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This paper considers the prescribed-time event-triggered consensus for a class of nonholonomic multi-agent systems (MASs) with external disturbances. Firstly, the nonholonomic chained MASs are divided into two subsystems, and a switching control scheme is introduced. Secondly, a distributed prescribed-time continuous protocol is proposed to ensure that all agents reach average consensus within a prescribed finite-time. Moreover, to reduce the communication costs, an event-triggered consensus protocol is further established and some related theorems are given. In addition, the Zeno behaviour can be excluded by choosing parameters appropriately. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

In this article, a robust index named first-order network coherence (FONC) for the multi-agent systems (MASs) with layered lattice-like structure is studied via the angle of the graph spectra theory. The union operation of graphs is utilized to construct two pairs of non-isomorphic layered lattice-like structures, and the expression of the index is acquired by the approach of Laplacian spectra, then the corresponding asymptotic results are obtained. It is found that when the cardinality of the node sets of coronary substructures with better connectedness tends to infinity, the FONC of the whole network will have the same asymptotic behavior with the central lattice-like structure in the considered classic graph frameworks. The indices of the networks were simulated to illustrate the the asymptotic results, as described in the last section. [ABSTRACT FROM AUTHOR]

This paper considers the distributed cluster optimisation problem of multi-agent systems (MASs). Different from existing optimisation problems, the MASs are divided into several clusters, and each cluster has its own optimisation objective which is the sum of their local objective functions. Firstly, based on communication topology, the distributed optimisation problem with two clusters is considered and a kind of distributed control protocol is proposed. By using the fixed-time stability theory and the convexity of function, it is proved that the MASs can not only achieve cluster consensus in a fixed-time interval, but also solve the optimisation problem asymptotically. Secondly, the MASs with multiple clusters are further considered. We extend the proposed protocol to a more general case and also prove that MASs can achieve cluster consensus in fixed-time and asymptotically reach the optimal solution of the optimisation objective. Finally, some numerical simulations are presented to show the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]

This article considers the fixed‐time distributed optimization problem of multi‐agent systems with external disturbances, in which the global optimization objective is a convex combination of local objective functions. To solve this issue, a directed communication network is carefully designed, and an integral sliding mode control protocol is proposed based on the gradient of global objective function first. Moreover, two distributed optimal protocols are designed by using the gradient and the Hessian matrix of local objective function, respectively. By employing Lyapunov stability theory, graph theory, convex analysis, and inequality techniques, we prove that all proposed protocols can make agents achieve consensus and converge accurately to the optimal solution of the considered problem in some fixed‐time intervals. Finally, some numerical simulations are given to verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system's robustness. Graph operations are applied to design the novel multi-layered networks, and a graph spectrum approach, along with analysis methods, is applied to derive the mathematical expression of the coherence, and the corresponding asymptotic results on the performance index have been obtained. In addition, the coherence of these non-isomorphic multi-layered networks with three different graph parameters are compared and analyzed. We find that, when the cardinalities of the vertex sets of corresponding counterpart layers are the same, the multi-layered topology class with a balanced, complete, multi-partite structure has the best robustness of all the considered networks, if the sufficient conditions for the node-related parameters hold. Finally, simulations are given to verify the asymptotic results. [ABSTRACT FROM AUTHOR]

This study concentrates on a fixed-time distributed optimization problem for multi-agent systems (MASs) with input delay and external disturbances. First, by adopting the Artstein model reduction technique, the time-delay system is first transformed into a delay-free one, and external disturbances are then effectively eliminated by using an integral sliding mode control strategy. Second, a new centralized optimization mechanism is developed that allows all agents to reach the same state in a fixed time and then converge to the optimal value of the global objective function. Meanwhile, the optimization problem is extended to switching topologies. Moreover, as the gradient information of the global objective function is difficult to obtain in advance, we construct a decentralized optimization protocol that enables all agents to acquire the same state in a certain amount of time while also optimizing the global optimization problem. Finally, two numerical simulations are presented to validate the effectiveness and reliability of the developed control strategy. [ABSTRACT FROM AUTHOR]

