A Matlab library that implements a system identification framework for nonlinear dynamics -- referred to as Koopman Reduced-Order Nonlinear Identification and Control (KRONIC). For details see Kaiser et. al (2017) [arXiv].
The Koopman operator has emerged as a principled linear embedding of nonlinear dynamics, and its eigenfunctions establish intrinsic coordinates along which the dynamics behave linearly. KRONIC aims to identify Koopman eigenfunctions using sparse regression from data, and then derives the controller in these intrinsic coordinates.
- Clone this repository to your desktop.
- Add path to
KRONIC/utilsfolder to Matlab search path using
addpath('<path to kronic>/KRONIC/utils').
There are no dependencies.
See examples in the main folder
KRONIC for demonstrating the approach on various dynamical systems. Just execute this file in MatLab and it will generate the plot files in
AsymmetricPotentialWell.m -- Well hopping in an asymetric potential double well AutonomDoubleGyre.m -- Control of drifters in a double gyre flow, a simple model for ocean mixing NonAutonomDoubleGyre.m -- Similarly for the non-autonomous case DiscoverDuffing.m -- Discovery of Koopman eigenfunctions/conserved quantities from data DiscoverDuffing_Convergence.m -- Convergence analysis (error, estimation, control) [data and computational efficiency] DiscoverDuffing_KRONICvsEDMDc.m -- Comparison of KRONIC with extended dynamic mode decomposition (EDMD) for control SlowManifold.m -- Control of system with slow manifold (analytical example) ... several other examples