Premium
A Model Problem for Optimal Control of a Parabolic PDE Fully Coupled to ODEs
Author(s) -
Kimmerle Sven-Joachim
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900447
Subject(s) - ode , ordinary differential equation , optimal control , partial differential equation , mathematics , parabolic partial differential equation , class (philosophy) , elliptic partial differential equation , differential equation , mathematical analysis , mathematical optimization , computer science , artificial intelligence
In many applications we encounter fully coupled systems involving a partial differential equation (PDE) and an ordinary differential equation (ODE). A particular class is the case in which the PDE is parabolic. This coupled optimal control problem is considered in theory in [1]. Here we consider a toy example with the heat equation and a second order ODE given by Newton dynamics. The acceleration in the ODE may be controlled and is subject to box constraints. We present numerical optimal control results for this toy example.