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Optimal control of the delay linear systems with allowance for the terminal state constraints

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Abstract

Consideration was given to the linear problem of optimal control of one type of the delay systems where the delay appears in one equation of the system mathematical model. The terminal states of the system are bounded, the optimal control is realized by the discrete control actions obeying the geometrical constraints. Consideration was given to two types of solutions—program and positional. A dual method of calculation of the optimal programs was presented. Described was an algorithm of the optimal controller generating in real time the current values of the positional solution (optimal feedback). The results obtained were illustrated by the example of control of a system with the fourth-order delay.

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Authors and Affiliations

  1. Belarussian State University, Minsk, Belarus

    R. Gabasov & O. P. Grushevich

  2. Institute of Mathematics, Belarussian National Academy of Sciences, Minsk, Belarus

    F. M. Kirillova

Authors
  1. R. Gabasov
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  2. O. P. Grushevich
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  3. F. M. Kirillova
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Additional information

Original Russian Text © R. Gabasov, O.P. Grushevich, F.M. Kirillova, 2007, published in Avtomatika i Telemekhanika, 2007, No. 12, pp. 3–20.

This work was supported by BRFFI, project no. F06M-027 and GPFI (Mathematical Models-14).

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Gabasov, R., Grushevich, O.P. & Kirillova, F.M. Optimal control of the delay linear systems with allowance for the terminal state constraints. Autom Remote Control 68, 2097–2112 (2007). https://doi.org/10.1134/S0005117907120016

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  • DOI: https://doi.org/10.1134/S0005117907120016

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