Illustrating Optimal Control Applications with Discrete and Continuous Features

  • Suzanne LenhartEmail author
  • Erin Bodine
  • Peng Zhong
  • Hem Raj Joshi
Part of the Fields Institute Communications book series (FIC, volume 66)


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.



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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Suzanne Lenhart
    • 1
    Email author
  • Erin Bodine
    • 2
  • Peng Zhong
    • 3
  • Hem Raj Joshi
    • 4
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of Mathematics & Computer ScienceRhodes CollegeMemphisUSA
  3. 3.Department of Ecology, Evolution and Natural ResourcesRutgers UniversityNew BrunswickUSA
  4. 4.Mathematics and CS DepartmentXavier UniversityCincinnatiUSA

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