Linear optimal control of time delay systems via Hermite wavelet

Akram Kheirabadi; Asadollah Mahmoudzadeh Vaziri; Sohrab Effati

doi:10.3934/naco.2019044

Article Contents

2020, Volume 10, Issue 2: 143-156. Doi: 10.3934/naco.2019044

This issue Previous Article Resource allocation and target setting based on virtual profit improvement Next Article Quasilinear iterative method for the boundary value problem of nonlinear fractional differential equation

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

^* Corresponding author: Asadollah Mahmoudzadeh Vaziri
^* Corresponding author: Asadollah Mahmoudzadeh Vaziri

Received: June 30, 2018

Revised: June 30, 2019

Published: April 2020

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Abstract

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.

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Mathematics Subject Classification: Primary: 49J15, 49N05; Secondary: 90C20.

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Table 1. Estimated values for $ J $ for Example 5.1

Proposed method Dadkhah[4] Palanisamy [25] Wang [30]

1.64787419 1.64787419 1.6497 0.85124283

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Table 2. Estimated values for $ J $ for Example 5.2

Proposed method Haddadi[9] Khellat[14] Palanisamy[25]

4.6192 4.7404 5.1713 6.0079

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Table 3. Estimated value for $ J $ for Example 5.3

Proposed method Wang[31]

2.7930174564 2.7930174564

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References

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