Dieter Grass, Hannes Uecker
Abstract:
We present a numerical framework to treat infinite time horizon
spatially distributed optimal control problems via the associated canonical
system derived by Pontryagin's maximum principle.
The basic idea is to consider the canonical system in two steps.
First we perform a bifurcation analysis of canonical steady states using the
continuation and bifurcation package pde2path, yielding
a number of so called flat and patterned canonical steady states.
In a second step we link pde2path to the two point boundary value problem
solver TOM to study time dependent canonical paths to steady
states having the so called saddle point property.
As an example we consider a shallow lake model with diffusion.
Submitted June 10, 2015. Published January 4, 2017.
Math Subject Classifications: 49J20, 49N90, 35B32.
Key Words: Optimal control; Pontryagin's maximum principle; bioeconomics;
canonical steady states; connecting orbits.
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Dieter Grass ORCOS, Institute of Mathematical Methods in Economics Vienna University of Technology A-1040 Vienna, Austria email: dieter.grass@tuwien.ac.at | |
Hannes Uecker Institut für Mathematik Universität Oldenburg D26111 Oldenburg, Germany hannes.uecker@uni-oldenburg.de |
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