorithms make agents converge to the network optimizer under any initial state and finite time, respectively. Lyapunov method and the properties of sign function are employed to verify the convergence of the proposed algorithms. Besides, the adaptive method is also considered to avoid complex parameter conditions and centralized parameters. Finally, numerical simulations are provided to testify the presented results. [ABSTRACT FROM AUTHOR]

This paper proposes an H ∞ / H ∞ optimization technique to distributed fault detection (FD) for multi-agent systems (MASs). To simultaneously consider the effects of unknown disturbances and faults in the MASs and event-triggered transmission errors (ETTEs) on the residual signal, a residual generator related to the event-triggered threshold coefficient is designed. The generated residuals achieve the best compromise between robustness to unknown disturbances and sensitivity to faults. The obtained results have a better detection performance by using H ∞ / H ∞ optimization technique compared with other optimized schemes. In addition, the applicability of the proposed H ∞ / H ∞ optimized distributed FD scheme is verified by the simulation of a vehicle lateral dynamic system. [ABSTRACT FROM AUTHOR]

The Nash equilibrium seeking over networks of N players has been studied under the assumption that the network is static and strongly connected or switching and every time strongly connected. In this paper, we further consider the case where the network is jointly strongly connected. Since a jointly strongly connected network can be disconnected at any time instant, the existing approach cannot handle such a case. Like the literature, assuming the pseudogradient dynamics has a globally exponentially stable Nash equilibrium, we first establish a distributed estimator for actions of all players over jointly strongly connected networks. Then we compose the pseudogradient dynamics with the distributed estimator to obtain an extended gradient system with N + 1 subsystems. Under the assumption that the pseudogradient of the game is strongly monotone and Lipschitz continuous, we show that, starting from any initial condition, the state of every subsystem of the extended gradient system will exponentially converge to the Nash equilibrium of the game concerned. [ABSTRACT FROM AUTHOR]

In this paper, the bipartite consensus problem for second-order multi-agent systems with no leader, one leader and multiple leaders are investigated, where the information exchange is disturbed by measurement noise and antagonistic information. In order to attenuate the effect of communication noise, a time-varying gain c (t) is utilized and the stochastic approximation bipartite control protocol is proposed. It is given that the underlying protocol can solve the bipartite consensus problem for MASs with no leader/one leader/multiple leaders if the communication topology is strongly connected/has a spanning tree/has a spanning forest and the c (t) satisfies some mild condition. Meanwhile, for system with these three cases, a series of sufficient and necessary conditions are given. Especially, for the case with no leader, we obtain that the final state of agent is related with the initial position and initial velocity of each agent. For the case with one leader, we can get that the followers in one group can follow up the state of one leader, and the followers in another group tend to the opposite value. Additionally, for the case with multiple leaders, the containment control can be achieved where followers' states in one group can converge to the quai-convex hull of leaders' state and the ones in another group converge to the opposite convex hull. Finally, some numerical examples are given to support our new results. [ABSTRACT FROM AUTHOR]

• Distributed optimization problems of consensus are examined by a frequency-domain analysis approach. • An optimized distributed protocol is proposed such that the nonuniform time-delay FDMSs with SF have better consensus performance. • The double-integral dynamics of delayed FDMSs with SF is considered. This paper addresses distributed optimization problems concerning consensus in delayed fractional-order double-integrator multi-agent systems (FDMSs). To start with, an optimized distributed protocol with state-fractional-order-derivative feedback (SF) is presented for delayed FDMSs. Then, the consensus problems are studied for the two kinds of delayed FDMSs with SF in the presence of symmetric time-delays over undirected network topology and asymmetric time-delays over directed network topology. Next, by the means of graph theory, matrix theory and frequency-domain analysis method, the sufficient conditions to guarantee consensus of delayed FDMSs with SF are derived. Compared to the traditional distributed protocol without SF, the proposed distributed optimization protocol with SF are taken into account to enable better consensus performance in delayed FDMSs with SF. Finally, numerical experiments are carried out to verify the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

