【作者】 吴正平；

【导师】 关治洪；

【作者基本信息】 华中科技大学 ， 控制理论与控制工程， 2007， 博士

【摘要】 自1998年的Watts和Strogatz提出“小世界”网络模型,1999年Barabàsi和Albert提出“无标度”网络演化模型以来,复杂网络的研究在实证分析、网络的演化模型、网络的动力学行为和复杂网络理论的应用这四个方面取得了惊人的进展。在机器人及人工智能领域,多移动智能体的协调控制是当前的一个热点问题。受到当前复杂动态网络理论迅速发展的启发,将多移动智能体系统看成一个复杂动态网络,网络中的节点表示智能体,两个节点之间的边表示两智能体之间的协作关系(比如感应关系、通信关系等),节点的动力学特性则表示智能体群运动特性。本文以多移动智能体系统为研究背景,以复杂网络理论为工具,在网络建模、网络的一致性问题等方面展开了研究,本文主要工作如下:受多移动智能体通信网络的启发,提出了一类基于物理位置近邻的演化网络模型。在这些模型的基础上,对这些模型生成的网络的聚类系数、平均路径长度、度分布、对网络延时的鲁棒性和达到一致性所需要的时间等在不同的演化参数下不同的特性作了深入研究。研究表明,随着近邻节点数M的增大,这5个模型产生的网络的聚类系数都急剧减小、一致性问题收敛时间都会变短;对于模型4,它对网络延时的鲁棒性是最差,当M由小变大时,其度分布由指数分布到幂律分布过渡,BA无标度模型仅仅是它的一种特殊(极限)情况。研究了几种不同拓扑结构的网络对节点失效和边失效的鲁棒性、对网络延时的鲁棒性以及一致性问题的收敛速度等方面的特性,这些网络包括小世界网络、无标度网络、最临近耦合网络、星网络和全耦合网络等。通过研究发现,第一,星网络作为一个边较少的网络,却具有很快的一致性问题收敛速度,其收敛速度要比和它具有相同节点数和节点平均度的小世界网络和无标度网络都要快,但星网络对网络延时的鲁棒性很弱;第二,小世界网络和无标度网络在相同平均度和节点数的情况下,其一致性问题的收敛速度相差不大,但它们要比和它们具有相同平均度和节点数的最邻近耦合网络的收敛速度快很多倍;第三,全耦合网络是所有网络中一致性收敛速度最快的,但其对网络延时的鲁棒性很弱;第四,网络节点最大度和网络的延时鲁棒性有近似的线性关系,因此网络节点的最大度可以用来对网络延时鲁棒性进行预测;最后,对无标度网络而言,通过对网络中很小一部分边进行解耦,可以显著提高网络对延时的鲁棒性。提出了设计一致性速度优化的小世界网络的两种方法。一种基于NW小世界网络模型(由Newman和Watts提出)和遗传算法,另一种是基于WS小世界模型(由Watts和Staogtz提出)和长程节点优先连接。研究表明,当使用NW模型来构建节点数不多、长程连接数固定的小世界网络时,可以使用遗传算法来优化选择长程连接的连接图,以获得小世界网络更快的一致性收敛速度;当使用WS模型来构建小世界网络,在断边重连的每一步,当重连的另一个节点选择和固定节点距离最长的节点时,所形成的小世界网络的一致性收敛速度会明显加快。受复杂动态网络一致性理论的启发,提出了一个简单新颖的、适用固定和动态变化两种通信拓扑的多移动智能体系统的队形控制和群运动控制模型。在该模型的基础上,使用复杂网络的一致性理论,给出和证明了两个关于系统在固定和动态变化通信拓扑下的系统稳定性的两个定理。受复杂动态网络的同步理论的启发,提出了另一个多移动智能体系统的队形控制和群运动控制的控制器设计方案,并为系统给出了一个新颖的控制模型。在该模型的基础上,研究了每一个智能体的控制器的具体设计方案,对系统的稳定性进行了分析和证明。该方案更适用于智能体运动特性特别复杂的情况。群集运动控制是模拟自然界中生物聚集运动的新型分布式控制方法,在当前多移动智能体群集控制理论的基础上,提出了基于领航者跟随者模式的动态变化拓扑的有序化群集运动控制算法,使得群集运动成为有序化控制行为。当智能体网络在切换的情况下,该方案设计出的控制输出仍然是光滑的。最后对全文的研究工作进行了总结,并对将来要做的研究工作进行了展望。更多还原

【Abstract】 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.更多还原