Proper orthogonal decomposition in sparse optimal control of some reaction diffusion equations using model predictive control

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 883-884 ◽  
Author(s):  
Christopher Ryll ◽  
Fredi Tröltzsch
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Proper Orthogonal Decomposition ◽  
Predictive Control ◽  
Reaction Diffusion ◽  
Orthogonal Decomposition ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Sparse Optimal Control ◽  
Proper Orthogonal

Sparse Optimal Control of the Schlögl and FitzHugh–Nagumo Systems

2013 ◽  
Vol 13 (4) ◽  
pp. 415-442 ◽  
Author(s):  
Eduardo Casas ◽  
Christopher Ryll ◽  
Fredi Tröltzsch
Keyword(s):  
Optimal Control ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Optimal Controls ◽  
Wave Fronts ◽  
First Order ◽  
Schlögl Model ◽  
Sparse Optimal Control ◽  
Objective Functional

Abstract. We investigate the problem of sparse optimal controls for the so-called Schlögl model and the FitzHugh–Nagumo system. In these reaction–diffusion equations, traveling wave fronts occur that can be controlled in different ways. The L1-norm of the distributed control is included in the objective functional so that optimal controls exhibit effects of sparsity. We prove the differentiability of the control-to-state mapping for both dynamical systems, show the well-posedness of the optimal control problems and derive first-order necessary optimality conditions. Based on them, the sparsity of optimal controls is shown. The theory is illustrated by various numerical examples, where wave fronts or spiral waves are controlled in a desired way.

Sign in / Sign up

Export Citation Format

Share Document