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Improved Optimal Control Methods Based Upon the Adjoining Cell Mapping Technique

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Abstract

In this paper, cell mapping methods are studied and refined for the optimal control of autonomous dynamical systems. First, the method proposed by Hsu (Ref. 1) is analyzed and some improvements are presented. Second, adjoining cell mapping (ACM), based on an adaptive time of integration (Refs. 2–3), is formulated as an alternative technique for computing optimal control laws of nonlinear systems, employing the cellular state-space approximation. This technique overcomes the problem of determining an appropriate duration of the integration time for the simple cell mapping method and provides a suitable mapping for the search procedures. Artificial intelligence techniques, together with some improvements on the original formulation lead to a very efficient algorithm for computing optimal control laws with ACM (CACM). Several examples illustrate the performance of the CACM algorithm.

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Authors and Affiliations

  1. Grupo de Redes Neuronales, Departamento de Matemática Aplicada a las Tecnologías de la Información, Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, Madrid, Spain

    P.J. Zufiria (Associate Professor)

  2. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal, Universidad de Alicante, Alicante, Spain

    T. Martínez-Marín (Associate Professor)

Authors
  1. P.J. Zufiria
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  2. T. Martínez-Marín
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Zufiria, P., Martínez-Marín, T. Improved Optimal Control Methods Based Upon the Adjoining Cell Mapping Technique. Journal of Optimization Theory and Applications 118, 657–680 (2003). https://doi.org/10.1023/B:JOTA.0000004876.01771.b2

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  • DOI: https://doi.org/10.1023/B:JOTA.0000004876.01771.b2

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