Search

Leader–follower consensus control is a kind of consensus control, where some special agents, called the leaders, have relatively high flexibility in changing their states, and the other agents, called the followers, follow the leaders. One of the important issues for leader–follower consensus control is a leader selection problem, i.e. determining leaders to achieve a desired performance. On the other hand, the notion of a feedback vertex set is well-known in graph theory. Feedback vertex sets are known to play an important role in various problems, e.g. deadlock avoidance and sensing node selection of biological networks. Thus, they are expected to be closely related to leader–follower consensus control. However, their relationship has never been studied so far. This paper discloses the relationship between leader selection and feedback vertex sets. We deal with a problem of finding a minimum leader set to achieve the fastest convergence to consensus and show that a solution to the leader selection problem is given by a feedback vertex set. [ABSTRACT FROM AUTHOR]

In this paper, a distributed peer-to-peer multi-agent framework is proposed for managing the power sharing in microgrids with power electronic inverter-interfaced distributed energy resources (DERs). Recently, the introduction of electric vehicles (EVs) has gained much popularity by offering vehicle-to-home (V2H) technologies to support the sustainable operation of microgrids. Since microgrids often exhibit volatile characteristics due to natural intermittency and uncertainty, it is necessary to maintain the balancing of generation and demand through the proper management of power sharing. Therefore, the main purpose of this paper is to design an agent-based control framework to ensure the coordinated power management within the microgrids through effective utilization of EVs. The required agent communication framework is adhered to the graph theory where the control agents interact with each other using local as well as neighboring information and their distributed coordination effectively steers the proportional sharing of real and reactive powers among the inverter-interfaced EVs to maintain the stability of microgrids. The well known Ziegler-Nichols method is used to tune the proportional-integral (PI) controller of the inner current control loop within each individual control agent to perform necessary shared control tasks. A microgrid with solar photovoltaic (PV) and V2H systems is chosen to illustrate the results and it is seen that the proposed scheme improves the system performance in a smarter way through information exchange. Furthermore, the proposed framework is also validated by a comparison with an existing traditional approach and it is found that, the proposed scheme provides excellent robust and faster performance. [ABSTRACT FROM AUTHOR]

In this paper, the consensus for second-order heterogeneous multi-agent system is investigated. The heterogeneous system consists of linear and nonlinear second-order agents, where the nonlinear agents are still with different structures. First, the consensus of the system with and without a static leader is discussed, respectively. Then, we consider a general case where the inputs of linear second-order agents are bounded by virtue of the limitation of the actuators. Effective control protocols to achieve consensus are presented for these cases. Based on graph theory and Lyapunov stability theory, sufficient conditions are established for the consensus of heterogeneous system, where the communication topology is undirected and connected. Finally, several numerical examples are presented to verify the validity of the developed method. [ABSTRACT FROM AUTHOR]

This paper studies how to control large formations of autonomous agents in the plane, assuming that each agent is able to sense relative positions of its neighboring agents with respect to its own local coordinate system. We tackle the problem by adopting two types of controllers. First, we use the classical gradient-based controllers on three leader agents to meet their distance constraints. Second, we develop other type of controllers for follower agents: utilizing the properties of rooted graphs, one is able to design linear controllers incorporating relative positions between the follower agents and their neighbors, to stabilize the overall large formations. The advantages of the proposed method are fourfold: (i) fewer constraints on neighboring relationship graphs; (ii) simplicity of linear controllers for follower agents; (iii) global convergence of the overall formations; (iv) implementation in local coordinate systems, in no need of a global coordinate system. Numerical simulations show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies state synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling. We identify four classes of agents, for which static linear protocol can be designed. They are agents which are squared-down passive, squared-down passifiable via output feedback, squared-down passifiable via input feedforward and squared-down minimum-phase with relative degree 1. We find that, for agents which are squared-down passive, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree. For the other three classes of agents, the static protocol needs rough information on the network graph, that is either a lower bound for the real part or an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network can be dispensed with. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem for heterogeneous multi-agent systems consisting of third-order and first-order agents. The interaction topology includes both fixed and switching cases. First, by a model transformation, heterogeneous multi-agent systems are converted into equivalent error systems. Then we analyze the consensus problem of the multi-agent systems by analyzing the stability problem of the error systems. For a fixed topology, a sufficient condition for consensus of heterogeneous multi-agent systems is obtained based on algebraic graph theory and linear system theory. For a switching topology, a necessary and sufficient condition for mean-square consensus of multi-agent systems is obtained based on algebraic graph theory and Markovian jump system theory. Finally, we give some simulation examples. [ABSTRACT FROM AUTHOR]

