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

TL;DR

This paper introduces a novel MCMC-based approach for generating uncertainty sets in nonlinear dynamical systems using operator-theoretic metrics, enabling robust optimization applications.

Contribution

It develops a Hamiltonian Monte Carlo method to efficiently sample transfer operators, applicable to general nonlinear systems, filling a gap in existing uncertainty set generation methods.

Findings

Validated the method with numerical examples.

Demonstrated efficient sampling of high-dimensional transfer operators.

Showed applicability to nonlinear dynamical systems.

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.