Qichao Ma

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 Group Synchronization for Interacting Clusters of Heterogeneous Systems

This paper investigates group synchronization for multiple interacting clusters of nonidentical systems that are linearly or nonlinearly coupled. By observing the structure of the coupling topology, a Lyapunov function-based approach is proposed to deal with the case of linear systems which are linearly coupled in the framework of directed topology. Such an analysis is then further extended to tackle the case of nonlinear systems in a similar framework. Moreover, the case of nonlinear systems which are nonlinearly coupled is also addressed, however, in the framework of undirected coupling topology. For all these cases, a consistent conclusion is made that group synchronization can be achieved if the coupling topology for each cluster satisfies certain connectivity condition and further, the intra-cluster coupling strengths are sufficiently strong. Both the lower bound for the intra-cluster coupling strength as well as the convergence rate are explicitly specified.

Containment Control for Second-Order Multiagent Systems Communicating Over Heterogeneous Networks

The containment control is studied for the second-order multiagent systems over a heterogeneous network where the position and velocity interactions are different. We consider three cases that multiple leaders are stationary, moving at the same constant speed, and moving at the same time-varying speed, and develop different containment control algorithms for each case. In particular, for the former two cases, we first propose the containment algorithms based on the well-established ones for the homogeneous network, for which the position interaction topology is required to be undirected. Then, we extend the results to the general setting with the directed position and velocity interaction topologies by developing a novel algorithm. For the last case with time-varying velocities, we introduce two algorithms to address the containment control problem under, respectively, the directed and undirected interaction topologies. For most cases, sufficient conditions with regard to the interaction topologies are derived for guaranteeing the containment behavior and, thus, are easy to verify. Finally, six simulation examples are presented to illustrate the validity of the theoretical findings.

Cluster Synchronization for Interacting Clusters of Nonidentical Nodes via Intermittent Pinning Control

The cluster synchronization problem is investigated using intermittent pinning control for the interacting clusters of nonidentical nodes that may represent either general linear systems or nonlinear oscillators. These nodes communicate over general network topology, and the nodes from different clusters are governed by different self-dynamics. A unified convergence analysis is provided to analyze the synchronization via intermittent pinning controllers. It is observed that the nodes in different clusters synchronize to the given patterns if a directed spanning tree exists in the underlying topology of every extended cluster (which consists of the original cluster of nodes as well as their pinning node) and one algebraic condition holds. Structural conditions are then derived to guarantee such an algebraic condition. That is: 1) if the intracluster couplings are with sufficiently strong strength and the pinning controller is with sufficiently long execution time in every period, then the algebraic condition for general linear systems is warranted and 2) if every cluster is with the sufficiently strong intracluster coupling strength, then the pinning controller for nonlinear oscillators can have its execution time to be arbitrarily short. The lower bounds are explicitly derived both for these coupling strengths and the execution time of the pinning controller in every period. In addition, in regard to the above-mentioned structural conditions for nonlinear systems, an adaptive law is further introduced to adapt the intracluster coupling strength, such that the cluster synchronization for nonlinear systems is achieved.

On Group Synchronization for Clusters of Agents with Collectively Acyclic Intercluster Couplings

This paper investigates the group synchronization problem for interacting clusters of agents, which can be either generic linear systems or nonlinear oscillators, by focusing on in-depth understanding of how the couplings among agents influence the group behavior. To this end, we work on both the homogeneous case that agents have the same system dynamics and the heterogeneous case that agents from different clusters have different system dynamics. It is shown that the synchronization for each cluster of agents is irrelevant to the strength of the intercluster couplings as long as the intercluster couplings are collectively acyclic; that is, the intercluster couplings do not incur desynchronization and, thus, no extra effort beyond the strengths of the intracluster couplings, which are necessary to guarantee the synchronization of each cluster in the absence of intercluster couplings, are needed. Moreover, we provide an example demonstrating that the condition of having collectively acyclic intercluster couplings is not a necessity in guaranteeing the above property.

