Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order…

• UO
  University of Washington
• UA
  U.S. Air Force

  Awards: FA9550, FA9550-14-1-0398
• AF
  Air Force Office of Scientific Research

  Awards: FA9550-, FA9550-09-0174, FA9550-14-1-0398, FA9550