学术报告第201910期

报告题目：Singularly perturbed systems: stability analysis of hybrid systems and modelling of consensus

报 告 人：Irinel Constantin Morarescu，法国洛林大学教授

报告时间：2019年3月21日（周四）下午14:00-15:00

报告地点：南一楼中314室

报告摘要:

The talk contains two different problems related to dynamical systems evolving on multiple time-scales.

In the first part we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be mode-dependent. This means that, at switching instants, some of the slow variables can become fast and vice-versa. Firstly, we show that using a mode-dependent variable reordering we can rewrite this class of systems in a form in which the variables preserve their slow or fast nature over time. Secondly, we establish, through singular perturbation techniques, an upper bound on the minimum dwell-time ensuring the overall system’s stability. Remarkably, this bound is the sum of two terms. The first term, which can be equal to zero, only depends on the matrices of the reduced order linear hybrid system describing the slow dynamics and corresponds to an upper bound on the minimum dwell time ensuring the stability of that system. The order of magnitude of the second term is determined by that of the parameter defining the ratio between the two time-scales of the singularly perturbed system.

In the second part of the talk, we consider the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to densely and intensively connected clusters into aggregate variables. It will be shown that under suitable conditions, the states of the agents in each cluster converge fast toward a local agreement. Local agreements correspond to aggregate variables which slowly converge to consensus. Existing results concerning the time-scale separation in large networks focus on fixed and undirected graphs. The aim of this work is to extend these results to the more general case of time-varying directed topologies. It is noteworthy that in the fixed and undirected graph case the average of the states in each cluster is time-invariant when neglecting the interactions between clusters. Therefore, they are good candidates for the aggregate variables. This is no longer possible here. Instead, we find suitable time-varying weights to compute the aggregate variables as time-invariant weighted averages of the states in each cluster. This allows to deal with the more challenging time-varying directed graph case. We end up with a singularly perturbed system which is analyzed by using the tools of two time-scales averaging which seem appropriate to this system.

报告人简介：

Irinel Constantin Morarescu，法国洛林大学全职教授，法国南希自动化研究中心研究员。他分别于1997年和1999年在罗马尼亚布加勒斯特大学获得数学学士和硕士学位，2006年于罗马尼亚布加勒斯特大学和贡比涅技术大学获得博士学位。2016年获洛林大学研究指导资格文凭。2007年3月至2010年10月，分别在法国国家信息与自动化研究所(INRIA)、格勒诺布尔大学Jean Kuntzmann实验室和法国国家科学研究中心GIPSA实验室从事博士后研究工作。他的主要研究方向包括动态系统（如混杂系统、双时间尺度系统、时滞系统）的分析与综合、多智能体系统的分布式控制和优化，社会网络中观点动力学的建模、分析和控制。

他担任IMA Journal of Mathematical Control & Information和IEEE Control Systems Society-Conference Editorial Board等期刊和国际会议的副编辑。他是国际自动控制联合会(IFAC)网络化系统技术委员会成员，2018年IFAC混杂系统分析与设计会议程序委员会委员，第七届IFAC网络化系统分布式估计与控制研讨会程序委员会委员。