• Agents communicate indirectly and asynchronously via a shared cloud repository. • Both globally and locally Lipschitz nonlinearity in system dynamics are discussed. • Adaptive control scheme is considered for multi-agent systems under directed graph. • Practical tracking consensus is achieved for multi-agent systems with disturbances. • Zeno-freeness is guaranteed for the proposed cloud-based self-triggered scheme. This paper addresses the practical tracking consensus problem for first-orderheterogeneous nonlinear multi-agent systems in presence of external disturbances under directed graphs. Agents with limited communication capability interact with each other through a cloud repository, where the information exchange is asynchronous and indirect. The system model is more general than the ones in existing results, moreover, locally Lipschitz nonlinearities and adaptive control schemes are taken into account. It is proven that under the designed self-triggered protocol, agents can track a virtual leader with bounded error and Zeno behaviour is excluded for real implementation. Finally, a numerical simulation demonstrates the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Almost all systems are inevitably subject to various uncertainties or disturbances from the external environment in practical applications. Taking these factors into consideration, in this paper a distributed algorithm with state noise and gradient disturbance is proposed for solving distributed optimization problem with closed convex set constraint based on multi-agent system under weight-balanced graph. Moreover, based on the gradient tracking and projection methods, the proposed distributed algorithm with gradient tracking can improve the convergence rate by introducing a projection error term and an auxiliary parameter. In contrast to some existing constrained distributed gradient algorithms, the proposed one can make the convergence faster and enhance the performance of convergence. The proposed algorithm is illustrated with two simulation examples to show its effectiveness and robustness. [ABSTRACT FROM AUTHOR]

In multi-agent reinforcement learning, multiple agents learn simultaneously while interacting with a common environment and each other. Since the agents adapt their policies during learning, not only the behavior of a single agent becomes non-stationary, but also the environment as perceived by the agent. This renders it particularly challenging to perform policy improvement. In this paper, we propose to exploit the fact that the agents seek to improve their expected cumulative reward and introduce a novel Time Dynamical Opponent Model (TDOM) to encode the knowledge that the opponent policies tend to improve over time. We motivate TDOM theoretically by deriving a lower bound of the log objective of an individual agent and further propose Multi-Agent Actor-Critic with Time Dynamical Opponent Model (TDOM-AC). We evaluate the proposed TDOM-AC on a differential game and the Multi-agent Particle Environment. We show empirically that TDOM achieves superior opponent behavior prediction during test time. The proposed TDOM-AC methodology outperforms state-of-the-art Actor-Critic methods on the performed tasks in cooperative and especially in mixed cooperative-competitive environments. TDOM-AC results in a more stable training and a faster convergence. Our code is available at https://github.com/Yuantian013/TDOM-AC. [ABSTRACT FROM AUTHOR]

This paper addresses the fully distributed adaptive time-varying formation protocols design problem for singular multiagent systems with directed topology. The pinning control method is introduced into the design of the adaptive distributed protocols, which can effectively adjust the formation position among agents and greatly relax the constraints of the communication topology among agents. Then, the distributed algorithm that independent of the global information of the communication graph is designed to solve the proposed fully distributed protocols. Next, the sufficient conditions of time-varying formation control are provided by the feedback pulse elimination method and stability analysis. Finally, the time-varying formation simulation results are presented to verify the feasibility of the proposed theory. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal consensus problem for heterogeneous discrete-time(DT) linear multi-agent systems. The optimal consensus problem is formulated as finding a global Nash equilibrium solution subjected to the defined local performance index. A reinforcement learning(RL) value iteration(VI) algorithm is introduced to obtain the optimal policies in the sense of Nash equilibrium. To ensure the effectiveness of the VI algorithm, the admissibility of the iterative control policies for multi-agent systems is considered. With theoretical analysis, a new termination criterion is established to guarantee the admissibility of the iterative control policies. Furthermore, an online learning framework is designed with an actor-critic neural network(NN) to implement the VI algorithm. Finally, two simulation examples are presented respectively for leader–follower and leaderless multi-agent systems to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on the distributed online optimization problem in multi-agent systems considering privacy preservation. Each agent exchanges local information with neighboring agents on the strongly connected time-varying directed graphs. Since the process of information transmission is prone to information leakage, a distributed push-sum dual averaging algorithm based on the differential privacy mechanism is proposed to protect the privacy of the data. In addition, to handle situations where the gradient information of the node cost function is unknown, the one-point gradient estimation is designed to calculate the true gradient information and guide the update of the decision variables. With the appropriate choice of the stepsizes and the exploration parameters, the algorithm can effectively protect the privacy of agents while achieving sublinear regret with the convergence rate O (T 3 4 ). Furthermore, this paper also explores the effect of one-point estimation parameters on the regret in the online setting and investigates the relation between the convergence effect of individual regret and differential privacy levels. Finally, several federated learning experiments were conducted to verify the efficacy of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, for the multi-agent system, the Nash equilibrium (NE) search problem for non-cooperative game with state constraints under false data injection (FDI) attack is studied. The FDI attack can directly destroy the connectivity between agents, resulting in the performance degradation or even failure for most NE search algorithms. We propose a new distributed NE search method to improve the performance of NE algorithms under FDI attacks. The NE algorithm is designed to find the solution of NE under network attack and make the system recover after the attack. However, most of the existing results only studied the NE algorithm of the non-attacking system, and the existing results rarely take into account whether the system state exceeds the safety limit, which can cause the system to crash. This paper solves the state constraints problem of the multi-agent game under the FDI attack. Finally, the reliability of the algorithm is verified by a numerical result. [ABSTRACT FROM AUTHOR]