Multi-agent consensus has been widely applied in engineering. A novel protocol that can achieve an average state consensus for multi-agent systems in finite time is presented in this paper. The proposed protocol contains a non-linear and a linear term. The state consensus is achieved in finite time by the non-linear term and convergence performance is improved by the linear term to some degree. The protocol can be applied to systems with a switching topology as long as the communication graph is always undirected and connected. The upper bound of convergence time is obtained. The relationship between convergence time and protocol parameter, communication topology and initial state is analysed. Lastly, simulations are conducted to verify the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper studies the distributed event-triggered output consensus problem of heterogeneous multiagent system with general linear dynamics under an undirected connected graph. With the state-dependent triggering function, we design a novel distributed event-triggered output consensus controller for each agent to reach consensus with zero final consensus error. This strategy has several distinguishing features, including the fact that individual agent does not require continuous, or even periodic, communication with their neighbours to update the controller or monitor the triggering condition, and all parameters required by its implementation can be locally determined by the agent. We also prove that events cannot be triggered infinitely in finite time (i.e. no Zeno behaviour). Furthermore, the simulation examples are given to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, robust containment problem is investigated for a class of multi-leader multi-agent linear systems in the presence of time-varying uncertainties. To achieve containment, a new kind of adaptive containment protocols are proposed for the multi-agent systems. Specifically, the designed protocols consist of a continuous linear term and a discontinuous term. The linear term of the designed protocol is employed to achieve containment while the discontinuous term is utilized to eliminate the effect of uncertain dynamics on the achievement of containment. By using tools from non-smooth analysis and algebraic graph theory, some efficient criteria for achieving robust containment in the closed-loop multi-agent systems are obtained and analyzed. One favorable property of the designed protocol is that containment in the closed-loop multi-agent systems can be achieved in a fully distributed fashion over any given connected and detail-balanced communication graph without using any global information about the communication graph. The effectiveness of the analytical results is finally verified by performing numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the leaderless consensus problem of multi-agent systems with jointly connected topologies and nonlinear dynamics is considered, in which the nonlinear dynamics are assumed to be non-identical and unknown. The unknown nonlinear dynamics existing in the systems are assumed to be linearly parameterized, and an adaptive design method for leaderless multi-agent systems is presented. By just using the relative position information between each agent and its neighbors, a distributed adaptive consensus control algorithm for the considered systems is proposed, in which the network graphs are jointly connected. Both the global uniform asymptotical stability and the global uniform asymptotical parameter convergence analysis of the adaptive control algorithm are carried out by using adaptive control theory, Lyapunov theory and algebraic graph theory. Finally, an example is given to illustrate the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem of discrete-time descriptor multi-agent systems is considered. Each agent’s dynamics is modelled by a discrete-time linear descriptor system, and the interaction topology among the agents is assumed to be directed. To solve the multi-agent consensus problem, three different architectures of connecting observers and controllers are used to construct the consensus protocols. A kind of modified generalized algebraic Riccati equation is provided to design the protocol’s gain matrices. Based on graph theory, matrix theory and the Lyapunov method, some sufficient convergence conditions are established to guarantee the descriptor multi-agent system achieves consensus. Finally, a simulation example is provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Time-varying group formation control problems for second-order multi-agent systems with directed topologies are investigated. Firstly, a time-varying group formation control protocol is constructed using local relative positions and velocities of each agent and its neighbors. Then based on graph theory, nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for second-order multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, by solving an algebraic Riccati equation, an approach to design the time-varying group formation protocol is proposed. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained results. In contrast to the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation discussed in the current paper, agents are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation via inter-subgroup and intra-subgroup interactions. [ABSTRACT FROM AUTHOR]

This paper proposes a consensus state estimator for sensor networks of distributed parameter structures. A thin beam with clamped-clamped boundary conditions enhanced by piezoelectric sensors is considered, and individual observers are assigned for each of these sensors. The so-called estimation agents are then connected to one another in a network with certain directed topology, and consensus is enforced between the agents estimated output in observers dynamics. Observer gains are optimized using algebraic Riccati equations (AREs), and robustness to measurement disturbances is applied via H∞ design. The consensus state estimator is then numerically investigated for a sensor network of five agents. According to the results of the optimal and robust designs, the proposed consensus observer successfully estimates the modal system states in finite time, whereas the estimation output is resilient to measurement disturbances. Implementation of the consensus sensor network increases the robustness of the estimation, due to its inherent redundancy. [ABSTRACT FROM AUTHOR]

