Bridging Data Assimilation and Control: Ensemble Model Predictive Control for High-Dimensional Nonlinear Systems

Abstract. Model predictive control (MPC) is an optimization-based control framework for linear and nonlinear systems. MPC estimates control inputs by iterative optimization of a cost function that minimizes deviations from a desired state while accounting for control costs over a finite prediction horizon. This process typically involves direct computations in state space through full model evaluations, making it computationally expensive for high-dimensional nonlinear systems. This study introduces ensemble model predictive control (EnMPC), a novel framework for nonlinear control that combines MPC and ensemble data assimilation. EnMPC directly solves the MPC cost function using ensemble smoother methods, including the four-dimensional ensemble variational assimilation method, ensemble Kalman smoother, and particle smoother. By assimilating pseudo-observations that incorporate information about reference trajectories and constraints, EnMPC mitigates nonlinearity and uncertainty in high-dimensional systems, outperforming conventional MPC in computational efficiency through ensemble approximations. In addition, EnMPC is able to determine optimal weights for control inputs by using the analysis error covariance derived from ensemble data assimilation. We present two different approaches for defining control objectives. The penalty term approach applies penalties when model predictions violate pre-defined constraints by assimilating constraint information as pseudo-observations. In contrast, the trajectory tracking approach assimilates pseudo-observations derived from a reference trajectory to lead the system in the direction of the desired state. We perform numerical experiments with idealized models that capture the chaotic nature of atmospheric systems to show that EnMPC efficiently controls the system and offers flexibility for a variety of control objectives.