This paper investigates the development of an adaptive cooperative control scheme for the consensus of uncertain nonlinear multi-agent systems subjected to uncertain time-varying control direction, disturbances, and dead-zone nonlinearity. The dead-zone nonlinearity is described by an uncertain nonlinear function of the control input which can represent a wide class of practical input nonlinearities. It is assumed that no prior knowledge about the uncertain nonlinearities of agents, disturbances, dead-zone parameters, magnitude and sign of the control gain is available. In this paper, a Nussbaum function is used to deal with the unknown time-varying control directions problem and a disturbance-like term in the dead-zone description is approximated by an adaptive TSK-type fuzzy system. Then, by using the dynamic surface control approach and radial-basis function neural network, an adaptive distributed controller is designed for each follower agent. Stability analysis shows that all signals of the closed-loop multi-agent system are semi-globally uniformly ultimately bounded and the consensus error can be made arbitrary small by the proper selection of design parameters. Simulation and comparison results demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed output tracking problem via linear sampled-data control for a class of uncertain nonlinear multi-agent systems. Specifically, for the case where the graph topology is directed and the leader is the neighbor of only a small portion of followers, by combining the backstepping method with sampled-data method, a series of linear sampled-data controllers are obtained. Stability analysis is performed by using calculus, comparison principle and so on. The main results of this paper are concluded that all the states of the closed-loop system are globally bounded and the output tracking errors can be tuned arbitrarily small. Finally, a numerical example is given to verify the validity of the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, the measured input–output data sequences with pinning gain are proposed via the topology of multi-agent systems (MAS), where the requirement of reinforcement learning algorithm on internal state is avoided by pinning gain and the measured data of leader and neighbors. Besides, a data-based tracking state is given, which can be applied to MAS with different control matrices. According to the sequences and tracking state, a distributed control policy and corresponding reinforcement learning algorithm are proposed for the output synchronization. The proposed algorithm overcomes the shortcoming that previous algorithms can not be applied to MAS with different control matrices in the absence of model information and full-state vector. Finally, the effectiveness of proposed algorithm is verified by simulation examples. [ABSTRACT FROM AUTHOR]

• A distributed adaptive control methodology is proposed to solve the mean-square consensus control problem. • Parameter-dependent Lyapunov functions and free-weighting matrix methods are introduced. • The controllers are independent of randomly switching topologies. • The disturbance rejection performance of MASs over switching topologies are also discussed. This paper considers the stochastic consensus problem of high-order linear discrete-time multiagent systems (MASs) with uncertain topologies and external disturbances. The randomly switching interaction signed topologies are governed by a time-homogenous Markov chain with incomplete knowledge of the transition probabilities. Based on Lyapunov function theory and adaptive control strategies, we employ a homogeneous parameter-dependent Lyapunov function to propose sufficient conditions under a set of linear matrix inequality (LMI) constraints. A free-weighting matrix method is introduced to give the proposed LMIs extra freedom to search feasible solutions. Furthermore, the adaptive controllers applied in this paper are independent of topologies and fully distributed; i.e., the system achieves robust consensus without continuously updating the controller and dealing with global data. Additionally, we extend the theoretical framework to analyze the disturbance rejection performance of MASs under the stochastic process. Two numerical examples are provided to show the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

