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Control of Nonlinear Dynamic Systems with the Cell Mapping Method

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EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 175))

Abstract

This paper studies control problems of nonlinear dynamic systems using the cell mapping method. We first present the formulation of optimal control problem and Bellman’s principle of optimality. Then, we present the cell mapping methods and their application to optimal control problems of deterministic nonlinear dynamic systems. Examples of population dynamics control of two competing species are presented to demonstrate the effectiveness of the cell mapping method.

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Authors and Affiliations

  1. School of Engineering, University of California, Merced, CA, 95343, U.S.A.

    Jian-Qiao Sun

Authors
  1. Jian-Qiao Sun
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Corresponding author

Correspondence to Jian-Qiao Sun .

Editor information

Editors and Affiliations

  1. , Computer Science Department, CINVESTAV-IPN, Col. San Pedro Zacatenco 2508, Mexico City, 07360, Mexico

    Oliver Schütze

  2. , Computer Science Department, CINVESTAV-IPN, Col. San Pedro Zacatenco 2508, Mexico City, 07360, Mexico

    Carlos A. Coello Coello

  3. , Computer Science and Communications, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, 1359, Luxembourg

    Alexandru-Adrian Tantar

  4. Computer Science and Communications, Research Unit, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, L-1359, Luxembourg

    Emilia Tantar

  5. Computer Science, and Communications, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, L-1359, Luxembourg

    Pascal Bouvry

  6. Bordeaux Mathematical Institute, INRIA Bordeaux-Sud Ouest, Université Bordeaux I, cours de la Libération 351, Talence Cedex, 33405, France

    Pierre Del Moral

  7. Bâtiment Leyteire, UFR Sciences et Modélisation, Université Bordeaux II, 3ter place de la Victoire, Bordeaux, 33000, France

    Pierrick Legrand

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Sun, JQ. (2013). Control of Nonlinear Dynamic Systems with the Cell Mapping Method. In: Schütze, O., et al. EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II. Advances in Intelligent Systems and Computing, vol 175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31519-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-31519-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31518-3

  • Online ISBN: 978-3-642-31519-0

  • eBook Packages: EngineeringEngineering (R0)

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