This paper presents a frequency domain resilient consensus problem of time-delayed multi-agent systems (MASs) under attacks. An internal model principle-based attack, a kind of network attack, is firstly analyzed and modeled in frequency domain. Then, a Quasi- H ∞ robust controller is designed for resilient consensus of the MAS with the help of an internal model controller. This scheme is different from the existing works in the sense that the attacker may inject an attacking signal on the node of an agent instead of a communication link. It is also novel because it can eliminate the impacts of attack without excluding compromised nodes and restricting the number of compromised nodes. The proposed control scheme is applied to a linear delayed MAS with single-input single-output agents and then transformed into multi-input and multi-output agents. An innovative approach is employed for the tuning of the proposed controller to track the performance of the MAS and its robustness. Some necessary and sufficient conditions are extracted using Pade ́ approximation and graph theory to minimize the impacts of time delay and attacks simultaneously. The results are extended for resilient consensus of the MAS under non-internal model principle-based attack. The simulation results are presented to demonstrate the validity of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Abstract: Using the semi-tensor product of matrices, this paper investigates the maximum (weight) stable set and vertex coloring problems of graphs with application to the group consensus of multi-agent systems, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for the internally stable set problem, based on which a new algorithm to find all the internally stable sets is established for any graph. Secondly, the maximum (weight) stable set problem is considered, and a necessary and sufficient condition is presented, by which an algorithm to find all the maximum (weight) stable sets is obtained. Thirdly, the vertex coloring problem is studied by using the semi-tensor product method, and two necessary and sufficient conditions are proposed for the colorability, based on which a new algorithm to find all the -coloring schemes and minimum coloring partitions is put forward. Finally, the obtained results are applied to multi-agent systems, and a new protocol design procedure is presented for the group consensus problem. The study of illustrative examples shows that the results/algorithms presented in this paper are very effective. [Copyright &y& Elsevier]

Abstract: Without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree, this paper studies the second-order leader-following consensus problem of nonlinear multi-agent systems with general network topologies. Based on graph theory, matrix theory, and LaSalle’s invariance principle, a pinning control algorithm is proposed to achieve leader-following consensus in a network of agents with nonlinear second-order dynamics. Furthermore, a pinning consensus protocol is developed for coupled double-integrators with a constant reference velocity. In particular, this paper addresses what kind of agents and how many agents should be pinned, and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader. Numerical simulations are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This study proposes a collective motion and self-organization control of a swarm of 10 UAVs, which are divided into two clusters of five agents each. A cluster is a group of UAVs in a dedicated area and multiple clusters make a swarm. This paper designs the 3D model of the whole environment by applying graph theory. To address the aforesaid issues, this paper designs a hybrid meta-heuristic algorithm by merging the particle swarm optimization (PSO) with the multi-agent system (MAS). First, PSO only provides the best agents of a cluster. Afterward, MAS helps to assign the best agent as the leader of the nth cluster. Moreover, the leader can find the optimal path for each cluster. Initially, each cluster contains agents at random positions. Later, the clusters form a formation by implementing PSO with the MAS model. This helps in coordinating the agents inside the nth cluster. However, when two clusters combine and make a swarm in a dynamic environment, MAS alone is not able to fill the communication gap of n clusters. This study does it by applying the Vicsek-based MAS connectivity and synchronization model along with dynamic leader selection ability. Moreover, this research uses a B-spline curve based on simple waypoint defined graph theory to create the flying formations of each cluster and the swarm. Lastly, this article compares the designed algorithm with the NSGA-II model to show that the proposed model has better convergence and durability, both in the individual clusters and inside the greater swarm. [ABSTRACT FROM AUTHOR]