This paper discusses the containment control (CC) problem of general linear multi-agent systems (MAS)s by means of two kinds of distributed event-triggered mechanisms. Two types of event-triggered control protocols, namely, the state feedback control law and the dynamic output feedback control protocol, are designed for each follower. Under the proposed control protocols and triggering mechanisms, the containment control problem can be solved by proving that the containment error converges to zero based on the assumption and algorithms. At last, we verify the rationality of the theoretical results. Through two numerical simulation, we can see that the trajectory of each follower converges to the convex hull formed by all leaders. In addition, in order to verify the advantages of the obtained results, we give a simulation example and compare the methods designed in this paper with the methods in other literature. [ABSTRACT FROM AUTHOR]

This paper studies the leader-following output consensus problem of a class of nonlinear switched multi-agent systems described by the T-S fuzzy models. A sufficient condition on the leader-following output consensus and the bumpless transfer performance is developed via co-design of the observer-based bumpless transfer fuzzy controllers and the agent-dependent switching law, which the local stabilizability of all the fuzzy subsystems of each agent is not required. By using the distributed dynamic event-triggered rule, the fuzzy estimator for each agent is constructed to estimate the state of leader. Besides, Zeno behaviour is ruled out via discussing the existence of the lower bound on inter-event intervals. Finally, two examples are given to validate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper considers the event-triggered predictive control(ETPC) problem for linear discrete-time multi-agent systems. To achieve accurate state estimation under event-triggered communication between agents, an event-triggered predictive control scheme as well as a novel class of triggering condition are proposed for synchronization of multi-agent systems with single-integrator dynamics, where the control input of each agent no longer remains constant but updates periodically within the time interval between two consecutive triggering instants. Then, the proposed scheme is extended to the general linear multi-agent systems. By comparing with the time-triggered control(TTC) method and the existing event-triggered control(ETC) methods, the control performance of the proposed ETPC scheme is almost the same as that of the TTC approach, and the communication payload between agents is reduced with much less triggering times than existing ETC methods. Finally, two numerical examples are given to verify the theoretical analysis and demonstrate the superiority of the proposed method comparing with some existing methods. [ABSTRACT FROM AUTHOR]

• A novel distributed bipartite consensus control law based on quantized relative state measurements is proposed, in which only the relative output information of neighboring agents is utilized. We consider a broad class of Lipschitz nonlinear dynamics, which are reflective of many real-world scenarios. • Both quantized communication and aperiodic DoS attacks are studied in the context of secure bipartite consensus over signed graph. The observer-based control strategy, based on the leader–follower framework, can guarantee that the consensus and observer errors go to zero or bounded by selecting the control parameters properly. • We also develop a new control law depending on quantized output state measurements, which is fully distributed and do not need to know a priori knowledge of any global information. In particular, two adaptive couplings constructed in sensor-to-observer, and controller-to-actuator channels, respectively, which can alleviate the burden of the limited bandwidth and energy consumption more effectively. • The elements, including fully distributed control, logarithmic quantizer, DoS attacks, observer based control approach, and antagonistic interactions are investigated simultaneously for the first time to consider secure control. The derived results are more general. This paper is intended to solve the fully distributed secure bipartite consensus problem of nonlinear multi-agent systems (MASs) with quantized information under Denial-of-Service (DoS) attacks. The attacks, which constrained on attack frequency and duration are studied. Firstly, we propose a novel secure output feedback control protocol integrated of the logarithmic quantizer and relative output measurements of neighboring agents, which can realize secure control under DoS attacks by choosing the design parameters correctly. Secondly, an adaptive control protocol that includes dynamic coupling strengths into the control law and the state observer function is developed. Contrast to the single adaptive control strategy, two adaptive couplings constructed in sensor-to-observer, and controller-to-actuator channels, respectively, which can alleviate the burden of the limited bandwidth and energy consumption more effectively. Furthermore, this control strategy with dynamic coupling gains is fully distributed, under which agents are not required to know a priori knowledge of any global information and the quantizer only needs to quantize the output state error information of agents. Then, theoretical guarantees on the effectiveness of the proposed controllers in steering the system to a secure bipartite (bounded) consensus under quantized output measurements and intermittent DoS attacks are derived. Finally, the numerical simulation inspired by a real-world physical network system is developed to verify the usefulness of the presented controllers. [ABSTRACT FROM AUTHOR]

