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On Infinite Horizon Optimal Control of a Lotka-Voltera-System

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Recent Advances in Optimization and its Applications in Engineering

Summary

We describe a prey-predator model by a nonlinear optimal control problem with infinite horizon. This problem is non convex. Therefore we apply a duality theory developed in [17] with quadratic statements for the dual variables S. The essential idea is to use weighted Sobolev spaces as spaces for the states and to formulate the dual problem in topological dual spaces. We verify second order sufficient optimality condition to prove local optimality of the steady state in [T, ∞).

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Authors and Affiliations

  1. Brandenburg University of Technology Cottbus, Cottbus, Germany

    Sabine Pickenhain

Authors
  1. Sabine Pickenhain
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Correspondence to Sabine Pickenhain .

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Editors and Affiliations

  1. Dept. Electrical Engineering (ESAT), Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, Leuven, 3001, Belgium

    Moritz Diehl

  2. CORE-UCL, Voie du Roman Pays 34, Louvain-la-Neuve, 1348, Belgium

    Francois Glineur

  3. , Department Computerwetenschappen, Katholieke Universiteit Leuven, Leuven, 3001, Belgium

    Elias Jarlebring

  4. Dept. Computer Science, Katholieke Universiteit Leuven, Celesijnenlaan 200a, Leuven, 3001, Belgium

    Wim Michiels

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Pickenhain, S. (2010). On Infinite Horizon Optimal Control of a Lotka-Voltera-System. In: Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds) Recent Advances in Optimization and its Applications in Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12598-0_24

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  • DOI: https://doi.org/10.1007/978-3-642-12598-0_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12597-3

  • Online ISBN: 978-3-642-12598-0

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