Optimal sensor scheduling for two linear dynamical systems under limited resources in sensor networks

Abstract In this paper, we aim to design the optimal transmission scheme for two Gauss–Markov systems with finite resources. The setup that only two sensor nodes were scheduled, which monitor different linear dynamical systems, respectively. Two scenarios : the sensor has abundant calculation capability and the sensor has limited calculation capability are considered. For the second scenario, considering that the optimal schedule should collected a finite sequence of previous measurements. We are able to construct a quasi-optimal schedules. Due to bandwidth limitation and transmission power restriction, the sensors cannot communicate with the remote center and send the measurement data all the times. By exploiting the estimation error covariance at the remote estimation center to describe the quality of communication, the transmission schedule problem is formulated as an optimal problem. A necessary condition for the scheduling scheme of the sensors to be optimal is provided. Based on this necessary condition, we propose an explicit optimal periodic schedule, which is rigorously proved to have a minimal estimation error at the estimation center while satisfying the transmission power and channel bandwidth constraints. Simulation examples are given at last to verify the validity of the theoretical results.

On the delay bound for coordination of multiple generic linear agents under arbitrary topology with time delay

Abstract A coordination control of multiple generic linear homogeneous agents under arbitrary network topology with uniform and fixed time delay is proposed in this paper. From the network topology, the agents are categorized into two groups: those within the closed strong components (group 1) and those outside the closed strong components (group 2). It is shown that under allowable delay bound, the agents of group 1 reach synchronization while the agents of group 2 converge asymptotically to the convex hull spanned by the synchronized agents of group 1. The technique of semi-discretization is applied for computing the delay bound. For a specific time delay, the method is also feasible in finding an optimal coordination control gain with the fastest decay rate. A linear matrix inequality method is also given to show an alternative way to find the maximum allowable delay bound. An illustrative simulation is presented to validate our obtained theoretical results.

Output Group Synchronization for Networks of Heterogeneous Linear Systems Under Internal Model Principle

In this paper, we aim to investigate the output group synchronization problem for a network of heterogeneous linear systems such that the outputs of the nodes, each representing a linear system, synchronize with each other in every cluster. Two different setups in terms of availability of the states of the reference generators are taken into consideration. A unified approach inspired by the internal model principle is proposed. First, the coupled reference generators are constructed so as to produce synchronized reference trajectories. Second, feedback controllers are designed to steer the output of each node to its corresponding reference trajectory. The two setups differ from each other in that the coupling configuration for reference generators and design of feedback controllers are rather different. Specifically, when the states of the reference generators are not available, the small gain theorem is exploited to drive the outputs of the nodes to the synchronized ones of virtual reference generators. Finally, simulations are carried out to validate the theoretical findings.

On cluster synchronization of heterogeneous systems using contraction analysis

Abstract In this paper, we employ contraction theory to solve cluster synchronization problem under directed topology. According to the cluster structure, we develop an invariant subspace. Then we take the advantage of the complementary space to prove that the whole systems will synchronize to this invariant subspace, leading to cluster synchronization. We first deal with the linear systems which are linearly coupled under the framework of directed topology. Some sufficient conditions are given to guarantee that the coupled linear systems can achieve cluster synchronization. Moreover, the case of linearly coupled non-linear systems is also considered. Two simulation examples are given to verify our theoretical findings.

Fault-tolerant cooperative tracking control via integral sliding mode control technique

In this paper, we aim to deal with the cooperative tracking problem for a group of nonlinear systems with actuator faults and external disturbance/model uncertainty. The faults in the actuator are allowed to be in arbitrary forms such as actuator degradation, amplification, or even total failure. Moreover, the disturbance/model uncertainty under consideration is of Lipschitz type by assuming that the derivative of disturbance/model uncertainty is uniformly bounded. Then, provided that the actuator has sufficient healthy components when the faults happen, we employ the integral sliding mode technique to design the controller that can tolerate the actuator faults, meanwhile the external disturbance can also be rejected. The controller design is separated into two steps. First, a nominal controller is designed such that the estimated disturbance/model uncertainty from disturbance observer is completely rejected and the desired performance is guaranteed. Second, by the integral sliding mode control technique, a compensating controller is designed such that the matched estimation error of actuator faults and the external disturbance/model uncertainty can be compensated. The designed controller, formed by the sum of the nominal controller and compensating controller, finally proves to guarantee practical synchronization of nonlinear systems. Simulations demonstrate the effectiveness of our theoretical findings.