复杂网络的同步与控制.pptxVIP

Complex Network Synchronization and Topology indentification第5讲：复杂网络的动力学同步与控制;  内 容 提 要 ; 1.复杂动力网络的 一般同步概念 近年非线性、连接性、以及复杂性问题的研究已取得了重要的进展。如何把复杂网络理论、动力系统理论和現代控制理论三者密切結合,深入地研究复杂动力网络的动力学特性、同步与控制是一个重要课题。;Chaos Communications Francis C M Lau, Michael C K Tse, PolyUCentre for Chaos Control and Synchronization; Synchronization Is one of the most Pervasive phenomena in the Universe;起源于钟摆的发明者 惠更斯(Huygens) ;The study of synchronous systems cuts across the disciplines of modern science. But the underlying phenomenon was first documented over three centuries ago. In 1665, Dutch physicist Christiaan Huygens lay ill in bed, watching the motions of two pendulum clocks he had built. To his surprise, he detected an “odd kind of sympathy” between the clocks: regardless of their initial state, the two pendulums soon adopted the same rhythm, one moving left as the other swung right. Elated, Huygens announced his finding at a special session of the Royal Society of London, attributing this synchrony to tiny forces transmitted between the clocks by the wooden beam from which they were suspended. In 1960s, Arthur Winfree, a theoretical biologist began to study coupled oscillators;Biological Clock; Self-organization in the concert-hall: the dynamics of rhythmic applause, Nature, 2001;Pedestrians make London’s Millennium Bridge wobble;Tacoma Narrows Bridge Disaster;2.复杂动力网络的一般理论框架; 复杂动力网络的一般理论模型 ;即写成 其中c是耦合强度， 是0-1矩阵 如果设:A为耗散矩阵（行和为0： ), 且不可约矩阵(连通)，则经常写成 如果A是常数矩阵，内联是自治的,则动力网络是非时变的，否则是时变动力网络。;例：两个节点（Lorenz系统）的双向连接 ;网络同步定义: 首先定义同步流形为线性子空间 如果当 时，x趋近于M，则称网络同步. 即 对于所有的节点，在任意初始条件下 ;对于耗散耦合 ，则有特征值 零特征值对应的右特征向量为[1,1,…,1]，它对应同步??形。 A为扩散矩阵时，同步流形一般是指孤立节点（动力系统）解，它满足 所谓同步也就是所有节点状态在横截同步流形的N-1维子空间上的投影渐近地趋于零。 研究同步关心：A 和 的特征值，动力系统f的Lipschitz条件 ;同步判定准则;注意到：耗散耦合的条件, = 0 总是耦合矩阵的一个特征值, 且其特征向