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Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Author

Listed:
  • N. Haddadi

    (Alzahra University)

  • Y. Ordokhani

    (Alzahra University)

  • M. Razzaghi

    (Mississippi State University)

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.

Suggested Citation

  • N. Haddadi & Y. Ordokhani & M. Razzaghi, 2012. "Optimal Control of Delay Systems by Using a Hybrid Functions Approximation," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 338-356, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9932-1
    DOI: 10.1007/s10957-011-9932-1
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    References listed on IDEAS

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    1. F. Khellat, 2009. "Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 107-121, October.
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    Cited by:

    1. Postavaru, Octavian & Toma, Antonela, 2022. "A numerical approach based on fractional-order hybrid functions of block-pulse and Bernoulli polynomials for numerical solutions of fractional optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 269-284.
    2. Keshavarz, E. & Ordokhani, Y. & Razzaghi, M., 2019. "The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 83-98.
    3. Yusheng Zhou & Zaihua Wang, 2014. "Optimal Feedback Control for Linear Systems with Input Delays Revisited," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 989-1017, December.
    4. Mohamed Karim Bouafoura & Naceur Benhadj Braiek, 2019. "Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    5. Zogheib, Bashar & Tohidi, Emran, 2016. "A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 1-13.

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    1. Mohamed Karim Bouafoura & Naceur Benhadj Braiek, 2019. "Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems," Complexity, Hindawi, vol. 2019, pages 1-14, April.

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