Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization

Data-driven optimal control via linear transfer operators: A convex approach

(2023) Joseph Moyalan et al.   AUTOMATICA

Learning Dynamical Systems with Side Information

(2023) Amir Ali Ahmadi et al.   SIAM REVIEW

Combining dynamic mode decomposition with ensemble Kalman filtering for tracking and forecasting

(2023) Stephen A. Falconer et al.   PHYSICA D-NONLINEAR PHENOMENA

Modern Koopman Theory for Dynamical Systems

(2022) Steven L. Brunton et al.   SIAM REVIEW

Promoting global stability in data-driven models of quadratic nonlinear dynamics

(2021) Alan A. Kaptanoglu et al.   Physical Review Fluids

Converging outer approximations to global attractors using semidefinite programming

(2021) Corbinian Schlosser et al.   AUTOMATICA

A study of the double pendulum using polynomial optimization

(2021) J. P. Parker et al.   CHAOS

Weak SINDy for partial differential equations

(2021) Daniel A. Messenger et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

(2020) Stefan Klus et al.   PHYSICA D-NONLINEAR PHENOMENA

Bounding extrema over global attractors using polynomial optimisation

(2020) David Goluskin   NONLINEARITY

Poincaré maps for multiscale physics discovery and nonlinear Floquet theory

(2020) Jason J. Bramburger et al.   PHYSICA D-NONLINEAR PHENOMENA

Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization

(2020) Jason J. Bramburger et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

(2020) Kadierdan Kaheman et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Koopman operator-based model reduction for switched-system control of PDEs

(2019) Sebastian Peitz et al.   AUTOMATICA

Koopman Operator Spectrum for Random Dynamical Systems

(2019) Nelida Črnjarić-Žic et al.   JOURNAL OF NONLINEAR SCIENCE

Active Learning of Dynamics for Data-Driven Control Using Koopman Operators

(2019) Ian Abraham et al.   IEEE Transactions on Robotics

Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

(2018) Milan Korda et al.   AUTOMATICA

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

(2018) Ian Tobasco et al.   PHYSICS LETTERS A

Dynamic mode decomposition using a Kalman filter for parameter estimation

(2018) Taku Nonomura et al.   AIP Advances

On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

(2017) Milan Korda et al.   JOURNAL OF NONLINEAR SCIENCE

Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System

(2017) David Goluskin   JOURNAL OF NONLINEAR SCIENCE

Global Stability Analysis Using the Eigenfunctions of the Koopman Operator

(2016) Alexandre Mauroy et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization

(2016) G. Fantuzzi et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming

(2016) Juan Kuntz et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

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

(2016) Steven L. Brunton et al.   PLoS One

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

(2015) Matthew O. Williams et al.   JOURNAL OF NONLINEAR SCIENCE

Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems

(2014) Milan Korda et al.   SIAM JOURNAL ON CONTROL AND OPTIMIZATION

Convex Computation of the Region of Attraction of Polynomial Control Systems

(2013) Didier Henrion et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Pre- and Post-Processing Sum-of-Squares Programs in Practice

(2009) J. Lofberg   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Uncertainty propagation in dynamical systems

(2008) Igor Mezić et al.   AUTOMATICA

Lyapunov Measure for Almost Everywhere Stability

(2008) Umesh Vaidya et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations

(2008) Jean B. Lasserre et al.   SIAM JOURNAL ON CONTROL AND OPTIMIZATION