In this paper, the recent developments of distributed coordination control problems are summarized in a graph-theory-based framework. Distributed coordination has attracted tremendous attention in control and robot communities because of its potential applications in the past decade. The graph is used to describe the interconnections among agents, and different distributed coordination control problems, such as consensus, formation control, rendezvous, alignment, swarming, flocking, containment control and circumnavigation control, are adopted to this description by considering different cooperative objects. Therefore it is natural to study the distributed coordination control problems via graph theory, and the graph-theory-based results on consensus, formation control, and some closely related issues, i.e., rendezvous/alignment, swarming/flocking, containment control and circumnavigation control, are reviewed, and provide a cohesive overview in the coordination control problems, in system modeling, control law designs and analysis, and structure transformation. Finally, towards the practical applications, some potential directions possibly deserving investigation in distributed coordination control are discussed. [ABSTRACT FROM AUTHOR]

This paper studies the group consensus problem in networks of multi-agent systems, in which the nonlinear dynamics of all agents are unknown and nonidentical. We assume that the unknown dynamics are linearly parameterized. Adaptive control method is adopted in the algorithm design. A novel algorithm is proposed for the multi-agent systems to reach group consensus via pinning control strategies, which only rely on the relative position information between neighboring agents. The stability and parameter convergence analysis are done based on Lyapunov theory, Barbalat's lemma, adaptive control theory and algebraic graph theory. Finally, a simulation example is given to validate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, four observer-based distributed controllers are proposed for general linear multi-agent systems to achieve finite-time coordinated tracking under different situations. Specifically, for the cases of undirected communication graphs and directed communication graphs among the followers, both the situations of relative state measurement and relative output measurement among neighboring agents are considered. Under both kinds of communication topologies, when relative state information of the neighbors is available, distributed observer-based controllers are designed which achieve exact coordinated tracking in finite-time. When only relative output information is available, another finite-time observer is introduced for each follower to estimate the relative state information. Together with the distributed controllers designed for the state feedback case, finite-time exact coordinated tracking can still be achieved in this situation. Numerical simulations are provided to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

In this paper, consensus problem of general nonlinear multi-agent systems with communication failures is studied based on a distributed consensus algorithm. Under the assumption that the communication graphs are strongly connected, we derive some sufficient consensus criterion for both cases fixed and switched topologies using the relative measured output states of each agent. Moreover, the case that there is a leader in the communication graph is also explicitly investigated. Finally, simulation examples are presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, observer-based distributed consensus for general nonlinear multi-agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable. Theoretical analysis method is further extended to the case of general nonlinear multi-agent systems under switching setting. Moreover, tracking problem on the leader–follower scenario is also explicitly investigated under a mutual assumption that the communication graph, which represents the interaction among agents, contains a directed spanning tree with the leader as its root. It is shown that the consensus for underlying considered multi-agent systems can be desirable as long as the data missing rate does not exceed a certain threshold. Finally, simulation examples are presented to effectively corroborate the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, group consensus problems in fixed directed networks of dynamic agents are investigated. Group consensus means that the agents in each group share a consistent value while there is no agreement between any two groups. Based on algebraic graph theory, sufficient conditions guaranteeing group consensus under the proposed control protocol in the presence of random noises and communication delays are derived. The analysis uses a stability result of Mao for stochastic differential delay equations, which ensures the consensus can be achieved almost surely and exponentially fast. Numerical examples are provided to demonstrate the availability of the obtained results as well as the effect of time delay/noise intensity. [ABSTRACT FROM PUBLISHER]

