This paper focuses on the synchronization analysis of a class of multiagent systems, where both speed and heading of each agent depend on the states of its local neighbors. The neighbors are defined through the distance between agents and all agents are interconnected via proximity nets. In the variable speed model, the speed of each agent depends on the polarization order of its neighbors in a power-law manner, and the heading is updated according to the average heading of its neighbors. Therefore, the speeds, headings, and positions of all agents are strongly coupled together. For the uniformly and independently distributed initial states, we provide sufficient conditions, imposed only on model parameters, to guarantee synchronization of the variable speed model in the following two cases: 1) the maximum speed and the neighborhood radius are fixed constants and 2) the maximum speed and the neighborhood radius are changing with the population size. Our results reveal that the permitted maximum speed in the variable speed model can be larger than that in the relevant constant speed model.

This paper investigates the consensus problem of a three dimensional (3D) version of the widely studied Vicsek model, where each member moves in 3D Euclidean space with a constant speed with headings updated according to the average direction of neighbors. In comparison with the original Vicsek model, each agent’s heading is determined by two angle sequences interacting with each other, one of which evolves according to a “linear” non-homogeneous equation, which makes the theoretical analysis quite complicated. By analyzing the underlying structure of the system and relying on estimation of some characteristics concerning the initial states, we will establish consensus results for 3D Vicsek model under random framework without resorting to any a priori connectivity assumption.

A central and fundamental issue in the theory of complex systems is to understand how local rules lead to collective behavior of the whole system. This paper will investigate a typical collective behavior (synchronization) of a self-propelled particle system modeled by the nearest neighbor rules. While connectivity of the dynamic neighbor graphs associated with the underlying systems is crucial for synchronization, it is widely known that the verification of such dynamical connectivity is at the core of theoretical analysis. Ideally, conditions used for synchronization should be imposed on the model parameters and the initial states of the particles. One crucial model parameter is the interaction radius, and we are interested in the following natural and basic question: What is the smallest interaction radius for synchronization? In this paper, we will show that, in a certain sense, the smallest possible interaction radius approximately equals $\sqrt{\log n/(\pi n)}$, with $n$ being the population size, which coincides with the critical radius for connectivity of static random geometric graphs known in the literature.

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.

In this paper we provide a brief survey on recent research on multi-agent systems. We focus on results in three areas of the research, namely, estimation and filtering, intervention by external means, and interactive control.

This paper investigates the synchronization behavior of a class of flocks modeled by the nearest neighbor rules. While connectivity of the associated dynamical neighbor graphs is crucial for synchronization, it is well known that the verification of such dynamical connectivity is the core of theoretical analysis. Ideally, conditions used for synchronization should be imposed on the model parameters and the initial states of the agents. One crucial model parameter is the interaction radius, and we are interested in the following natural but complicated question: What is the smallest interaction radius for synchronization of flocks? In this paper, we reveal that, in a certain sense, the smallest possible interaction radius approximately equals √ log n/(πn), with n being the population size, which coincides with the critical radius for connectivity of random geometric graphs given by Gupta and Kumar [Critical power for asymptotic connectivity in wireless networks, in Stochastic Analysis, Control, Optimization and Applications, Birkhäuser Boston, Boston, MA, 1999, pp. 547-566].

In order to have a self-organized multi-agent system exhibit some expected collective behavior, it is necessary to add some special agents with information (called leaders) to intervene the system. Then a fundamental question is: how many such leaders are needed? Naturally the answer depends on the model to be studied. In this paper a typical model proposed by Vicsek et al. is used for answering the question. By estimating the characteristics concerning the initial states of all agents and analyzing the system dynamics, we provide lower bounds on the ratio of leaders needed to guarantee the expected consensus.

The consensus problem of multi-agent systems has attracted wide attention from researchers in recent years, following the initial work of Jadbabaie et al. on the analysis of a simplified Vicsek model. While the original Vicsek model contains noise effects, almost all the existing theoretical results on consensus problem, however, do not take the noise effects into account. The purpose of this paper is to initiate a study of the consensus problems under noise disturbances. First, the class of multi-agent systems under study is transformed into a general time-varying system with noise. Then, for such a system, the equivalent relationships are established among (i) robust consensus, (ii) the positivity of the second smallest eigenvalue of a weighted Laplacian matrix, and (iii) the joint connectivity of the associated dynamical neighbor graphs. Finally, this basic equivalence result is shown to be applicable to several classes of concrete multi-agent models with noise.

Multi-agent systems arise from diverse fields in natural and artificial systems, such as schooling of fish, flocking of birds, coordination of autonomous agents. In multi-agent systems, a typical and basic situation is the case where each agent has the tendency to behave as other agents do in its neighborhood. Through computer simulations, Vicsek et al. (1995) showed that such a simple local interaction rule can lead to a certain kind of cooperative phenomenon (synchronization) of the overall system, if the initial states are randomly distributed and the size of the system population is large. Since this model is of fundamental importance in understanding the multi-agent systems, it has attracted much research attention in recent years. In this paper, we will present a comprehensive theoretical analysis for this class of multi-agent systems under a random framework with large population, but without imposing any connectivity assumptions as did in almost all of the previous investigations. To be precise, we will show that for any given and fixed model parameters concerning with the interaction radius r and the agents’ moving speed v, the overall system will synchronize as long as the population size n is large enough. Furthermore, to keep the synchronization property as the population size n increases, both r and v can actually be allowed to decrease according to certain scaling rates.

The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents’ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie’s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0, 2π), which reveals some fundamental differences between the Vicsek model and its linearized version.

We present a framework for the stability problem in a class of multi-agent systems with local-global feedback control.It has the following features:1) each agent has its own dynamics described by linear discrete dynamical equations with noises;2) each agent is coupled with other agents by optimizing its own cost functions.In this framework,we derive the optimal local-global feedback control law,and analyzed the effect of the system parameters on the mean-square stability of the closed-loop system.