Hybrid Control For Synchronization And Consensus Of Complex Multi-agent Networks

Complex network is new and emerging scientific discipline that has drawn a great deal of attentions in recently years. In this field, synchronization and consensus of networks are important and essential problems for many network applications. Therefore, synchroniza-tion and consensus problem of networks is a focal and hot topic of great interest recently in control community. Roughly speaking, Synchronization and consensus is to design a network algorithm based on locally available information such that all nodes finally reach a state of agreement. This dissertation, based on previous works of the others, systemati-cally and deeply investigates the hybrid control for synchronization of complex dynamical networks and consensus of multi-agent systems. The main contents of this dissertation are outlined as follows.The synchronization of complex dynamical networks is studied via impulsive control. Many control schemes were reported to achieve the network synchronization. In the most of the control schemes, all nodes should obtain the same information as control input. This may lead to the difficulty in some practical applications. Because it is not easy for all node to obtain the same information in a large scale network. In order to avoid above imple-mentation difficulty, the concept of control topology is introduced to describe the whole controller structure, which consists of some directed connections between nodes, and the control topology can be designed according to different practical situations. Based on the control topology, the distributed impulsive control scheme is proposed to achieve the expo-nential synchronization of the network.Complex dynamical networks with time delay are considered. It is noted that in the practical networks time delays are often encountered. Ignoring them may lead to design flaws and incorrect analysis conclusions. For time delay, based on the concept of control topology, the synchronization problem of the network with system delay and multiple cou-pling delays is studied via distributed impulsive control. By stability theory for impulsive delayed systems, some sufficient conditions for global exponential synchronization are de-rived, and moreover, the exponential convergence rate can be specified.The distributed consensus problem of the first-order discrete-time multi-agent systems on directed networks are studied. For the communication of agents, it is assumed that only one agent can be selected with a prescribed probability and broadcasts its own state to neigh-bors via quantized communication (any arbitrary quantization) at each time step. For this kind of communication, the fundamental question is how to design distributed algorithms and what kinds of network topology that together lead to the quantized consensus. A class of broadcast gossip algorithms is proposed and a necessary and sufficient graphical condition is given to ensure the quantized consensus. In particular, the obtained graphical condition does not require symmetric network topology, which is weaker than those in some other literature. Several numerical simulations are given to show the effectiveness of the proposed algorithms.The distributed consensus problem of the second-order continuous-time multi-agent networks with sampled-data communication are investigated. Motivated by the impulsive control strategy, two kinds of impulsive distributed algorithms are proposed for achieving consensus, These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, some necessary and sufficient conditions are obtained to ensure the con-sensus of the networks. It is shown that the control gains, the sampling size and the eigen-values of the Laplacian matrix of communication graph play key role in achieving the con-sensus.The leader-following consensus problem of the multi-agent network is studied via the impulsive distributed algorithm. In the system, the agents only have local interaction and partial agents can obtain the information from the leader. Necessary and sufficient condition for fixed topology, and sufficient condition for switching topology are obtained.The impulsive algorithm is proposed for consensus of the continuous-time second-order multi-agent system under switching topology with aperiodic sampled communication, when the agents are not able to obtain any information about velocity, but only position information. Some sufficient conditions are given to ensure consensus of the multi-agent system. When the conditions on the control gains and the time-varying sampling period are satisfied, the multi-agent system achieves consensus if the communication graph has a directed spanning tree jointly.Finally, a summary has been done for all discussions in the dissertation. The research works further study are presented for the multi-agent networks.