Lyapunov equations that depend on communication graph topologies provide building blocks of Lyapunov functions, which play an important role in controller design and stability analysis of multi-agent systems. However, construction of such a Lyapunov equation in some published works has a flaw or requires unnecessarily strong graph conditions. This paper presents several choices of Lyapunov equations over various graph topologies. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus tracking problem for leader-following multi-agent systems with general dynamics. The agents that are at most critically unstable and with time-varying delays and arbitrary switching topology are considered in our work. A novel framework for cooperative tracking control with time-varying input delay and communication delay under switching topology is constructed. The distributed observer-based tracking protocol is proposed for desired tracking based on the truncated predictor feedback method, algebraic graph theory and Riccati equation. Moreover, we design the observer gain and feedback gain independent of each other. A simulation example is provided to demonstrate the effectiveness of our proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, we study the adaptive coordinated tracking problem for continuous-time first-order integrator systems with quantized information under switching undirected and fixed directed communication graphs, respectively. The combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated. Both the logarithmic quantizers and uniform quantizers are considered. It is shown that when logarithmic quantizers are used, exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used, practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter. Simulation examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we consider distributed H consensus problem for multi-agent systems with discrete-time high-dimensional linear coupling dynamics subjected to external disturbances. The interaction topology among the agents is assumed to be switching and undirected. To achieve consensus, a neighbor-based dynamic output feedback protocol is proposed for each agent. By using Schur orthogonal transformation, the considered multi-agent H consensus control problem is converted into H control problem of a discrete-time switching subsystem. Based on graph theory and common Lyapunov function method, a sufficient condition in terms of linear matrix inequalities is established to solve H consensus problem of the considered multi-agent systems. Moreover, the feedback gain matrix can be obtained from the feasible solution to the linear matrix inequalities. Finally, a simulation example is given to illustrate our established theoretical result. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics for both the cases without and with a leader whose control input might be nonzero and time varying. For the case without a leader, based on the relative output information of neighboring agents, two types of distributed adaptive dynamic consensus protocols are proposed, namely, the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication graph and the node-based adaptive protocol which uses a time-varying coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for all undirected connected communication graphs. It is shown that the edge-based adaptive consensus protocol is applicable to arbitrary switching connected graphs. For the case where there exists a leader whose control input is possibly nonzero and bounded, a distributed continuous adaptive protocol is designed to guarantee the ultimate boundedness of the consensus error with respect to any communication graph which contains a directed spanning tree with the leader as the root and whose subgraph associated with the followers is undirected, requiring neither global information of the communication graph nor the upper bound of the leader’s control input. A distributed discontinuous protocol is also discussed as a special case. Simulation examples are finally given to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: Finite-time consensus problems of the leader-following multi-agent systems with jointly-reachable leader and switching jointly-reachable leader are studied in this paper. Based on the graph theory, LaSalle’s invariance principle and Lyapunov stability theory, the finite-time consensus protocols are presented for the first-order and second-order leader-following systems. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical 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, we discuss the finite-time consensus problem for leaderless and leader–follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader–follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis. [Copyright &y& Elsevier]

In multi-agent system (MAS), the communication topology of agent network plays a very important role in its collaboration. Small-world networks are the networks with high local clustering and small average path length, and the communication networks of MAS can be analyzed within the frame of small-world topology. Yet the real multiagent communication networks are abundant and the classical WS small-world model is not suitable for all cases. In this paper, two new small-world network models are presented. One is based on random graph substrate and local nodes preference reconnection and the other is based on regular graph substrate and long-range nodes preference reconnection. The characteristic of the network parameter such as the clustering coefficients, average path length, and eigenvalue λ2 and λn of the Laplacian matrix for these two models and WS model is studied. The consensus problem that based on these three models is also studied. An example is given and the conclusions are made in the end. [ABSTRACT FROM AUTHOR]

In this paper, the controllability of leader–follower multi-agent systems is studied from the perspective of graph theory. It is known that, for a given graph, the number of cells of an almost equitable partition (AEP) provides an upper bound on the controllability index. In this context, the main contribution here is an efficient algorithm to construct the maximal AEP for a given graph with a set of leaders. Specifically, we first establish the relationship between an AEP and the distance partition (DP) for the single-leader setting. It is shown that the cells of an AEP are subsets of cells of the DP. We extend the results to the multiple-leader case and develop a convergent algorithm to efficiently compute the maximal AEP. Finally, numerical examples are provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the recent paper (Monshizadeh et al. in IEEE Trans Control Netw Syst 1(2):145-154, 2014. 10.1109/TCNS.2014.2311883), model reduction of leader-follower multi-agent networks by clustering was studied. For such multi-agent networks, a reduced order network is obtained by partitioning the set of nodes in the graph into disjoint sets, called clusters, and associating with each cluster a single, new, node in a reduced network graph. In Monshizadeh et al. (2014), this method was studied for the special case that the agents have single integrator dynamics. For a special class of graph partitions, called almost equitable partitions, an explicit formula was derived for the H2 model reduction error. In the present paper, we will extend and generalize the results from Monshizadeh et al. (2014) in a number of directions. Firstly, we will establish an a priori upper bound for the H2 model reduction error in case that the agent dynamics is an arbitrary multivariable input-state-output system. Secondly, for the single integrator case, we will derive an explicit formula for the H∞ model reduction error. Thirdly, we will prove an a priori upper bound for the H∞ model reduction error in case that the agent dynamics is a symmetric multivariable input-state-output system. Finally, we will consider the problem of obtaining a priori upper bounds if we cluster using arbitrary, possibly non almost equitable, partitions. [ABSTRACT FROM AUTHOR]