Modeling And Consensus Of Complex Network And Their Application In Multiple Mobile Agents System

Since Watts and Strigatz's work in small-world network in 1998 and Barabàsi and Albert's work in scale-free in 1999, an explosion of work about complex networks emerges, from the analysis of the topologies of real networks, the evolution models and dynamics of complex networks to the applications of the complex network theory. And in the field of Robotics and Artificial Intelligence, the coordinate control of multiple motion agent system (MMAS) is nowadays a hot topic. Motivated by the recent advances in theory of complex dynamical network, we regard MMAS as a complex dynamical network, where the node represents an agent, the edge between two nodes represents the coordinate relation (such as sensor relation or communication relation) between two agents and the dynamics of node represents the motion dynamics of agent. Based on complex dynamical network theory, the mode construction and consensus problem of multiple motion agent complex dynamical network are studied in this dissertation, and the main work and research results lie in the following.Motivated by the communication network of MMAS, a class of evolving network models with physical position neighbourhood connectivity are proposed. Based on these models, the clustering coefficients, average distances, degree distributions, the tolerance to the network delay and the time to reach consensus for different evolving parameters in different models are studied detailedly. This study shows with the increasing of depth of neighbourhood M, the clustering coefficients decrease notably, the time to reach consensus becomes shorted in these five models. It also shows that Model 4 is most vulnerable to time-delay in these five models and its degree distribution represents a transition between that of an exponential network and that of a power-law scaling network with M increase, and the Barábasi-Albert scale-free model is only one of its special (limiting) cases.We study the robustness to node and edge failure, the tolerance to network time-delay and the time to reach a consensus for different complex network topologies. And the topologies include small-world network, scale-free network, nearest neighbour coupled network, star network and global coupled network. By this study, we find the following results: First, as a topology with fewer edges, star network has a rapid convergence speed in the consensus problem, and its speed is faster than that of small-world network and scale-free network, which have the same number of node and average node degree. However, star network is vulnerable to time-delay. Second, the small-world network and scale-free network have the similar convergence speeds in consensus problem, and their convergence speeds are many times larger than that of the nearest neighbour coupled network with the same number of node and average node degree. Third, for global network, its speed is the fastest among all networks, but it is vulnerable to time-delay. Fourth, there is a near linear relationship between the robustness to time-delay and the maximum node degree of the network, so the maximum node degree of the network is a good predictor for time-delay robustness in all networks. Finally, for scale-free network, the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges of the network.Two methods of devising a speed-optimized small-world network in consensus problem are presented. One bases on NW model (proposed by Newman and Watts) and genetic-algorithm (GA), another bases on WS model (proposed by Watts and Staogtz) and long-range nodes preference reconnection. It is found that, as we construct a small-world network with a smaller network size and fixed long-range links using NW model, we can optimize the long-range link configuration using GA methodology to obtain a small-world network with faster consensus speed. It is also find that in the every step of edges rewiring of small-world construction using WS model, as the distance between two rewiring nodes are the longest, the resulting network is faster significantly in reaching consensus.Motivated by recent advances in consensus theory of complex dynamical network, we present a novel motion model about the formation control and group motion control of MMAS for fixed and changing interactions. Based on this model and the consensus theory of complex network, two theorems about motion stability of MMAS with fixed and switched topology are presented and proved.Motivated by recent advances in synchronization theory of complex dynamical network, we develop another method of controller design for formation reaching and group motion controlling of the MMAS. A novel motion model of the system is presented. Based on this model, the design method of decentralized controller for each agent is investigated. The stability property of the system is also analyzed and proved in detail. This control method is useful espically as the motion dynamics of agent is complicated.Flocking control is a new pattern of decentralized approach imitating animal cooperative behavior. A leader-follower flocking control mechanism for changing topology is introduced based on existed theory on flocking of mobile agents, which makes flocking motion be sequencable behaviour. The control output of this scheme is smooth even as the agent network is switching.Finally, a summary has been done for all the discussion in the disseration. And the research work in further study is presented.