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In this paper, the $ H_{\infty } $ H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and $ (x, u, v) $ (x , u , v) -dependent noises is studied. Firstly, the $ H_{\infty } $ H ∞ consensus problem is transformed into a standard $ H_{\infty } $ H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified $ H_{\infty } $ H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It $ \hat {\rm {o}} $ o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: Event‐triggered consensus of multi‐agent systems (MASs) under directed topology is investigated in this paper. First, one shortcoming about the event‐trigger conditions in some recent results is pointed out through a counterexample. Then, two reasonable event‐trigger conditions are proposed and analyzed. Meanwhile, a novel dynamic event‐trigger strategy is applied in the two designed event‐trigger conditions, in which an auxiliary term is introduced for each agent to regulate its threshold dynamically. It is proved that the dynamic term plays an essential role in excluding Zeno behavior. The case of strongly connected topology is first investigated. Then, the results are extended to the more general topology containing a spanning tree. Numerical example is provided to illustrate the effectiveness of the designed event‐trigger conditions. [ABSTRACT FROM AUTHOR]

In this article, the effects of different models on the controllability of leader‐follower dynamics system based on Laplacian matrix are studied, and the controllability results applicable to general model are obtained. Our research is based on three different control modes, namely, broadcast control, UI$$ {U}_I $$ control, and non‐broadcast control, which cover all the control modes in the general model. Specifically, we first identify the relation of different UI$$ {U}_I $$ control, that is, if the system is controllable under i1$$ {i}_1 $$ different control signals, then increasing the number of control signals does not change the controllability of the system. Furthermore, it is proved that in a fixed topology, when the number of control inputs is increased, the controllability of the system is not correlated with the controllability of the original system, which appears counter‐intuitive. But the spectral radius of the Gramian matrix of the controllable system is increased. In addition, we analyze the condition number of Gramian matrix. Based on the above conclusions, we put forward the concept of hierarchical equivalent partition (HEP), and prove that under the general model, the existence of HEP makes the system uncontrollable. Finally, we expect to find a way to make the system controllable under the general model. Therefore, we obtain sufficient conditions for the system to be controllable. As a by‐product, we find that there is no completely uncontrollable graph when the general model with broadcast control is removed. [ABSTRACT FROM AUTHOR]

In this paper, the structural controllability of leader–follower systems over digraphs is discussed. Firstly, with the aid of leader–follower partition, we analyze the topological characteristics of systems without dilations. Moreover, we divide the digraph into the leader subgraph and the follower subgraph. By analyzing the topological characteristics of the follower subgraph, a sufficient condition to ensure the system structurally controllable is given. Furthermore, some special topologies of follower graphs are analyzed, such as unidirectional cycle graphs and directed paths, and the corresponding sufficient conditions of structural controllability are given. Meanwhile, a method to construct digraphs with structural controllability is presented. Finally, the strong structural controllability of directed tree graphs is considered, as well as the selection mechanism of leaders and the lower bound of the number of leaders under strong structural controllability are given. The above results reflect the effects of topologies on strong (or weak) structural controllability. [ABSTRACT FROM AUTHOR]

In view of the problems of large consumption of communication and computing resources in the control process, this paper studies a fundamental property for a class of multi-agent systems under event-triggered strategy: the S-stabilizability of a group of multi-agent systems with general linear dynamics under weakly connected directed topology. The results indicate that the S-stabilizability can be described in some way that the stabilizability region and feedback gain can evaluate the performance of the protocol. Firstly, a new distributed event-triggered protocol is proposed. Under this protocol, a kind of hybrid static and dynamic event-triggered strategy are presented, respectively. In particular, by using Lyapunov stability theory and graph partition tool, it is proved that the proposed event-triggered control strategy can guarantee the closed-loop system achieve S-stabilizability effectively, if at least one vertex in each iSCC (independent strongly connected component) cell receives information from the leader, which reflects the ability of distributed control law. Further, we demonstrate that the stabilizability can be realized if the initial system matrix A is Hurwitz. Moreover, it is confirmed that the designed static event-triggered condition is a limit case of dynamic event condition and can guarantee Zeno-free behavior. Finally, the validity of the theoretical results is proved by numerical simulation. [ABSTRACT FROM AUTHOR]

