Jiahu Qin

Second-order consensus for multi-agent systems with switching topology and communication delay

In this paper, two kinds of consensus problems for second-order agents under directed and arbitrarily switching topologies are investigated, that is, the cases without and with communication delay. For the former, by constructing a new kind of digraph and employing a new graphic method, we can specify the least convergence rate for all the agents to reach consensus. For the latter, in virtue of a matrix inequality method, a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus. This, on the other hand, shows that consensus can be reached if the delay is small enough. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology

This paper investigates two kinds of different consensus strategies for multi-vehicle systems with a time-varying reference velocity under directed communication topology, where the systems are modeled by double-integrator dynamics. For the fixed communication topology case, we provide a necessary and sufficient condition for all the vehicles with reference velocity to reach consensus by the use of a new graphic methodology. We then extend this method to deal with the general case, that is, both the communication topologies and weighting factors are dynamically changing. In particular, it is shown that all the vehicles can reach consensus even though the dynamically changing interaction topology may not have a globally reachable node.

Coordination for Linear Multiagent Systems With Dynamic Interaction Topology in the Leader-Following Framework

This paper considers mainly the leader-following consensus for multiple agents with general linear system dynamics under switching topologies. Three different settings are systematically considered. We first consider the setting that the underlying interaction topologies switch arbitrarily among the possible weakly connected digraphs and then extend it to a more general setting that the weak connectivity of the interaction topologies is kept for some disconnected time intervals with short length due to the communication constraints among agents. Exponentially, consensus control is proved to be achieved, and the convergence rate can be specified as well for both settings in spite of the relaxed conditions on the system dynamics of each individual agent which even allow that each agent has exponentially unstable mode, while for the last case where the weak connectivity is only maintained on the joint of the interaction topologies, consensus control is proved to be achieved when the system matrix of each individual agent satisfies certain stability conditions.

Coordination of Multiple Agents With Double-Integrator Dynamics Under Generalized Interaction Topologies

The problem of the convergence of the consensus strategies for multiple agents with double-integrator dynamics is studied in this paper. The investigation covers two kinds of different settings. In the setting with the interaction topologies for the position and velocity information flows being modeled by different graphs, some sufficient conditions on the fixed interaction topologies are derived for the agents to reach consensus. In the setting with the interaction topologies for the position and velocity information flows being modeled by the same graph, we systematically investigate the consensus algorithm for the agents under both fixed and dynamically changing directed interaction topologies. Specifically, for the fixed case, a necessary and sufficient condition on the interaction topology is established for the agents to reach (average) consensus under certain assumptions. For the dynamically changing case, some sufficient conditions are obtained for the agents to reach consensus, where the condition imposed on the dynamical topologies is shown to be more relaxed than that required in the existing literature. Finally, we demonstrate the usefulness of the theoretical findings through some numerical examples.

Exponential Synchronization of Complex Networks of Linear Systems and Nonlinear Oscillators: A Unified Analysis

A unified approach to the analysis of synchronization for complex dynamical networks, i.e., networks of partial-state coupled linear systems and networks of full-state coupled nonlinear oscillators, is introduced. It is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks, thus making it feasible to consider the error dynamics for the whole network system. Different from the other various methods given in the existing literature, the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form, but also explicitly specifying the convergence rate.

Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control

This paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure. For the case with fixed topology, it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters, the couplings within the each cluster are sufficiently strong. An extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies. Such a balanced condition can be removed via the use of dwell-time technique. For all the cases, the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified. Finally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings.

On Discrete-Time Convergence for General Linear Multi-Agent Systems Under Dynamic Topology

This note aims to develop the nonnegative matrix theory, in particular the product properties of infinite row-stochastic matrices, which is widely used for multiple integrator agents, to deal with the convergence analysis of general discrete-time linear multi-agent systems (MASs). With the proposed approach, it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions, i.e. the individual uncoupled system is allowed to be strictly unstable (in the discrete-time sense) and it is only required that the joint of the communication topologies has a spanning tree frequently enough. Moreover, a least convergence rate as well as an upper bound for the strictly unstable mode, which are independent of the switching mode of the system, are specified as well.

Recent Advances in Consensus of Multi-Agent Systems: A Brief Survey

In this paper, we mainly review the topics in consensus and coordination of multi-agent systems, which have received a tremendous surge of interest and progressed rapidly in the past few years. Focusing on different kinds of constraints on the controller and the self-dynamics of each individual agent, as well as the coordination schemes, we categorize the recent results into the following directions: consensus with constraints, event-based consensus, consensus over signed networks, and consensus of heterogeneous agents. We also review some applications of the very well developed consensus algorithms to the topics such as economic dispatch problem in smart grid and k -means clustering algorithms.

On average consensus in directed networks of agents with switching topology and time delay

In this article, the average consensus problem in directed networks of agents with both switching topology and coupling delay is investigated. First, based on a specific orthogonal transformation of the Laplacian matrix, an important proposition for verifying the positive definiteness of a class of quadratic forms is provided, which is of independent interest in matrix theory. And the relation between weakly connected and strongly connected digraphs is also investigated. Then, it is proved that all the agents reach the average consensus asymptotically for appropriate time delay if the communication topology keeps weakly connected and balanced. Finally, a numerical example is given to demonstrate the effectiveness and advantage of the new result.

On the Bipartite Consensus for Generic Linear Multiagent Systems With Input Saturation

The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.