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The consensus problems of fractional-order multi-agent systems(FOMAS) are investigated under a fixed interaction graph. A consensus protocol that has current and time-delay states is designed. The conception of practical consensus of FOMAS is proposed. The asymptotical consensus condition is obtained by taking advantage of Laplace transform. Furthermore, the practical consensus condition of the FOMAS with the protocol is given by direct derivation. Through numerical simulation, we find that the standard control protocol can not achieve consensus in some situations. However, the proposed protocol could make the states of multi-agent be consensus or even practical consensus. [ABSTRACT FROM AUTHOR]

The group consensus problems of heterogeneous multiagent networks with input time delays are investigated in this paper. In this complex networks, the agents’ dynamics are modeled by the first-order and the second-order multiagent systems, where a novel dynamic group consensus protocol is designed through the competitive relationship among the agents. By using matrix theory and the frequency-domain method, some algebraic criteria are theoretically established for reaching a group consensus in the following two cases: 1) with the identical and 2) different input time delays. Meanwhile, the conservative assumptions existed in the relevant literatures are absolutely relaxed, i.e., the in-degree balance and the geometric multiplicity of zero eigenvalue of Laplacian matrix are at least two. Finally, the effectiveness of our results is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper proposes a control framework, called pulse-modulated intermittent control, which unifies impulsive control and sampled control. Specifically, the concept of pulse function is introduced to characterize the control/rest intervals and the amplitude of the control. By choosing some specified functions as the pulse function, the proposed control scheme can be reduced to sampled control or impulsive control. The proposed control framework is applied to consensus problems of multiagent systems. Using discretization approaches and stability theory, several necessary and sufficient conditions are established to ensure the consensus of the controlled system. The results show that consensus depends not only on the network topology, the sampling period and the control gains, but also the pulse function. Moreover, a lower bound of the asymptotic convergence factor is derived as well. For a given pulse function and an undirected graph, an optimal control gain is designed to achieve the fastest convergence. In addition, impulsive control and sampled control are revisited in the proposed control framework. Finally, some numerical examples are given to verify the effectiveness of theoretical results. [ABSTRACT FROM PUBLISHER]

This study studies the protocol of robust synchronisation of second‐order multi‐agent systems via pinning control. First, it is shown that, for the second‐order multi‐agent system with disturbances, by pinning one node with small coupling strength, the whole system can reach synchronisation. Then, these results are applied to the cooperative control of multiple 3‐degree of freedom helicopters systems with disturbances. Finally, simulations are performed to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the distributed average tracking (DAT) problem for disturbed second-order multiagent systems, where a crowd of agents is required to track the average of the multiple time-varying signals. First, a new kind of distributed average estimator is developed for each agent to estimate the average of the multiple time-varying signals in finite time. The protocol possesses the distinguished feature of robustness to initialization errors, which can recover from network alterations. Then, an observer-based finite-time tracking protocol is proposed to make each agent exactly track the average of the multiple time-varying signals in finite time in the absence of velocity measurement. By carefully analyzing the dynamic properties of the tracking error system, a suitable Lyapunov function is constructed to estimate the settling time for convergence of the tracking error system theoretically. Furthermore, an adaptive DAT protocol is proposed, which is a fully distributed protocol because it can solve the DAT problem without using any global information. Finally, two simulation examples are provided to verify the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

Distributed consensus tracking problem of networked agent systems with directed topologies under denial-of-service (DoS) attacks is investigated. The considered networked agent network consists of a physical layer with fixed physical links and a cyber layer with cyber control units. Both the communication network connecting these two layers and the cyber communication network within the cyber layer may subject to malicious DoS attacks. These two types of attacks have different impacts on the networked system; the former one affects the timely update of control inputs, and the latter influences the connection weights of the cyber communication graph. First, for DoS signals occurring in the communication network which transmits the state and control input information between the two layers, the distributed control protocol based on the event-triggered scheme and locally deployed estimators are designed. Efficient algorithms for selecting event-triggered control parameters and Zeno-free triggered parameters are given to ensure the mean-square consensus. The relationships between the system’s parameters and the features of DoS attacks are successfully revealed. Second, corresponding theoretical analysis is derived for consensus tracking of the networked systems when DoS attacks are launched within the cyber layer. Conditions concerning the length of repairing time and indexes of DoS attacks are given by utilizing hybrid control theory. At last, the effectiveness of the obtained results is demonstrated by performing simulations on multirobot systems. [ABSTRACT FROM AUTHOR]

