Modern Koopman Theory for Dynamical Systems

The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator-theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with…

• NS
  National Science Foundation

  Award: 1934292
• DA
  Defense Advanced Research Projects Agency

  Award: HR011-16-C-0016
• AR
  Army Research Office

  Awards: W911NF-19-1-0045, W911NF-17-1-0045