Expediting the transition from non-renewable to renewable energy via optimal control

Helmut Maurer; Willi Semmler

doi:10.3934/dcds.2015.35.4503

Article Contents

2015, Volume 35, Issue 9: 4503-4525. Doi: 10.3934/dcds.2015.35.4503

This issue Previous Article Uniform convergence of the POD method and applications to optimal control Next Article Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data

Expediting the transition from non-renewable to renewable energy via optimal control

Helmut Maurer^1, and
Willi Semmler^2,

1.
Institute of Computational and Applied Mathematics, University of Muenster, Einsteinstr. 62, D-48149 Muenster
2.
New School for Social Research, Department of Economics, 6 East 16th Street, D-1123, New York, NY 10003

Received: March 31, 2014

Revised: September 30, 2014

Published: May 2017

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Abstract

Much recent climate research suggests that the transition from non-renewable to renewable energy should be expedited. To address this issue we use an optimal control model, based on an integrated assessment model of climate change that includes two types energy production. After setting up the model, we derive necessary optimality conditions in the form of a Pontryagin type Maximum Principle. We use a numerical discretization method for optimal control problems to explore various policy scenarios. The algorithm allows to compute both state and co-state variables by providing a consistent numerical approximation for the adjoint variables of the various scenarios. Our numerical method applies to control and state-constrained control problems as well as to delayed control problems. In the policy scenarios, we explore ways how the transition from non-renewable to renewable energy can be expedited.

Keywords:

Mathematics Subject Classification: Primary: 49J15; Secondary: 37N25, 37N40.

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