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Illustrating Optimal Control Applications with Discrete and Continuous Features

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Advances in Applied Mathematics, Modeling, and Computational Science

Part of the book series: Fields Institute Communications ((FIC,volume 66))

Abstract

In this paper, we present the basic idea of optimal control of models with discrete and continuous features. We first consider ordinary differential equation (ODE) models where we emphasize problems which are linear in the control and have discrete values for the optimal control. Three examples with ODEs illustrate how the bang-bang and singular controls could be handled. The first example utilizes a simple model with one ODE. The next two examples use systems of ODEs. One example comes from a mobile robot with one or more steerable drive wheels that steer together. The other example models species augmentation where two populations of the same species are modeled with a target/endangered population and a reserve population. Then we present an extension to an integrodifference model that is discrete in time and continuous in space. This optimal pest control problem is modeled by integrodifference equations and we illustrate how to construct the necessary conditions.

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Acknowledgements

Lenhart’s work is partially supported by the National Institute for Mathematical and Biological Synthesis funded through the National Science Foundation EF0832858. We would like to thank David Reister and Louis Gross for some assistance.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-1320, USA

    Suzanne Lenhart

  2. Department of Mathematics & Computer Science, Rhodes College, Memphis, TN, 38112, USA

    Erin Bodine

  3. Department of Ecology, Evolution and Natural Resources, Rutgers University, New Brunswick, NJ, USA

    Peng Zhong

  4. Mathematics and CS Department, Xavier University, Cincinnati, OH, 45207-4441, USA

    Hem Raj Joshi

Authors
  1. Suzanne Lenhart
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  2. Erin Bodine
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  3. Peng Zhong
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  4. Hem Raj Joshi
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Corresponding author

Correspondence to Suzanne Lenhart .

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Editors and Affiliations

  1. , Department of Mathematics, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Ontario, Canada

    Roderick Melnik

  2. , Dept. of Physics and Computer Science, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Canada

    Ilias S. Kotsireas

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Lenhart, S., Bodine, E., Zhong, P., Joshi, H.R. (2013). Illustrating Optimal Control Applications with Discrete and Continuous Features. In: Melnik, R., Kotsireas, I. (eds) Advances in Applied Mathematics, Modeling, and Computational Science. Fields Institute Communications, vol 66. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5389-5_9

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