We are leading the effort to interface classical function theoretic operator theory with the budding field of data driven methods in dynamical systems.
Our Mission
In most data driven approaches to dynamical systems theory, the Koopman operator takes center stage. However, the Koopman operator only gets you so far, since it can only represent forward complete dynamical systems. Our objective is to design a host of operators, which are generalizations of Liouville and other operators, and Hilbert spaces that allow us to study dynamical systems that are beyond the scope of Koopman theory. We aim to provide a suite of tools so that everyday practitioners working with dynamical systems can access this rich world of operators.
“I think that this is an important step in Koopman Theory
and Dynamic Mode Decomposition research. Not only is the approach novel but the topic is an ambitious attempt in this segment where numerous algorithms for exogenous control exist.”
What We've Achieved
Modeling using Liouville operators and occupation kernels.
Control analysis from data using vector valued RKHSs and new operators.
Noise robust system identification using integrals rather than derivatives.
Introduced several new Hilbert spaces with signals playing the central role.
Created a Hilbert space with no Densely Defined Multiplication Operators.
Introduced state following kernels for optimal control synthesis (while a postdoc at NCR)
Developed DMD methods for nonlinear fractional order systems.
Nonlinear System ID for fractional order systems.