On LQ optimization problem subject to fractional order irregular singular systems

• Autorzy: Muhafzan , Nazra Admi , Yulianti Lyra , Zulakmal , Revina Refi

Identyfikatory

DOI

10.24425/acs.2020.135850

• Języki publikacji: EN

Abstrakty

EN

In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.

Słowa kluczowe

EN

linear quadratic optimization; fractional order; irregular singular system; Caputo fractional derivative; Mittag-Leffler function

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2020
• Tom: Vol. 30, No. 4
• Strony: 745--756
• Opis fizyczny: Bibliogr. 14 poz., wykr., wzory

Twórcy

autor

Muhafzan

• Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Kampus UNAND Limau Manis, Padang, 25163, Indonesia

autor

Nazra Admi

• Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Kampus UNAND Limau Manis, Padang, 25163, Indonesia

autor

Yulianti Lyra

• Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Kampus UNAND Limau Manis, Padang, 25163, Indonesia

autor

Zulakmal

• Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Kampus UNAND Limau Manis, Padang, 25163, Indonesia

autor

Revina Refi

• Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Kampus UNAND Limau Manis, Padang, 25163, Indonesia

Bibliografia

• [1] G. R. Duan, Analysis and design of descriptor linear systems, Springer, 2010.
• [2] Muhafzan: Use of semidefinite programming for solving the LQR problem subject to descriptor systems, Int. J. Math. Computh. Sci., 20 (2010), 655– 664.
• [3] L. Yulianti, A. Nazra, Zulakmal, A. Bahar, and Muhafzan: On discounted LQR control problem for disturbanced singular system, Archives of Control Sciences, 29(1) (2019), 147–156.
• [4] X. Wang and B. Liu: Singular linear quadratic optimal control problem for stochastic nonregular descriptor systems, Asian Journal of Control, 20(6) (2018), 1–11.
• [5] A. Younus, I. Javaid, and A. Zehra: On controllability and observability of fractional continuous-time linear systems with regular pencils, Bulletin of The Polish Academy of Sciences, 65(3) (2017), 297–304.
• [6] T. Chiranjeevi, R. K. Biswas, and C. Sethi: Optimal control of fractional order singular system, International Journal of Electrical Engineering & Education, (2019), DOI: 0.1177/0020720919833031.
• [7] T. Chiranjeevi and R. K. Biswas: Linear quadratic optimal control problem of fractional order Continuous-time singular system, Procedia Computer Science, 171 (2020), 1261–1268.
• [8] Q. Fang, B. Zhang, and J. Feng: Singular LQ problem for irregular singular systems, Journal of Applied Mathematics, 2014 (853415) (2014), DOI: 10.1155/2014/853415.
• [9] I. Matychyn and V. Onyshchenko: Optimal control of linear systems with fractional derivatives, Fractional Calculus & Applied Analysis, 21(1) (2018), 134–150.
• [10] I. Matychyn and V. Onyshchenko: On time-optimal control of fractional order systems, Journal of Computational and Applied Mathematics, 339 (2018), 245–257.
• [11] Y. Li and Y.Q. Chen: Fractional order linear quadratic regulator, Proceeding of IEEE/ASME International Conference on Mechtronic and Embedded Systems and Applications, (2008), 363–368.
• [12] V. C. Klema and A. J. Laub: The singular value decomposition: its computation and some applications, IEEE Transactions on Automatic Control, 25(2) (1980), 164–176.
• [13] Zulakmal, Narwen, B. Rudianto, A. I. Baqi, and Muhafzan: On the LQ optimization subject to descriptor system under disturbance, Asian Journal of Scientific Research, 11(4) (2018), 540–543.
• [14] O. M. Fuentes and R.M. Guerra: A novel Mittag–Leffler stable estimator for nonlinear fractional-order systems: a linear quadratic regulator, Nonlinear Dynamics, 94 (2018), 1973–1986.

Uwagi

This work was supported by PNBP funding of FMIPA Universitas Andalas under Grant No. 03/UN.16.3.D/PP/FMIPA/2020.