An-Najah University Journal for Research - A (Natural Sciences)

An Optimal Control for AHomogeneous Linear Dynamical Systems
Authors:

Article info

2018-09-19
2018-12-06
93 - 114

Keywords

  • Homogeneoussystems
  • Optimalcontrol
  • Closed-loop systems.
  • Riccatiequation

Abstract

In this article we introduce an approach to find the optimal control for homogeneous linear dynamical systems. Wei ntroduce the linear quadratic regulator problem for the reduced order model of a dynamical system. We apply the singular perturbation approximations techniques to the original system and obtained our reduced order system. In this paper, our goal is to examine the solution of the problem as the positive parameter ε tends to zero. Our approach that is based on a formal asymptotic expansion of an algebraic Riccati equations associated with the Pontryagin maximum principle. We derive an approximate expressions for the optimal feedback controls. We compute the L2-norm beween the optimal control of the original and reduced system and compare it with the L2-norm of the solution of the Riccati equations of the original and reduced systems. We test the results numerically and obtained a good closed-loop performance for the model reduction.

Recommended Citation

Daraghmeh, A. (2019). An Optimal Control for AHomogeneous Linear Dynamical Systems. An-Najah University Journal for Research - A (Natural Sciences), 33(1), 93–114. https://doi.org/10.35552/anujr.a.33.1.1617
[1]A. Daraghmeh, “An Optimal Control for AHomogeneous Linear Dynamical Systems,” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, pp. 93–114, Feb. 2019, doi: 10.35552/anujr.a.33.1.1617.
Daraghmeh, Adnan. “An Optimal Control for AHomogeneous Linear Dynamical Systems.” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, Feb. 2019, pp. 93–114. Crossref, https://doi.org/10.35552/anujr.a.33.1.1617.
1.Daraghmeh A. An Optimal Control for AHomogeneous Linear Dynamical Systems. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2019 Feb;33(1):93–114. Available from: http://dx.doi.org/10.35552/anujr.a.33.1.1617
Daraghmeh, Adnan. “An Optimal Control for AHomogeneous Linear Dynamical Systems.” An-Najah University Journal for Research - A (Natural Sciences) 33, no. 1 (February 2019): 93–114. https://doi.org/10.35552/anujr.a.33.1.1617.

التحكم الأمثل للأنظمة الديناميكية الخطية المتجانسة
المؤلفون:

معلومات المقال

2018-09-19
2018-12-06
93 - 114

الكلمات الإفتتاحية

  • Homogeneoussystems
  • Optimalcontrol
  • Closed-loop systems.
  • Riccatiequation

الملخص

في هذا العمل، قمنا بدراسة الانظمة الخطية المتجانسة والهدف العام ايجاد التحكم الامثل لها. قمنا باستخدام احدى الطرق المتبعة في نظرية التحكم لايجاد نظام مصغر عن النظام الاصلي. قمنا بدراسة معادلة ريكاتي الجبرية لكل من النظامين الاصلي والمصغر وكذلك استخدام مبدأ بنتريتدين المطلق. قمنا باشتقاق معادلات جبرية للتحكم الامثل لكل من النظامين الاصلي والمصغر. لاختبار هذه النتائج التي توصلنا اليها، قمنا بتطبيق مثال عددي وقياس الفرق بين التحكم الامثل للنظامين.

Recommended Citation

Daraghmeh, A. (2019). An Optimal Control for AHomogeneous Linear Dynamical Systems. An-Najah University Journal for Research - A (Natural Sciences), 33(1), 93–114. https://doi.org/10.35552/anujr.a.33.1.1617
[1]A. Daraghmeh, “An Optimal Control for AHomogeneous Linear Dynamical Systems,” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, pp. 93–114, Feb. 2019, doi: 10.35552/anujr.a.33.1.1617.
Daraghmeh, Adnan. “An Optimal Control for AHomogeneous Linear Dynamical Systems.” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, Feb. 2019, pp. 93–114. Crossref, https://doi.org/10.35552/anujr.a.33.1.1617.
1.Daraghmeh A. An Optimal Control for AHomogeneous Linear Dynamical Systems. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2019 Feb;33(1):93–114. Available from: http://dx.doi.org/10.35552/anujr.a.33.1.1617
Daraghmeh, Adnan. “An Optimal Control for AHomogeneous Linear Dynamical Systems.” An-Najah University Journal for Research - A (Natural Sciences) 33, no. 1 (February 2019): 93–114. https://doi.org/10.35552/anujr.a.33.1.1617.

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