In this paper, the privacy-preserving-based bipartite consensus control problem is investigated for a class of discrete-time nonlinear multi-agent systems (MASs). The classical bipartite consensus control implementation relies on the explicit information exchange between agents, which will lead to the possible leakage of agents' private information, especially the initial states. Therefore, to prevent data disclosure to neighbors inside the MASs and the outside eavesdroppers, the data is encrypted by means of Paillier encryption scheme during information transmission. This means each agent first sends the relative data in the form of ciphertext to its neighbors for further encryption process, and then restores the control protocol based on the returned encrypted information from the neighbors. Since homomorphic encryption only works for integers, the data must be quantized before encryption, and it will inevitably result in the quantization error. On the other hand, for the purpose of saving communication resources, both decentralized and distributed event-triggered schemes are also proposed. Resorting to the Lyapunov stability theory and algebraic graph theory, sufficient conditions are derived ensuring that the MASs subject to a confidential communication agreement can achieve the bounded bipartite consensus. Two numerical examples are presented to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the distributed specified-time group consensus control with hard settling-time constraint and milder communication topology constraint. To this end, we propose two distributed control schemes by employing a motion planning approach for the single- and double-integrator systems. Compared with the most existing works over undirected communication topologies, the underlying topology of each group is required to be directed graphs in our proposed distributed controllers. Furthermore, the root vertex of one group is allowed to belong to the other group. The convergence analysis is performed via the algebraic graph theory and matrix theory. The results show that the agents in the same group can reach consensus within any prespecified settling-time instead of a conservative upper bound of the settling-time. Moreover, the designed specified-time group consensus protocols do not require continuous information exchange. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper studies the cooperative adaptive funnel tracking control problem for a class of uncertain nonlinear nonstrict feedback multi-agent systems with nonlinear faults, and the dynamic leader has nonlinear unknown function. By designing two value functions and combining with the back propagation neural networks, an event-triggered strategy that can be adjusted automatically is designed to reduce the waste of communication bandwidth. The Butterworth low-pass filter signal is introduced to solve the non-smooth function problems. In addition, the radial basis function neural networks are used to approximate unknown functions in the system. Then, an event-triggered control protocol is constructed, which can achieve the tracking performance and all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results confirm the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with consensus for fractional-order multi-agent systems by observer-type output feedback with positive constraint depicted by general linear model. First, an observer-based protocol is presented and the sufficient conditions for the consensus for fractional-order multi-agent systems with positive constraint are derived. Then, the simplified conditions without utilizing the detailed topology of the graph are given. In order to simplify the process of the solution of the feedback gain matrix and the observer gain matrix, the linear programming approach is used. When the system matrix is strictly Metzler, semidefinite programming approach is adopted. Finally, some illustration examples are presented as the verification of the obtained methods. [ABSTRACT FROM AUTHOR]

