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An approximate solution of linear multicriteria control problems through the multicriteria simplex method

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Abstract

This paper deals with multicriteria, linear, continuous optimal control problems through the application of the multicriteria simplex method. Since the system is linear, the state variables at a given time can be expressed in terms of definite integrals. Upon using standard numerical integration formulas, the definite integrals are approximately expressed by means of weighted sums of the integrands. Then, after introducing some suitable auxiliary variables, approximate linear multicriteria programming problems are formulated. Illustrative numerical examples are provided to indicate the efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Systems Engineering, Faculty of Engineering, Kobe University, Rokko, Nada, Kobe, Japan

    M. Sakawa (Research Associate)

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  1. M. Sakawa
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Communicated by P. Varaiya

The author is indebted to Professor Y. Sawaragi of Kyoto University for his constant encouragement. The author also wishes to thank T. Suwa for his cooperation in preparing the programming for the digital computer.

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Sakawa, M. An approximate solution of linear multicriteria control problems through the multicriteria simplex method. J Optim Theory Appl 22, 417–427 (1977). https://doi.org/10.1007/BF00932864

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