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Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

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Abstract

In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions, consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Authors and Affiliations

  1. Department of Mathematics, Alzahra University, Tehran, Iran

    N. Haddadi & Y. Ordokhani

  2. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS, 39762, USA

    M. Razzaghi

Authors
  1. N. Haddadi
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  2. Y. Ordokhani
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  3. M. Razzaghi
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Corresponding author

Correspondence to M. Razzaghi.

Additional information

Communicated by Ilio Galligani.

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Haddadi, N., Ordokhani, Y. & Razzaghi, M. Optimal Control of Delay Systems by Using a Hybrid Functions Approximation. J Optim Theory Appl 153, 338–356 (2012). https://doi.org/10.1007/s10957-011-9932-1

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  • DOI: https://doi.org/10.1007/s10957-011-9932-1

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