This paper addresses the consensus problem of multiagent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus protocol based on relative output measurements is proposed. A new framework is introduced to address in a unified way the consensus of multiagent systems and the synchronization of complex networks. Under this framework, the consensus of multiagent systems with a communication topology having a spanning tree can be cast into the stability of a set of matrices of the same low dimension. The notion of consensus region is then introduced and analyzed. It is shown that there exists an observer-type protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each agent is both stabilizable and detectable. A multistep consensus protocol design procedure is further presented. The consensus with respect to a time-varying state and the robustness of the consensus protocol to external disturbances are finally discussed. The effectiveness of the theoretical results is demonstrated through numerical simulations, with an application to low-Earth-orbit satellite formation flying.

Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint

Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The controller updates considered here are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation is considered first and then its distributed counterpart, in which agents require knowledge only of their neighbors' states for the controller implementation. The results are then extended to a self-triggered setup, where each agent computes its next update time at the previous one, without having to keep track of the state error that triggers the actuation between two consecutive update instants. The results are illustrated through simulation examples.

/pdf/distributed-event-triggered-control-for-multi-agent-systems-4p46fy7wt3.pdf

Distributed Event-Triggered Control for Multi-Agent Systems

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

/pdf/an-overview-of-recent-progress-in-the-study-of-distributed-1xnb6e12se.pdf

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

In a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents, expresses by a communication graph with nonnegative weights. The question we ask in this paper is the following: is it possible to achieve a form of agreement also in presence of antagonistic interactions, modeled as negative weights on the communication graph? The answer to this question is affirmative: on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign. Necessary and sufficient conditions are obtained to describe cases in which this is possible. These conditions have strong analogies with the theory of monotone systems. Linear and nonlinear Laplacian feedback designs are proposed.

Consensus Problems on Networks With Antagonistic Interactions

In this paper, without assuming symmetry, irreducibility, or linearity of the couplings, we prove that a single controller can pin a coupled complex network to a homogenous solution. Sufficient conditions are presented to guarantee the convergence of the pinning process locally and globally. An effective approach to adapt the coupling strength is proposed. Several numerical simulations are given to verify our theoretical analysis.

Pinning Complex Networks by a Single Controller

https://arxiv.org/pdf/math-ph/0601030.pdf

In this paper, we investigate the cluster synchronization problem for linearly coupled networks, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, etc., by adding some simple intermittent pinning controls. We assume the nodes in the network to be identical and the coupling matrix to be asymmetric. Some sufficient conditions to guarantee global cluster synchronization are presented. Furthermore, a centralized adaptive intermittent control is introduced and theoretical analysis is provided. Then, by applying the adaptive approach on the diagonal submatrices of the asymmetric coupling matrix, we also get the corresponding cluster synchronization result. Finally, numerical simulations are given to verify the theoretical results.

Cluster Synchronization in Directed Networks Via Intermittent Pinning Control

In this note, synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller. Nodes' dynamical behaviors in the network are described by continuous-time ordinary differential equations. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously. Finally, numerical simulations are given to demonstrate the correctness of obtained results.

Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control

In this paper, pinning synchronization problem for nonlinear coupled networks is investigated, which can be recurrently connected neural networks, cellular neural networks, Hodgkin–Huxley models, Lorenz chaotic oscillators, and so on. Nodes in the network are assumed to be identical and nodes’ dynamical behaviors are described by continuous-time equations. The network topology is undirected and static. At first, the scope of accepted nonlinear coupling functions is defined, and the effect of nonlinear coupling functions on synchronization is carefully discussed. Then, the pinning control technique is used for synchronization, especially the control type is aperiodically intermittent. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, the adaptive approach is also applied on the pinning control, and a centralized adaptive algorithm is designed and its validity is also proved. Finally, several numerical simulations are given to verify the obtained theoretical results.

Xiwei Liu

Papers

Pinning Complex Networks by a Single Controller

Pinning Complex Networks by a Single Controller

Cluster Synchronization in Directed Networks Via Intermittent Pinning Control

Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control

Synchronization of Nonlinear Coupled Networks via Aperiodically Intermittent Pinning Control