This article investigates the controllability of path and star graphs under the protocol of second-order neighbours. With identified special control nodes, a sufficient condition is first derived for the controllability of path graph by taking advantage of the protocol of second-order neighbours. Then necessary and sufficient conditions are developed respectively for the single and multiple leaders. Some differences between the protocol of second-order neighbours and first-order neighbours are also presented for path graph. Finally, a necessary and sufficient condition is proposed for the controllability of star graph by taking advantage of the protocol of second-order neighbours. [ABSTRACT FROM AUTHOR]

The event-triggered consensus problems of multi-agent systems without and with time delay under directed topology are investigated, respectively. The event-checkings are only implemented at periodic time instants. Under the designed consensus algorithm, the sampling period is permitted to be arbitrarily large. Another advantage of the designed consensus algorithm is that, for systems with time delay, consensus can be achieved for any finite delay only with the requirement that it is bounded by the sampling period. The case of strongly connected topology is first investigated. Then, the result is extended to the most general topology which only needs to contain a spanning tree. A novel method based on positive series is introduced to analyze the convergence of the closed-loop systems. A numerical example is provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The bipartite consensus of high-order edge dynamics is investigated for coopetition multiagent systems, in which the cooperative and competitive relationships among agents are characterized by positive weight and negative weight, respectively. By mapping the initial graph to a line graph, the distributed control protocol is proposed for the strongly connected, digon sign-symmetric structurally balanced line graph; and then we give sufficient conditions for the third-order multi-gent system to achieve both the bipartite consensus of edge dynamics and the final value of bipartite consensus. By transforming the coefficients of characteristic polynomial from complex domain to real number domain, the sufficient conditions for the bipartite consensus of high-order edge dynamics are also proposed, and the final values of the high-order edge dynamics on multiagent systems are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the optimal topology structure is studied for hybrid-weighted leader-follower multiagent systems (MASs). The results are developed by taking advantage of linear quadratic regulator (LQR) theory. We show that the multiagent star composite structure is the optimal topology which can enable the MAS to achieve the bipartite consensus. In particular, we prove that the optimal topology corresponding to the multiagent system with the first-order static leader and the second-order dynamic leader is, respectively, a hybrid-weighted star composite structure and an unevenly hybrid-weighted star composite structure. The results of the paper indicate that, in addition to the necessary information communication between leader and followers, the information exchange among followers increases the control cost of the system. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive consensus problem of general linear multi‐agent systems. Finite‐time consensus and fixed‐time consensus are both discussed. In order to remove the dependence on global information about system topology, distributed adaptive mechanisms are introduced. Compared with the existing asymptotic consensus results, the system's convergence speed is improved by the proposed distributed finite‐time consensus protocol. Furthermore, a distributed fixed‐time consensus protocol is proposed to remove the dependence on system's initial state. Under the fixed‐time consensus protocol, it is proved that an upper bound of the system's convergence time can be estimated. Sufficient conditions are given to ensure that all agents can achieve consensus in finite time and fixed time, respectively. Finally, the effectiveness of the proposed protocols is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper studies the controllability of multiagent systems based on path and cycle graphs. For paths or cycles, sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be realized. Specifically, the controllability of a path is shown to be determined by a set generated only from its odd factors, and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even (odd) factors when the number of its nodes is even (odd). For both graphs, the dimension of the controllable subspace is also derived. Moreover, the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies. These types of graphs can be regarded as typical topologies in the study of multiagent controllability, and accordingly the obtained results have meaningful enlightenment for the research in this field. [ABSTRACT FROM AUTHOR]

The consensus problem of first-order multi-agent systems with time delay is investigated. The periodic sample and event hybrid control method is applied. Specifically, each agent samples its own states periodically and decides when to transmit its sampled states to its neighbors based on certain event. The agents’ distributed consensus algorithms are based on these hybrid sampled and event-triggered state measurements, which can significantly decrease the number of the controllers’ updates. The Zeno behavior which is discussed in most works considering event-based consensus of multi-agent systems is excluded automatically since the span between two contiguous event-triggering time instants is not less than the sampling period. The cases of directed and undirected topologies are both considered. The obtained results improve the existing ones in the literature. A numerical simulation is provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the controllability of multi-agent systems is studied under leader-follower framework, where the interconnection between agents is directed. The concept of leader-follower connectedness is first introduced for directed graph to check controllability, and some graph-theoretic conditions are derived for constructively designed topologies. Then, distance partition and almost equitable partition are employed to quantitatively study the controllable subspaces. Moreover, the relationship between the state invariance of multi-agent systems and the existence of almost equitable partition is discussed. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

