Model Predictive Control of Ginzburg-Landau Equation

Abstract

This work explores the realization of model predictive control (MPC) design to an important problem of vortex shedding phenomena in fluid flow. The setting of vortex shedding phenomena is represented by a Ginzburg-Landau (GL) equation model and leads to the mathematical representation given by complex infinite dimensional parabolic PDEs. The underlying GL model is considered within the boundary control setting and the modal representation is considered to obtain discrete infinite dimensional system representation which is used in the model predictive control design. The model predictive control design accounts for optimal stabilization of the unstable GL equation model, and for the naturally present input constraints and/or state constraints. The feasibility of the optimization based model predictive controller is ensured through a large enough prediction horizon. The subsequent feasibility is ensured in a disturbance free model setting. The applicability of an easily realizable discrete controller design is demonstrated using simulation with known parameters from the literature.

Iterative learning control of complex Ginzburg–Landau system

“…Up to now, there are many existing control methods for the GL system including optimal control, robust control, boundary control, feedback control, model predictive control, finite element method, model order reduction method, and fuzzy control (Aamo et al, 2005;Cohen et al, 2003;Gunzburger et al, 1991;Hintermer and Wegner, 2017;Ilak et al, 2010;Izadi et al, 2019;Tissot and Raymond, 2017;Yuan et al, 2017). These methods give good results for GL systems.…”