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

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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).