In this paper, the consensus of fractional-order multi-agent systems is studied. By utilizing the unique properties of fractional-order calculus, namely hereditary and infinite memory, a new design scheme of the event-triggered pinning impulsive control strategy is proposed. Compared with the fixed pinning technique, the pinning agents here can be variable at each impulsive instant based on the considered two pinning rules (i.e., selecting randomly and according to the distances of error states). With the introduced rules, sufficient conditions are derived for consensus of systems, and the Zeno behavior is also excluded. Finally, our results show that the distance-ordered pinning can be achieved faster than the one with randomly pinning selection, and the inner impulsive gain of the impulsive controller can not be too large. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered output feedback consensus problem for feedforward nonlinear multi-agent systems with a directed topology graph. To avoid continuous monitoring and communication among agents, the periodic sampled-based output information is adopted to construct the observer. The observer-based controller for every agent updates under a newly designed triggering mechanism, which relies on its output and the relative output information of its neighbour agents at sampling points. With the designed event-triggered control protocol, the leader-follower consensus is achieved and the Zeno behavior is excluded effectively. Moreover, the sampling period and state delay of the considered system can be arbitrary positive numbers. Finally, the consensus result is extended to a class of feedforward multi-agent systems with the system nonlinearities satisfying the increment ratio of an unbounded time-varying function. A simulation example with two cases is given to demonstrate the proposed event-triggered control protocols. [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 studies the fixed-time containment of the second-order nonlinear multi-agent system (MAS) accompanied by switching topologies and event-triggered communication. The agent is subjected to unknown nonlinear dynamics. A fixed-time RBF observer was constructed based on information obtained from neural networks and event-triggered communication. By combining the controller with the identification information from the observer, it is demonstrated that the system can achieve practical fixed-time output feedback containment and exclude Zeno behavior during the control process. The effectiveness of the proposed event-triggered control method for fixed-time output feedback containment control of the second-order nonlinear MAS is verified by simulation examples. [ABSTRACT FROM AUTHOR]

Distributed optimization, combining cooperative control and optimization objectives, is vital for practical applications. While current research predominantly focuses on linear multi-agent systems, the real-world demands often involve nonlinear systems with finite or fixed time constraints. This paper addresses the finite-time/fixed-time distributed optimization for nonlinear multi-agent systems with time-varying cost function. Under appropriate assumptions, we propose a finite-time distributed protocol and a fixed-time distributed protocol for the nonlinear multi-agent systems to ensure all agents achieve consensus and minimize the time-varying cost function, relaxing the conditions for strong convexity and bounded gradient difference of the cost function. Simulation experiments validate the effectiveness of these distributed protocols. [ABSTRACT FROM AUTHOR]

The bumpless transfer consensus control problem for linear homogeneous multi-agent systems subject to agent-dependent switching directed communication topologies is investigated in this paper. According to the information of graph Laplacian matrix and relative state of agent, we propose a novel agent-dependent switching law to guide the switching among these topologies, then the leader-following consensus performance of multi-agent systems is achieved via using the multiple Lyapunov functions method. Further, since the switching consensus controllers are considered, the control signal bumps are inevitable at switching instants, and some sufficient conditions via linear matrix inequalities are developed to pursue the bumpless transfer performance of multi-agent systems. Besides, the agent-dependent switching law also allows the error dynamics under each directed subtopology to be unstabilizable. Finally, the theoretical results are verified by two illustrative examples. [ABSTRACT FROM AUTHOR]

The problem of distributed fixed-time leader-following consensus tracking control for nonholonomic chained-form dynamic systems with nonlinear disturbances is considered in this paper. Compared with the existing works, this paper considers a class of more general nonholonomic multi-agent systems where both the leader and the followers have nonlinear uncertainties. For undirected graphs, a distributed observer for each follower is investigated such that both the leader state and input can be estimated by the followers in a fixed time. Based on the distributed observers, a consensus tracking controller is proposed to ensure that the tracking errors convergence to zero within a fixed time. Lyapunov analysis proves the stability of the closed-loop system. A simulation example of wheeled mobile robots is given to demonstrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

This paper investigates the formation containment control under sampling and with time delays for multi-agent systems (MASs). First, a novel sampling control protocol for the MASs to achieve formation containment is proposed, where the communication among agents is only occurred at the sampling instance. Then the communication load and the waste of energy can be decreased significantly. In addition, time delays are considered in this paper. Second, by establishing an appropriate Lyapunov function, sufficient conditions for MASs with sampled data and time delays reaching formation containment are obtained by handling the established Lyapunov function. Finally, the obtained results are demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the consensus problem of nonlinear multiagent systems with uncertainties and switching network topology under truncated prediction feedback approach subjected to periodic scaling attacks. Here, a type of deception attack known as periodic scaling attack have been taken into consideration for both undirected and directed graphs during agent's communication. The fundamental purpose of this paper is to develop a state feedback controller that can withstand actuator faults while ensuring the resultant closed loop systems. Furthermore, the truncated prediction feedback approach is utilized for handling input delays and then, a set of necessary conditions are derived in terms of linear matrix inequalities by developing an appropriate Lyapunov–Krasovskii functional. Eventually, to demonstrate the significance of the established theoretical results, two numerical simulation are conferred. [ABSTRACT FROM AUTHOR]

