标题： 关于动态系统的参数识别与同步的同时可扩展性与收敛性 显示英文标题

标题： On the scalability and convergence of simultaneous parameter identification and synchronization of dynamical systems

摘要： 动态系统的同步是一种方法，可以使两个系统除了一个收敛到零的误差之外具有相同的态轨迹。 该方法包括从一个系统（驱动）到另一个系统（响应）的适当单向耦合。 这要求响应系统与驱动系统共享相同的动力学模型。 对于驱动未知的情况，陈氏在2002年提出了一种方法来调整响应系统，使得在满足以下条件时实现同步：（1）响应动力学模型是带有参数向量的线性模型，并且（2）存在一个参数向量使两个系统的动力学相同。 然而，这种方法有两个局限性：首先，对于复杂的参数模型，它不易扩展（例如，如果参数数量大于状态维度），其次，不能保证模型参数会收敛，特别是当同步误差接近零时。 本文提出了一个解决这两个局限性的自适应定律。 使用李雅普诺夫第二方法的稳定性及收敛性证明支持了所提出的自适应定律。 最后，数值模拟展示了所提出方法的优势，即展示了陈氏方法失败的情况下，所提出的方法仍然有效。 显示英文摘要

摘要： The synchronization of dynamical systems is a method that allows two systems to have identical state trajectories, appart from an error converging to zero. This method consists in an appropriate unidirectional coupling from one system (drive) to the other (response). This requires that the response system shares the same dynamical model with the drive. For the cases where the drive is unknown, Chen proposed in 2002 a method to adapt the response system such that synchronization is achieved, provided that (1) the response dynamical model is linear with a vector of parameters, and (2) there is a parameter vector that makes both system dynamics identical. However, this method has two limitations: first, it does not scale well for complex parametric models (e.g., if the number of parameters is greater than the state dimension), and second, the model parameters are not guaranteed to converge, namely as the synchronization error approaches zero. This paper presents an adaptation law addressing these two limitations. Stability and convergence proofs, using Lyapunov's second method, support the proposed adaptation law. Finally, numerical simulations illustrate the advantages of the proposed method, namely showing cases where the Chen's method fail, while the proposed one does not.