Auxiliary functions as Koopman observables: data-driven analysis of dynamical systems via polynomial optimization

DOI10.1007/s00332-023-09990-2arXiv2303.01483OpenAlexW4388098327MaRDI QIDQ6066022

Giovanni Fantuzzi, Jason J. Bramburger

Publication date: 15 November 2023

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.01483

zbMATH Keywords

Lyapunov functionsemidefinite programmingauxiliary functiondynamic mode decompositionKoopman operatortime average

Mathematics Subject Classification ID

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• A kernel-based method for data-driven Koopman spectral analysis
• On the numerical approximation of the Perron-Frobenius and Koopman operator
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• On the speed of convergence in the ergodic theorem
• The limit cycle of the van der Pol equation is not algebraic
• Semidefinite programming relaxations for semialgebraic problems
• Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
• Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system
• On convergence of extended dynamic mode decomposition to the Koopman operator
• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Koopman operator spectrum for random dynamical systems
• Data-driven approximation of the Koopman generator: model reduction, system identification, and control
• Poincaré maps for multiscale physics discovery and nonlinear Floquet theory
• Weak SINDy for partial differential equations
• Koopman operator-based model reduction for switched-system control of PDEs
• Region of attraction estimation using invariant sets and rational Lyapunov functions
• Uncertainty propagation in dynamical systems
• Barrier certificates for nonlinear model validation
• Converging outer approximations to global attractors using semidefinite programming
• Global Optimization with Polynomials and the Problem of Moments
• An Introduction to Polynomial and Semi-Algebraic Optimization
• Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming
• Global Stability Analysis Using the Eigenfunctions of the Koopman Operator
• Convex Computation of the Region of Attraction of Polynomial Control Systems
• Some NP-complete problems in quadratic and nonlinear programming
• Linear Programming Formulation for Optimal Stopping Problems
• The linear programming approach to deterministic optimal control problems
• Lyapunov Measure for Almost Everywhere Stability
• Pre- and Post-Processing Sum-of-Squares Programs in Practice
• Bounding Extreme Events in Nonlinear Dynamics Using Convex Optimization
• Modern Koopman Theory for Dynamical Systems
• Robust Approximation of the Stochastic Koopman Operator
• Computing Controlled Invariant Sets from Data Using Convex Optimization
• Bounding extrema over global attractors using polynomial optimisation
• Weak SINDy: Galerkin-Based Data-Driven Model Selection
• Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization
• SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
• Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems
• Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial Systems
• Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations
• DETERMINISTIC CHAOS SEEN IN TERMS OF FEEDBACK CIRCUITS: ANALYSIS, SYNTHESIS, "LABYRINTH CHAOS"
• Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization
• On the Continuity of the Generalized Inverse
• Learning Dynamical Systems with Side Information
• Combining dynamic mode decomposition with ensemble Kalman filtering for tracking and forecasting
• Data-driven optimal control via linear transfer operators: a convex approach

This page was built for publication: Auxiliary functions as Koopman observables: data-driven analysis of dynamical systems via polynomial optimization