As an efficient collective response of multi-agent systems, the realization of stabilizability needs appropriate information transfer among agents, thus the topology structure is paramount. To investigate the influences of network topology on stabilizability, the concept of quotient graph (equivalent transformation of original graph) is proposed to realize the stabilizability of large-scale network systems which can be reduced to a small-scale quotient graph. As a cornerstone of topology graph transformation, N S i graph division, which is proposed for the first time in this paper, plays a crucial role in stabilizability analysis and has far-reaching impact. It establishes an equivalent connection between the stabilizability of the original topology graph and the quotient graph. Results reveal a nontrivial relationship between stabilizability of uncontrollable multi-agent systems and network topology (i.e., the stabilizability of uncontrollable multi-agent systems is not only related to the selection of leaders, but also depends on uncontrollable modes.), which is established by quotient graph as a visual generalization of the original network topology. Surprisingly, structural balance is not always good, and unbalance has a positive effect on the stabilizability of the system. Finally, the simulation experiments demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]

In this paper, the influences of negative weights on the consensus problems of multi-agent systems are investigated. While the system is subject to external attacks or agents in the system break down, there are errors in information transmission between agents. As a result, for non-negative systems, the connection weights between agents may change, or even change from positive to negative. In this paper, we provide a unified approach to deal with the problem of how to ensure the consensus of the system when the connection weight becomes negative. It is found that the consensus of multi-agent systems and general linear multi-agent systems will be guaranteed while the weights change to a certain extent without changing the protocol and feedback gains. We obtain a necessary and sufficient condition to ensure that the system can still reach asymptotic consensus when the connection weight is negative. The result is applicable to first-order, high-order integrator type of multi-agent systems as well as the general linear multi-agent system. [ABSTRACT FROM AUTHOR]

This paper investigates the optimisation problem of second-order multi-agent systems. Distributed optimisation algorithms are proposed based on sampling data. Two kinds of sampling techniques, namely, aperiodic sampling and dynamic event-triggered sampling, are utilised. Moreover, the proportional integral (PI) strategy is utilised in the proposed algorithms. Compared with the existing distributed optimisation algorithm based on periodic sampling, the proposed algorithm dependent on aperiodic sampling is more general. Compared with the existing steady event-triggered algorithm, the distributed optimisation algorithm based on dynamic event-triggered sampling has the merit of lower energy consumption. Under the assumption that the global cost function is strongly convex about global minimum point, it is proved that the proposed algorithms solve the optimisation problem. Lyapunov stability theory is applied to give sufficient criteria guaranteeing convergence to optimal point. Finally, the effectiveness of the proposed algorithms is illustrated by numerical simulation. [ABSTRACT FROM AUTHOR]

Abstract: The paper studies decentralized stabilizability for multi-agent systems with general linear dynamics. The stabilizability problem is formulated in a way that the protocol performance can be evaluated by means of the stabilizability region and the feedback gain. For fixed topology, it is proved that the system is stabilizable if and only if external control inputs are exerted on some indicated agents. The result is further shown to be a prerequisite for subsequent design of the corresponding decentralized external self-feedback control, which is also necessary and sufficient. Based on this, two methods are presented to find the agents under which stabilizability can be reached, and the region of stabilizability is given to evaluate the protocol performance. For switching interaction topology, it is shown that the system is stabilizable even if each of its subsystems is not. Finally, the results are employed to cope with the decentralized set-point formation control problem, for which some necessary and/or sufficient conditions are developed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results. [Copyright &y& Elsevier]