This paper examines the concept of the leader–follower formation for fractional-order multi-agent systems (FO-MASs) by utilizing dynamic event-triggered sliding mode control (SMC) method. Firstly, a dynamic event-triggered mechanism (DETM) is designed relying on the combined measurement vector, in which an auxiliary variable is introduced to dynamically adjust the threshold for each fractional-order agent system. Unlike most existing event-triggered communication mechanisms, whose threshold parameters are always fixed, the threshold parameters in our designed event-triggered conditions can be dynamically adjusted according to the fractional-order dynamic rule. Numerical results show that the proposed DETM can achieve a better system performance in reducing the sampling frequency and the expected formation performance. Secondly, the leader–follower formation control problem is transformed into checking the asymptotic stability problem of the closed-loop system. In addition, due to the memorability of fractional calculus operators, a distinctive condition is established to avoid the occurrence of Zeno behaviors reported in existing dynamic event-triggered schemes. Finally, a simulation example is presented to illustrate the effectiveness and feasibility of the dynamic event-triggered SMC method proposed in this paper. [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]

This paper considers the point-to-point consensus tracking control for a class of nonlinear multi-agent systems with completely unknown dynamics, where the consensus is concerned with some given desired points instead of the entire desired trajectory. It is assumed that the multi-agent system executes repetitive coordination tasks in a finite time interval and the iterative learning control is also utilized to design a consensus protocol with learning ability. To deal with the unknown nonlinear agent's dynamic, the relationship between agent's output at these given points and agent's control input is first derived and then a data-based model referring to the agent's dynamic is established by utilizing the iteration-domain dynamical linearization technique. Then, a data-driven iterative learning protocol is developed by optimizing two performance indexes, which contains a control input updated algorithm, a parameter estimation algorithm and a reset algorithm. The results show that the proposed design can achieve the point-to-point consensus tracking task only by using the I/O data of the agent. Finally, simulation examples are provided to verify the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed linear quadratic tracking control problem for multi-agent leader–follower systems. Considering that only few followers can access the state information of the leader owing to the limited communication range, a novel distributed control law is designed to make followers convergent to the leader by introducing appropriate interconnections among the followers. Besides the tracking consensus of the leader–follower systems, the designed control law also enables the associated cost to be less than a given tolerance for any initial states of the leader and the followers. The implementation of the designed distributed control law can be executed by solving a single Riccati equation, requiring no global information of the communication topology. Two examples are finally provided to demonstrate the effectiveness of the proposed method. [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, distributed state and output feedback control law based on the dynamic event-triggered mechanism are proposed to solve the robust cooperative output regulation problem for a class of general linear uncertain multi-agent systems (MASs) subject to external disturbances. The discrete-time control law proposed for each agent is equivalent to a discrete one and thus directly implementable in the digital platform. Our design can handle parametric uncertainties, reject external disturbances and track a dynamic leader while excluding the Zeno phenomenon by providing the existence of a lower bound for inter-event times of each agent, the efficiency of which is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the finite-iteration tracking issue of multi-agent systems is investigated with the distributed optimization method. Since the infinite-iteration strategy is unrealistic, the finite-iteration approach is adopted to study the problem. Moreover, the tracking performance is undesired for the traditional iterative learning schemes. Then optimization technique is used to cover the drawback. The tracking error is regarded as the optimization objective, and the consensus tracking issue is considered as the distributed optimization problem. An appropriate learning control strategy is designed on the basis of the gradient of the tracking error. Further, the optimization issue can be solved by means of the finite-iteration approach, and the learning algorithm can improve the tracking performance. Theoretical results are proposed by using the norm estimation and some inequalities skills. At last, a numerical simulation is given to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

