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Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets

Author

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  • F. Khellat

    (Shahid Beheshti University)

Abstract

This paper introduces the application of linear Legendre multiwavelets to the optimal control synthesis for linear time-delayed systems. Based on some useful properties of linear Legendre multiwavelets, integration, product and delay operational matrices are proposed to solve the linear time-delayed systems first. Then, a quadratic cost functional is approximated by those properties. By using Lagrange multipliers, the quadratic cost functional is minimized subject to the solution of the linear time-delayed system and an explicit formula for the optimal control is obtained. The effectiveness of the method and accuracy of the solution are shown in comparison with some other methods by illustrative examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:1:d:10.1007_s10957-009-9548-x
    DOI: 10.1007/s10957-009-9548-x
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    Cited by:

    1. 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.
    2. 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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