Abstract: By controllability of multi-agent systems, we mean the property that all agents can be driven to arbitrary configurations only through regulating a few leaders externally, while the rest of the agents are subject to the nearest-neighbor-law. It is known that the controllability of multi-agent systems depends not only on the communication topologies among agents but also on the selection of leaders. The main objective of this paper aims to characterize the virtue that leaders should have from the perspective of algebraic and graphical conditions. We begin with a heuristic observation for tree graph. To gain more insights, necessary and sufficient conditions are then proposed in terms of downer branch and subgraphs, respectively. In particular, it is shown for path topologies that controllability completely depends on the leaders’ location. The obtained results may help us to pave the way towards a new method of formation and reconfiguration control in swarming robots. [Copyright &y& Elsevier]

Abstract: In this paper, the formation control problem of the network of multiple agents is studied in terms of controllability, where the network is of the leader–follower structure with some agents taking leaders role and others being followers interconnected via the neighbor-based rule. It is shown that the controllability of a multi-agent system can be uniquely determined by the topology structure of interconnection graph, for which the investigation comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of uncontrollable interconnection topologies are characterized, and a necessary and sufficient eigenvector-based condition is presented. Our studies also touch upon the selection of leaders. [Copyright &y& Elsevier]

Abstract: The paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete-time systems. Direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability/reachability algorithm and Kalman-type algebraic rank criteria. Also the existing geometric criteria is simplified and new algebraic conditions on controllability and reachability are given. [Copyright &y& Elsevier]

Abstract: This paper studies the reachability of discrete-time switched linear systems. A new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly. Detailed comparison between the obtained result and that reported in the open literature is also made, which verifies the advantage of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper, we study the problem of designing switching sequences for controllability of switched linear systems. Each controllable state set of designed switching sequences coincides with the controllable subspace. Both aperiodic and periodic switching sequences are considered. For the aperiodic case, a new approach is proposed to construct switching sequences, and the number of switchings involved in each designed switching sequence is shown to be upper bounded by Here d is the dimension of the controllable subspace, , where are subsystems. For the periodic case, we show that the controllable subspace can be realized within d switching periods. [Copyright &y& Elsevier]

In this paper, the notion of minimal strong component of a fuzzy matrix is proposed. By using this concept, the periodicity of the power sequence of a fuzzy matrix is described on the basis of the relation of periodicity between a fuzzy matrix and its cut matrices. Further the greatest value max∑li=n [li] of periodicity of all n×n fuzzy matrices is obtained. [Copyright &y& Elsevier]

This paper is concerned with adaptive event-triggered consensus of general linear multi-agent systems (MASs). Leaderless consensus and leader-following consensus are both considered. In order to avoid dependence on global information about system topology and reduce communication frequency, distributed adaptive event-triggered consensus protocols are designed. Through model transformation, the consensus problems of MASs are transformed into the stability problems of the corresponding error systems. By using algebraic graph theory and Lyapunov stability theory, some sufficient criteria for MASs to achieve consensus are obtained. Meanwhile, it is proved that the proposed event-trigger conditions can exclude Zeno behaviour effectively. One simulation example is provided to validate the effectiveness of obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the strong targeted controllability of multi-agent systems with time-varying topologies over finite fields from a graph theoretic perspective. We consider leader–follower networks, where only some of the agents are governed by external control inputs, namely the leaders. We develop a graph-theoretic characterization for strong targeted controllability of multi-agent systems with time-varying topologies over finite fields. Specifically, we show that a time-varying multi-agent system is strongly targeted controllable over any finite field if the graphs of the system satisfy certain properties. Our main results are applicable to time-varying topologies with arbitrary fields and coupling weights. We also present a necessary and sufficient condition for the strong structural controllability of the time-invariant multi-agent systems. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability of first-order and second-order discrete-time multi-agent systems with directed topology and input delay. The problem is studied in the leader–follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents. Sufficient and necessary conditions are derived for the controllability of first-order discrete-time multi-agent systems. With sampling period and feedback gain satisfying certain conditions, it is proved under three different protocols that the controllability of second-order discrete-time multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In addition, the controllability of both first-order and second-order discrete-time multi-agent systems with input delay is shown, through some transformations, to be equivalent to that of the transformed non-delayed systems. Finally, some simulation examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• Employing ionic liquids (ILs) in conjunction with β-CD-based MNPs for the synergic binding sites. • Achieving rapid and selective removal of anionic PFASs and Cr(VI) from electroplating plant wastewater. • Unveiling the involvement of electrostatic and hydrophobic interactions in the adsorption of PFASs, facilitated through β-CD cavities and ILs cationic group. • Excellent regeneration performance of Fe 3 O 4 -NH-β-CD-BP ILs, under mild cleaning conditions. Herein, we develop a versatile strategy for developing a Fe 3 O 4 -NH-β-CD-BP ILs based sorbent by installing synergistic bonding sites for simultaneous removal of per- and polyfluoroalkyl substances (PFASs) and heavy metals from contaminated water. This sorbent with its quaternary ammonium cation achieved remarkable removal efficiency (∼99 %)for both short and long chain anionic PFASs in pure water as compared to previous β-CD based materials. Moreover, when subjected to a challenging metal salt matrix, the adsorbents revealed that long-chain PFASs primarily relied on electrostatic and hydrophobic interactions, while short-chain PFASs depended solely on electrostatic attractions. The results indicate that the sorbent exhibits outstanding adsorption capacities for PFCAs, PFSAs and Cr (VI) coupled with fast adsorption kinetics featuring equilibrium times 5, 4 and 2 h, respectively. The simultaneous removal of PFOA, PFOS and Cr (VI) in multi-component systems (electroplating plant wastewater) was also determined due to their dual sites rendered by cationic and β-CD groups. The adsorption of PFCAs and Cr (VI) was significantly influenced by the initial pH compared to the sorption of PFSAs. Additionally, the viologen based sorbent also showed better photocatalytic hydrogen evolution activity. In summary, these results revealed the outstanding adsorption capacity and convenient regeneration process make the adsorbent as a promising candidate for efficient and rapid removal of PFASs from other pollutants. [ABSTRACT FROM AUTHOR]

