Optimization-based feedback control of mixing in a stokes fluid flow

This work considers efficient methods for the optimal control of a bilinear distributed parameter system representing the evolution of a scalar field in a fluid flow. The aim is to influence the flow field in order to maximize fluid mixing. The cost by which performance is judged is the ‘mix-norm’ defined in Mathew, Mezic and Petzold (Physica D 2005). The problem is particularly challenging as a large number of states (∼10
⁵
) are required to approximate the solution. The approach presented here involves solving a dynamic optimization problem based on a low-order model with diffusivity several orders of magnitude larger than that of the actual system. This significantly reduces the complexity of the optimization problem. By solving recursively, feeding back the current system state as the initial model state, this work demonstrates that a controller based on a low-order model can provide satisfactory performance.