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Koopman Reduced-Order Nonlinear Identification and Control (KRONIC)

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.

Some examples on which KRONIC is demonstrated:


  1. Clone this repository to your desktop.
  2. Add path to KRONIC/utils folder to Matlab search path using addpath('<path to kronic>/KRONIC/utils').


There are no dependencies.

Getting Started

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 KRONIC/FIGURES.

File description


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

License (CiteMe OSS)

The code is published under the CiteMe OSS license. See the LICENSE file for details.


Koopman Reduced-Order Nonlinear Identification and Control




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