Wenwu Yu

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

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.

Brief paper: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems

This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system facing communication delays. A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.

Brief paper: On pinning synchronization of complex dynamical networks

There exist some fundamental and yet challenging problems in pinning control of complex networks: (1) What types of pinning schemes may be chosen for a given complex network to realize synchronization? (2) What kinds of controllers may be designed to ensure the network synchronization? (3) How large should the coupling strength be used in a given complex network to achieve synchronization? This paper addresses these technique questions. Surprisingly, it is found that a network under a typical framework can realize synchronization subject to any linear feedback pinning scheme by using adaptive tuning of the coupling strength. In addition, it is found that the nodes with low degrees should be pinned first when the coupling strength is small, which is contrary to the common view that the most-highly-connected nodes should be pinned first. Furthermore, it is interesting to find that the derived pinning condition with controllers given in a high-dimensional setting can be reduced to a low-dimensional condition without the pinning controllers involved. Finally, simulation examples of scale-free networks are given to verify the theoretical results.

Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics

This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the systems ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.

Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies

Distributed consensus tracking is addressed in this paper for multi-agent systems with Lipschitz-type node dynamics. The main contribution of this work is solving the consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. By using tools from M-matrix theory, a class of consensus tracking protocols based only on the relative states among neighboring agents is designed. By appropriately constructing Lyapunov function, it is proved that consensus tracking in the closed-loop multi-agent systems with a fixed topology having a directed spanning tree can be achieved if the feedback gain matrix and the coupling strength are suitably selected. Furthermore, with the assumption that each possible topology contains a directed spanning tree, it is theoretically shown that consensus tracking under switching directed topologies can be achieved if the control parameters are suitably selected and the dwell time is larger than a positive threshold. The results are then extended to the case where the communication topology contains a directed spanning tree only frequently as the system evolves with time. Finally, some numerical simulations are given to verify the theoretical analysis.

Second-order leader-following consensus of nonlinear multi-agent systems via pinning control

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.

Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay

Many real-world large-scale complex networks demonstrate a surprising degree of synchronization. To unravel the underlying mechanics of synchronization in these complex networks, a generally linearly hybrid coupled network with time-varying delay is proposed, and its global synchronization is then further investigated. Several effective sufficient conditions of global synchronization are attained based on the Lyapunov function and a linear matrix inequality (LMI). Both delay-independent and delay-dependent conditions are deduced. In particular, the coupling matrix may be nonsymmetric or nondiagonal. Moreover, the derivative of the time-varying delay is extended to any given value. Finally, a small-world network, a regular network, and scale-free networks with network size are constructed to show the effectiveness of the proposed synchronous criteria.

Distributed Consensus Filtering in Sensor Networks

In this paper, a new filtering problem for sensor networks is investigated. A new type of distributed consensus filters is designed, where each sensor can communicate with the neighboring sensors, and filtering can be performed in a distributed way. In the pinning control approach, only a small fraction of sensors need to measure the target information, with which the whole network can be controlled. Furthermore, pinning observers are designed in the case that the sensor can only observe partial target information. Simulation results are given to verify the designed distributed consensus filters.

Consensus in Directed Networks of Agents With Nonlinear Dynamics

This technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network. Both local and global consensus are defined and investigated. Techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus. The local consensus problem is first studied via a combination of the tools of complex analysis, local consensus manifold approach, and Lyapunov methods. A generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees, for which ideas from algebraic graph theory, matrix theory, and Lyapunov methods are utilized.

Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics☆

Abstract This paper discusses the design of distributed control gains for consensus in multi-agent systems with second-order nonlinear dynamics. First, an effective distributed adaptive gain-design strategy is proposed based only on local information of the network structure. Then, a leader–follower consensus problem in multi-agent systems with updated control gains is studied. A distributed adaptive law is then proposed for each follower based on local information of neighboring agents and the leader if this follower is an informed agent. Furthermore, a distributed leader–follower consensus problem in multi-agent systems with unknown nonlinear dynamics is investigated by combining the variable structure approach and the adaptive method. Finally, simulation examples are given to illustrate the theoretical analysis.