Ensemble Kalman Filter Meets Model Predictive Control in Chaotic Systems

Abstract

Although data assimilation originates from control theory, the relationship between modern data assimilation methods in geoscience and model predictive control has not been extensively explored. In the present paper, I discuss that the modern data assimilation methods in geoscience and model predictive control essentially minimize the similar quadratic cost functions. Inspired by this similarity, I propose a new ensemble Kalman filter (EnKF)-based method for controlling spatio-temporally chaotic systems, which can be applied to high-dimensional and nonlinear Earth systems. In this method, the reference vector, which serves as the control target, is assimilated into the state space as a pseudo-observation by ensemble Kalman smoother to obtain the appropriate perturbation to be added to a system. A proof-of-concept experiment using the Lorenz 63 model is presented. The system is constrained in one wing of the butterfly attractor without tipping to the other side by reasonably small control perturbations which are comparable with previous works.