Analysis and Control of Emergent Dynamics in Multilayered Networks of Dynamical Systems

现代一些最具挑战性的科学问题涉及对相互关联的系统网络的理解。*在应用中，网络通常对外部环境开放，它们跨多个时间和空间尺度与其他网络交互。例如，大脑本身就是一个不断相互作用的子网络网络，内部(彼此之间)和外部(即感觉输入和运动输出)都是如此。类似的模块化结构在工程领域也很常见：耦合的社交网络(例如，Facebook、Twitter)；由不同层组成的多式联运网络(例如，公共汽车、地铁)；异类多机器人网络(例如，飞行无人机、水下机器人)，都是典型的例子。我们将这些网络称为“多层网络”。*我们的研究计划有两个主要的长期目标：i)提供一个理论框架来证明多层网络的动力学性质；ii)开发一个控制其(涌现)动力学的理论。在短期内，我们将应用我们的框架来帮助理解神经元网络中如何出现同步的节奏活动，并设计分布式控制策略来协调不同驱动不足的车辆团队。将图论工具集成到控制理论框架中是我们方法论的核心。*从长远来看，我们的研究结果可以用于对加拿大至关重要的一系列应用，并在科学、商业、经济和社会领域产生重大影响。这些领域包括监测和监测(例如，水下、海洋、地面、空中和空间应用)、生物学(细胞生物学、神经科学)和生物医学系统(例如，开发用于治疗神经疾病的神经刺激设备)。

Some of the most challenging scientific questions of the modern age involve the understanding of networks of interconnected systems. ***In applications, networks are typically open to the external environment and they interact with other networks across multiple time and spatial scales. For example, the brain is itself a network of subnetworks in constant interaction, both internally (between each other) and externally (that is, with sensory inputs and motor outputs). Similar modular structures are also common in the engineering world: coupled social networks (e.g., Facebook, Twitter); multimodal transportation networks composed of different layers (e.g., bus, subway); heterogeneous multi-robot networks (e.g., flying drones, underwater vehicles), are typical examples. We will call these networks "multilayer networks". ***Our research program has two main long term goals: i) to provide a theoretical framework to certify dynamical properties of multilayer networks ; ii) To develop a theory to control their (emergent) dynamics. In the short term we will apply our framework to help understanding how synchronized rhythmic activity emerges in neuronal networks and to design distributed control strategies to coordinate heterogeneous teams of underactuated vehicles. The integration of graph theoretical tools into a control theoretical framework is at the core of our methodology. ***In the long term, the results of our research can be used in a range of applications that are of vital importance to Canada and have significant impact in scientific, commercialization, economic, and societal domains. Those include surveillance and monitoring (e.g., underwater, maritime, ground, air, and space applications), biology (cellular biology, neuroscience), and biomedical systems (e.g., the development of neurostimulation devices for the treatment of neurological diseases).