Heuristic actuator selection with the use of data of nonlinear optimal control for fluid flows

Abstract

In this paper, we propose a heuristic method to select actuators for optimal control based on the Navier–Stokes equations. In the proposed method, the optimal control with the use of all candidates of actuators is applied to a fluid flow in a numerical simulation, and the optimal control inputs for all the candidates are acquired. Actuators are then selected in the descending order of the norms of these optimal control inputs. This procedure is numerically tractable for some of two-dimensional and three-dimensional fluid flows. The proposed method is demonstrated for an actuator selection problem for a two-dimensional flow around a circular cylinder at Reynolds number 100. Numerical simulations reveal that actuators are selected so that the optimal controller can take the state close to the steady state with a small control effort.