This paper studies a generalized distributed optimization problem for second-order multi-agent systems (MASs) over directed networks. Firstly, an improved distributed continuous-time algorithm is proposed. By using the linear transformation method and Lyapunov stability theory, some conditions are obtained to guarantee all agents' states asymptotically reach the optimal solution. Secondly, to reduce unnecessary communication transmission and control cost, an event-triggered algorithm is designed. Moreover, the convergence of the algorithm is proved, and the Zeno behavior can be avoided based on strict theoretic analysis. Finally, one example is given to verify the good performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article mainly studies first-order coherence related to the robustness of the triplex MASs consensus models with partial complete graph structures; the performance index is studied through algebraic graph theory. The topologies of the novel triplex networks are generated by graph operations and the approach of graph spectra is applied to calculate the first-order network coherence. The coherence asymptotic behaviours of the three cases of the partial complete structures are analysed and compared. We find that under the condition that the number of nodes in partial complete substructures n tends to infinity, the coherence asymptotic behaviour of the two sorts of non-isomorphic three-layered networks will be increased by r − 1 2 (r + 1) , which is irrelevant to the peripheral vertices number p; when p tends to infinity, adding star copies to the original triplex topologies will reverse the original size relationship of the coherence under consideration of the triplex networks. Finally, the coherence of the three-layered networks with the same sorts of parameters, but non-isomorphic graphs, are simulated to verify the results. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time distributed optimisation problem for multi-agent systems (MASs) is investigated by proposing a kind of new event-based aperiodically intermittent communication strategy. Firstly, the distributed optimisation problem with the sum of local objective functions is considered. A novel finite-time event-triggered intermittent control protocol is proposed over undirected networks, and some sufficient conditions are obtained to ensure the finite-time consensus of MASs and the asymptotical solvability of the optimisation problem. Secondly, a more general distributed optimisation problem, in which the optimisation objective is the convex combination of local objective functions, is considered and we also prove that MASs can achieve consensus in finite-time and asymptotically reach the optimal solution under the proposed protocol over directed networks. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper discusses the prescribed-time leader-follower consensus and containment control problems for a class of nonlinear multi-agent systems with external disturbances. First, an event-triggered control protocol with sign function is proposed, which can ensure that all agents achieve consensus within a prescribed time. Second, as the sliding mode control has the advantage of good robustness to external disturbances, an improved event-triggered control protocol is designed by using the integral sliding mode control method and some sufficient conditions are derived for achieving the prescribed-time leader-follower consensus. Moreover, the prescribed-time containment control problem for multi-agent systems with multiple leaders is investigated by using the event-triggered control strategy. It is shown that Zeno behavior can be excluded in the above consensus issues by choosing parameters appropriately. Finally, several numerical examples are given to demonstrate the effectiveness and reliability of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article considers the consensus of multi‐agent systems (MASs) with external disturbances by using sliding mode control. First, by establishing a novel sliding mode surface and designing a sliding mode control protocol with constant gains, the consensus of MASs with unknown bounded disturbances is studied. Second, based on the barrier function, a new type of adaptive sliding mode switching protocol is proposed, in which the control gains can be chosen randomly and the upper bound of the disturbance does not need to be known in a prior. By using this protocol, the consensus error can converge to any given region of zero in finite time. Moreover, the leaderless consensus and leader‐following tracking problem of MASs with general dynamics and external disturbances are also investigated via extending the proposed adaptive sliding mode protocol. Finally, some examples are presented to illustrate the effectiveness of the control strategies. [ABSTRACT FROM AUTHOR]

