Reduced Order Optimal Control of the Convective FitzHugh-Nagumo Equation

Abstract

In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective FitzHugh-Nagumo (FHN) equations. The convective FHN equations consists of the semi-linear activator and the linear inhibitor equations, modeling blood coagulation in moving excitable media. The semilinear activator equation leads to a non-convex optimal control problem (OCP). The most commonly used method in reduced optimal control is POD. We use DEIM and DMD to approximate efficiently the nonlinear terms in reduced order models. We compare the accuracy and computational times of three reduced-order optimal control solutions with the full order discontinuous Galerkin finite element solution of the convection dominated FHN equations with terminal controls. Numerical results show that POD is the most accurate whereas POD-DMD is the fastest.

References in corpus (5)

• Moment Closure - A Brief Review
• Space-time Galerkin POD with application in optimal control of semi-linear parabolic partial differential equations
• Optimal Control of Convective FitzHugh-Nagumo Equation
• Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems
• Structure preserving integration and model order reduction of skew-gradient reaction-diffusion systems