# American Institute of Mathematical Sciences

June  2020, 10(2): 143-156. doi: 10.3934/naco.2019044

## Linear optimal control of time delay systems via Hermite wavelet

 1 Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran 2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Received  July 2018 Revised  July 2019 Published  September 2019

To solve the time delay optimal control problem with quadratic performance index, a direct numerical method based on Hermite wavelet has been proposed in the present study. The idea is to convert the time delay optimal control problem into a quadratic programming problem. To do so, various time functions in the system are expanded as their truncated series and the properties of the operational matrices of integration, delay and product of two Hermite wavelet vectors are used as well. These matrices are utilized to reduce the solution of optimal control with time delay system, to the solution of a quadratic programming with linear constraints. Finally, three examples of time varying and time invariant coefficients are given to compare the results with some of the existing methods.

Citation: Akram Kheirabadi, Asadollah Mahmoudzadeh Vaziri, Sohrab Effati. Linear optimal control of time delay systems via Hermite wavelet. Numerical Algebra, Control & Optimization, 2020, 10 (2) : 143-156. doi: 10.3934/naco.2019044
##### References:

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##### References:
Estimated values for $J$ for Example 5.1
 Proposed method Dadkhah[4] Palanisamy [25] Wang [30] 1.64787419 1.64787419 1.6497 0.85124283
 Proposed method Dadkhah[4] Palanisamy [25] Wang [30] 1.64787419 1.64787419 1.6497 0.85124283
Estimated values for $J$ for Example 5.2
Estimated value for $J$ for Example 5.3
 Proposed method Wang[31] 2.7930174564 2.7930174564
 Proposed method Wang[31] 2.7930174564 2.7930174564
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