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Hybrid Functions Approach for Variational Problems and Optimal Control of Delay Systems

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Control and Systems Engineering

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 27))

Abstract

In this chapter, a numerical method for solving variational problems and optimal control of delay systems 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 variational problems, delay systems and 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 and Statistics, Mississippi State University, Starkville, Mississippi State, MS, 39762, USA

    Mohsen Razzaghi

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  1. Mohsen Razzaghi
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Correspondence to Mohsen Razzaghi .

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Editors and Affiliations

  1. Electrical Engineering Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico, USA

    Aly El-Osery

  2. Electrical and Computer Engineering Department, The University of Texas at San Antonio, San Antonio, Texas, USA

    Jeff Prevost

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Razzaghi, M. (2015). Hybrid Functions Approach for Variational Problems and Optimal Control of Delay Systems. In: El-Osery, A., Prevost, J. (eds) Control and Systems Engineering. Studies in Systems, Decision and Control, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-14636-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-14636-2_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14635-5

  • Online ISBN: 978-3-319-14636-2

  • eBook Packages: EngineeringEngineering (R0)

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