Finite-Dimensional MOR-Based RHC for Steering 2D Navier-Stokes Equations to Desired Trajectories
For control of fluid flows, this work provides a theoretically grounded and computationally efficient RHC method for steering Navier-Stokes equations to desired trajectories.
This paper achieves local exponential stabilization of 2D Navier-Stokes equations to a desired trajectory using receding horizon control with finitely many actuators, and demonstrates that a model-order-reduced approach based on proper orthogonal decomposition significantly reduces computational cost while maintaining stabilization performance in numerical experiments.
This paper investigates the local exponential stabilization of the two-dimensional Navier--Stokes equations to a given reference trajectory by means of receding horizon control (RHC). The control is realized as a linear combination of finitely many actuators, represented by indicator functions supported on subsets of a prescribed control subdomain. We establish local exponential stabilizability and suboptimality for the resulting RHC scheme. Numerical experiments for two flow configurations of increasing complexity illustrate the theoretical findings and assess the practical performance of the method. In addition, we propose a model-order-reduced RHC approach based on proper orthogonal decomposition, which significantly reduces the computational cost while maintaining favorable closed-loop stabilization performance in the numerical experiments.