In this paper, we devise a distributed protocol to study the consensus of multi-agent systems (MASs) with input saturation over directed networks. Firstly, a low-gain feedback control method is applied to overcome the saturation constraints, and an observation system without saturation constraints is designed. The semiglobal consensus condition over directed strongly connected networks is developed by using Ricatti equation. Secondly, a novel of tree-type error scheme is proposed to solve the consensus of MASs with general directed spanning tree networks. Combination with inequality techniques and Lyapunov stability theory, some criteria for achieving semiglobal consensus are obtained. In addition, the semiglobal consensus of MASs with directed switching networks is further considered, in which the network topologies only need to contain a directed spanning tree in some time intervals. Some related conditions are derived to ensure the consensus. Finally, some numerical simulations are given to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This study investigated the limited‐budget finite‐time average consensus problem of multi‐agent systems. Different from the existing results about the guaranteed‐cost asymptotical consensus, all agents can achieve the average consensus within a finite time and the limited budget can be given previously. Firstly, a novel consensus protocol is proposed with non‐linear cost indexes to trade off the control energy consumption against the consensus regulation performance for the limited budget within a finite time. Then, sufficient conditions for limited‐budget finite‐time average consensus design and analysis are respectively given, where the limited budget is utilised to determine the value range of the control gain, and the consensus value obtained by all agents is the average of initial states. Moreover, for the case without giving the limited budget, guaranteed‐cost finite‐time average consensus design and analysis criteria are presented, respectively, in which an upper bound of the cost index is determined. Finally, a numerical simulation is shown to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the guaranteed cost consensus problem for second-order multi-agent systems with directed topology is considered, in which each agent has a heterogeneous inertia and control gain. The distributed control protocols with the absolute and relative velocity dampings are proposed, respectively. In each kind of protocol, both the communications with and without the input time delay are also considered. By introducing the auxiliary variables and using Lyapunov stability theory, some sufficient conditions are given to achieve the consensus. Moreover, the upper bounds of the guaranteed cost functions are obtained. Finally, some simulation examples are presented to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, a periodic intermittent sampled data control strategy, which both reduces the load of updating rate of the controller and cuts down the working time of the controller in each sampling interval, is proposed to investigate the second-order consensus of multiagent systems. In order to reach consensus, a necessary and sufficient condition depending on the coupling gains, the communication width, the sampling period, and the spectrum of the Laplacian matrix, is established. Furthermore, the feasible region of communication width is derived for given coupling gains and structure of network. Besides, the coupling gains are also carefully designed. On the other hand, when the time delay exists in the sampling process, a time delayed protocol is proposed. A necessary and sufficient condition based on the communication width, the sampling period, the coupling gains, the time delay, and the network structure is also derived for achieving consensus. It is amazing found that the sampling period should have both lower and upper bounds for given time delay and communication width for the sake of reaching consensus. Finally, several numerical simulations are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the cluster consensus problem with delays of first-order nonlinear multi-agent systems is studied through pinning leader-following approach with periodic intermittent effect. The graph of the networked system is assumed to be directed and weakly connected. A new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link, specifically, the agents in each cluster are divided into three subsets due to the orientation of their topological degree, and each subset of agents is controlled by an individual law. A redefined notion on cluster consensus with two sorts of time delays is proposed in this article. Some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay, while agents in different clusters reach consensus with delays via following their leaders. Some numerical simulations are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper discusses the consensus problem of second-order multiagent systems with nonlinear dynamics. A directed spanning tree--based adaptive control protocol is developed, which overcomes the drawback that the spectrum of the Laplacian matrix must be known a priori. A scheme for reordering the nodes is proposed. Applying the developed method and the Lyapunov stability theory, some distributed adaptive laws are designed in the directed network. It is found that the consensus can be achieved by randomly choosing a directed spanning tree and using the developed distributed adaptive law. Finally, an example is presented to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consensus problem for second-order multi-agent systems with inherent delayed nonlinear dynamics and aperiodically intermittent communication. First, different from previous works, aperiodically intermittent communication is proposed. Moreover, two types of delay are considered. The first case is that the delay is small enough so that it is less than the minimum of communication width. The other one is that the delay is time-varying and large, and in this case, we do not restrict the delay less than the communication width. Different approaches are provided to study these two cases, and some conditions are obtained to achieve second-order consensus under a fixed strongly connected and balanced topology. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a class of consensus protocol for detail-balanced networks of agents with general Lipschitz-type nonlinear dynamics and external disturbances is investigated. To guarantee asymptotic consensus in such a multi-agent system, several distributed controllers are constructed based only on the relative state information of neighboring agents. By appropriately constructing Lyapunov function and using tools from M-matrix theory, some sufficient conditions for achieving distributed consensus are provided. Finally, two examples and simulations are given to illustrate the effectiveness of the obtained theoretical result. [ABSTRACT FROM AUTHOR]

Output swarm stability and stabilization problems for high-order linear swarm systems with directed interaction topologies are investigated. First, sufficient conditions for output swarm stability are presented, and an approach is proposed to determine the absolute output motion, where the influences of initial states of agents and swarm stabilizing protocols are given. Moreover, it is shown that swarm systems with the same initial states but different balanced interaction topologies have the same absolute output motion. Then, sufficient conditions for output swarm stabilization, which are independent of the number of agents, are presented. Finally, numerical simulations are shown to illustrate the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

The leader-following consensus problem of fractional-order multi-agent systems is considered. In the system, the dynamics of each agent and leader are nonlinear systems. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and Lyapunov method. Several simulation examples are presented as a proof of concept. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results. [ABSTRACT FROM AUTHOR]

In this paper, the observer-based leader-following consensus problem for multi-agent systems with input saturation is studied under fixed and switching topology. Firstly, based on the measurable output information of systems, we construct an auxiliary observation system to estimate the real state information of systems. At the same time, the centralized event-triggered control is considered in the fixed and switching topology, and the Lyapunov function and Cauchy's convergence criterion are used to prove that the consensus of systems can be achieved. Secondly, the sufficient conditions of the event-triggered function are given, and it is proved that the constructed centralized event-triggered function can exclude the Zeno behavior. Then, the group case is considered in the fixed topology, and it is emphasized that the group event-triggered mechanism has the idea of event-triggered and decentralized control. Finally, the validity and feasibility of the theoretical results are illustrated by numerical examples. [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]