Dynamical Systems and Nonlinear Control Theory
In a paper published online on September 2nd 2010, in the prestigious journal Science, Mezic, together with Sophie Loire, a postdoctoral fellow who works with Mezic and colleagues at the software development company Aimdyn, Inc. in Santa Barbara and at NASA’s Stennis Space Center in Mississippi, describe how they predicted the movement of oil spilled into the Gulf of Mexico after an explosion aboard the Deepwater Horizon rig on April 20.
UCSB Press Release:
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.