The problem of design, reverse engineering and retrofitting for robust operation of large-scale interconnected dynamical systems is perhaps the engineering grand challenge of our time. Mathematics and engineering tools for treatment of individual components have been developed to a high degree of sophistication. However, when these components are connected - whether physically or by communication devices - new, collective phenomena can emerge that are not necessarily related to properties of individual components. The local consequences of such phenomena can be sensed - and the drive towards reduced cost and ubiquity of sensors leads to a massive amount of dynamically changing data. The phenomena indicated by sensed data have to be recognized, counteracted or perhaps even utilized dynamically in attempts to achieve optimal design and operation. Here are some of the critical elements of the applied problem at hand, the "Big Data Dynamics in Systems of Systems", and our viewpoint on the associated research directions.
Certain dynamical systems, e.g., geophysical fluid flows, can be so complicated that it is difficult to provide concise mathematical models for their behavior. Nevertheless, simulations and experiments provide us with data in which we can recognize simple patterns that resemble systems that are well studied and understood. My research aimed to extract regions of such simpler behaviors and analyze how micro-structures fit together to form larger coherent structures, taking an approach alternative to classical geometric dynamical systems analysis.
In this work we study instability in networked systems which leads to a better understanding of their sensitivities and control requirements. The networks we study range from those inspired by biology to power grids and networked control systems. We use both deterministic and stochastic Dynamical Systems tools including high dimensional internal resonance, Hamiltonian dynamics, averaging, and analysis of stochastic differential equations.
I am currently building a physical model of 20 coupled oscillators, imposing a variety of initial conditions, from which we will measure and collect behavioral information via video capture.