With the development of big data and artificial intelligence, distributed optimization has emerged as an indispensable tool for solving large-scale problems. In particular, the multi-agent system based on distributed information processing can be elaborately designed for distributed optimization, in which the agents collaboratively minimize a global objective function made up of a sum of local objective cost functions subject to some local and/or global constraints. Inspired by the applications involving resource allocation, machine learning, power systems, sensor networks and cloud computing, a variety of distributed optimization models and algorithms have been investigated and developed. The optimization models include unconstrained and constrained problems in continuous and discontinuous systems with undirected and directed communication topology graphs. The constraints include bounded constraint, separable and inseparable equality and inequality constraints. Meanwhile, in distributed algorithms, every agent executes its local computation and updating on basis of its own data information and that exchanging with its neighboring agents by means of the underlying communication networks, in order to deal with the optimization problems in a distributed way. This paper is designed to provide a comprehensive overview of extant distributed models and algorithms for distributed optimization. [ABSTRACT FROM AUTHOR]

This paper focuses on the distributed adaptive finite-time control problem for nonlinear multi-agent systems (MASs). The fast practical finite-time criterion is extended to MASs. As such, a distributed adaptive finite-time protocol is established based on the recursion algorithm and neural networks (NNs), which provides a solution to cope with the adaptive finite-time regulate problem. Moreover, the proposed scheme is able to address the singular problem existing in the adaptive fuzzy/NN practical finite-time control. Furthermore, a simpler adaptive law is constructed. Finally, the presented method is applied to multiple robotic systems to illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

In this study, the novel fully distributed asynchronous event-triggered protocols that use sampled state information are developed to address the leader-follower and leaderless consensus issues for the general linear multi-agent systems with physically interconnected network. By designing the state estimate of each follower agent, the protocols avoid the requirements for the continuous communication. Meanwhile, this paper proves that the designed protocols don't exhibit the Zeno behavior in any finite time by giving a strictly positive lower-bound of the minimum inter-event interval. In contrast to the existing related papers, the salient features of this study are that both physically interconnected network and communication network of the multi-agent systems are considered and the developed protocols don't require global network information, which reduce the conservativeness of previous systems modeling and protocols. Finally, two simulation results are provided to display the performance and effectiveness of the protocols. [ABSTRACT FROM AUTHOR]

• This paper addressed the leader-following consensus of multi-agent systems (MASs) under a class of antagonistic networks. • For antagonistic and directed networks with structurally balanced properties, sufficient conditions are established under which the MASs will achieve bipartite consensus. • Simulation results are also given to verify the effectiveness of our methods. In this paper, we address the leader-following consensus of multi-agent systems (MASs) under a class of antagonistic networks. Different from the traditional literature, in our model, whether a follower can access the leader depends on a matrix instead of a scalar. For antagonistic and directed networks with structurally balanced properties, sufficient conditions are established under which the MASs will achieve bipartite consensus. Detailed algorithms are proposed to design the gain matrices and the coupling strength. What is more, we design adaptive laws to self-tune the value of the coupling strength. Simulation results are also given to verify the effectiveness of our methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel control scheme is developed to solve an optimal containment control problem of unknown continuous-time multi-agent systems. Different from traditional adaptive dynamic programming (ADP) algorithms, this paper proposes an internal reinforcement ADP algorithm (IR-ADP), in which the internal reinforcement signals are added in order to facilitate the learning process. Then a distributed containment control law is designed for each agent with the internal reinforcement signal. The convergence of this IR-ADP algorithm and the stability of the closed-loop multi-agent system are analyzed theoretically. For the implementation of the optimal controllers, three neural networks (NNs), namely internal reinforcement NNs, critic NNs and actor NNs, are utilized to approximate the internal reinforcement signals, the performance indices and optimal control laws, respectively. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study multi-agent systems with asymmetric information structure. Due to limited channel capacity in communication network, the information in routing path suffers a transmission delay. Instead of the game theoretic setting, we formulate the problem as an online quadratic optimization problem subject to stochastic systems involving input delay. Since the probability statistics of system noise is unknown, the decision-maker can not utilize the traditional optimal control strategies. Motivated by online convex optimization theory, we introduce the notion of regret, which measures the cumulative performance difference between the optimal statistics known (offline) index value and the statistics unknown (online) index value. The contributions of this paper are twofold. First, utilizing the linear minimum mean square biased estimate, we derive a learning based control policy and then characterize its behavior. Second, under some basic assumptions, we further prove that the regret grows at a sub-linear rate and it is explicitly bounded by O (ln T). [ABSTRACT FROM AUTHOR]