Position tracking control for the chaotic permanent magnet synchronous motor drive system is addressed in this paper. Neural networks are used to approximate the nonlinearities and indirect adaptive backstepping technique is employed to construct controllers. The designed indirect adaptive neural controllers can suppress chaos in the permanent magnet synchronous motor and guarantee that the position tracking error converges to a small neighborhood of the origin. Compared with the classical backstepping method, the proposed neural controllers׳ structure is very simple. Simulation results illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

• The information sets available to two controllers are different and mutually exclusive (i.e., either of both is not the subset of the other one). The problem under consideration in this paper is an asymmetric information control problem. It is highlighted that previous literature on asymmetric information control mainly focused on the case when the information set is a subset of the other one. However, the case of the information set s being mutually exclusive remains less investigated to the best of our knowledge, which brings essential difficulties in finding the optimal control strategies: the structures and forms of two controllers are not clear; seeking for the solvability conditions of the optimal control problem is challenging. • By adopting the convex variational method, the necessary and sufficient solvability conditions are derived under some basic assumptions, which are relied on the forward and backward di ff erence equations (FBSDEs). • Via some non symmetric Riccati equations the feedback form control strategies are derived by decoupling the FBSDEs Furthermore, the optimal performance index is also obtained as well. • Finally, the results are extended to investigate the general multiple controllers case. We also compare our result with single controller case which has been widely studied in some previous literature. Through the simulation result, one can see that more controllers will make the state stabler. This paper will investigate the linear quadratic (LQ) control problem for a stochastic system with different intermittent observations. Different from traditional LQ control problems, two controllers with different information structures are considered to minimize a quadratic performance index. Specifically, the information sets available to two controllers are different and mutually exclusive (i.e., either of both is not the subset of the other one). The problem under consideration in this paper is an asymmetric information control problem. It is highlighted that previous literature on asymmetric information control mainly focused on the case when the information set is a subset of the other one. However, the case of the information sets being mutually exclusive remains less investigated to the best of our knowledge, which brings essential difficulties in finding the optimal control strategies: the structures and forms of two controllers are not clear; seeking for the solvability conditions of the optimal control problem is challenging. We summarize the contributions of this paper as follows: Firstly, by adopting the convex variational method, the necessary and sufficient solvability conditions are derived under some basic assumptions, which are relied on the forward and backward difference equations (FBSDEs); Secondly, by decoupling the FBSDEs, the control strategies are derived; Finally, the results are extended to investigate the general multiple controllers case. [ABSTRACT FROM AUTHOR]