An MCMC Method for Uncertainty Set Generation via Operator-Theoretic Metrics

Abstract

Model uncertainty sets are required in many robust optimization problems, such as robust control and prediction with uncertainty, but there is no definite methodology to generate uncertainty sets for nonlinear dynamical systems. In this paper, we propose a method for model uncertainty set generation via Markov chain Monte Carlo. The proposed method samples from distributions over dynamical systems via metrics over transfer operators and is applicable to general nonlinear systems. We adapt Hamiltonian Monte Carlo for sampling high-dimensional transfer operators in a computationally efficient manner. We present numerical examples to validate the proposed method for uncertainty set generation.

6 pages

References in corpus (5)

• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
• Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators
• Linear Distances between Markov Chains
• Optimal construction of Koopman eigenfunctions for prediction and control