This article investigates the distributed optimal cooperation problems for multiple high-order systems, in which the dynamics of each agent is allowed to be subject to unknown nonlinearities. To eliminate the effect caused by unknown nonlinearities, a nonlinearity estimator is developed based on agents’ states, which successfully reconstructs the nonlinear dynamics if the unknown nonlinearities are bounded. And to minimize the sum of multiple local nonlinear cost functions with Lipschitz-type gradients, a couple of static and adaptive state-dependent algorithms are designed, respectively, where each agent may only have access to its own local cost function. It is challenging to solve such an optimal cooperation problem as the performance of the whole multiagent network is evaluated by the sum of all local performance functions. In order to fulfill the goal of cooperative optimization, a state-dependent distributed optimal cooperation algorithm is proposed first. By utilizing tools from the Lyapunov stability theory and convex optimization analysis, it is proven that the considered distributed optimal cooperation problem for high-order nonlinear systems can be solved by the proposed optimal cooperation algorithm if the state-dependent parameters are suitably selected. It is noted that the selections of the state-dependent parameters depend on some global information of the multiagent systems. Furthermore, by incorporating the proposed optimal cooperation algorithm with adaptive parameters strategy, the optimal cooperation problem is solved in a fully distributed manner. Finally, a numerical simulation is shown to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This study studies second‐order consensus of multi‐agent systems with noise in a leaderless architecture. Two distributed consensus algorithms are designed and sufficient conditions are established, which character how much the noise intensity or the delay multi‐agent systems can stand such that second‐order consensus can be reached almost surely for a given coupling strength and topology structure. Simulations are given to illustrate the effectiveness of the proposed consensus algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the robust fixed-time consensus problem for multiagent systems with nonlinear dynamics and uncertain disturbances under a weighted undirected topology is investigated. Some nonlinear control protocols are proposed under which fixed-time consensus in the considered multiagent systems can be ensured. Compared with the initial-condition based finite-time consensus, it is theoretically shown that any prescribed convergence time for the achievement of consensus can be guaranteed within fixed time regardless of the initial conditions. Furthermore, the achievement of consensus is shown to be robust against bounded uncertain disturbances affecting the agents. Finally, some numerical examples are provided to illustrate the performance and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: Nowadays, multi-agent systems (MAS) are ubiquitous in the real world. Consensus is a fundamental natural phenomenon. Over the past decade, consensus of MAS has received increasing attention from various disciplines. This paper aims to further investigate a novel kind of cluster consensus of MAS with several different subgroups. Based on Markov chains and nonnegative matrix analysis, two novel cluster consensus criteria are obtained for MAS with fixed and switching topology, respectively. Furthermore, numerical simulations are also given to validate the effectiveness of these proposed criteria. The proposed cluster consensus criteria have some potential applications in real world engineering systems. [Copyright &y& Elsevier]

In the above paper [1], there are errors regarding the description of (4), and misquotes in Algorithm 1 and 2. In Algorithm 1, the first equation referenced should be (5) and not (40). In Algorithm 2, the first equation referenced should be (40) and not (5). The correction for (4) is as follows: \begin{equation*} \mathcal {L}^{(\sigma (t))}=\left [{\begin{array}{cc} \widetilde {\mathcal {L}}^{(\sigma (t))}& \mathrm {a}^{(\sigma (t))}\\ \mathrm {0}_{N}^{T}& 0 \end{array}}\right ] \tag{4}\end{equation*} where \widetilde \mathcal L^(\sigma (t))\in \mathbb R^N\times N , \mathrm a^(\sigma (t))=-[a1(N+1)^(\sigma (t)),a2(N+1)^(\sigma (t)),\cdots ,~aN(N+1)^(\sigma (t))]^{T}\in \mathbb {R}^{N} , and \mathcal A^(\sigma (t)) = [aij^(\sigma (t))](N+1) \times (N+1) is the adjacency matrix of \mathcal G^(\sigma (t)) . [ABSTRACT FROM AUTHOR]