On discounted LQR control problem for disturbanced singular system

• Autorzy: Yulianti Lyra , Nazra Admi , Zulakmal , Bahar Arifah , Muhafzan

Identyfikatory

DOI

10.24425/acs.2019.127528

• Języki publikacji: EN

Abstrakty

EN

The LQR (linear quadratic regulator) control problem subject to singular system constitutes a optimization problem in which one must be find an optimal control that satisfy the singular system and simultaneously to optimize the quadratic objective functional. In this paper we establish a sufficient condition to obtain the optimal control of discounted LQR optimization problem subject to disturbanced singular system where the disturbance is time varying. The considered problem is solved by transforming the discounted LQR control problem subject to disturbanced singular system into the normal LQR control problem. Some available results in literatures of the normal LQR control problem be used to find the sufficient conditions for the existence of the optimal control for discounted LQR control problem subject to disturbanced singular system. The final result of this paper is in the form a method to find the optimal control of discounted LQR optimization problem subject to disturbanced singular system. The result shows that the disturbance is vanish with the passage of time.

Słowa kluczowe

EN

discounted LQR control; singular system; disturbance

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 1
• Strony: 147--156
• Opis fizyczny: Bibliogr. 10 poz., wzory

Twórcy

autor

Yulianti Lyra

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

autor

Nazra Admi

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

autor

Zulakmal

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

autor

Bahar Arifah

• Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia

autor

Muhafzan

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

Bibliografia

• [1] J. D. Cobb: Descriptor variable systems and optimal control state regulation. IEEE Trans. Aut. Cont., 28 (1983), 601–611.
• [2] G. R. Duan: Analysis and design of descriptor linear systems. Springer, 2010.
• [3] E. L. Yip and R. F. Sincovec: Solvability, controllability, and observability of continuous descriptor systems. IEEE Trans. Aut. Cont., 26(3) (1981), 702–707.
• [4] L. Chen: Singular LQR performance with the worst disturbance rejection for descriptor systems. J. Cont. Theor. Applic., 4 (2006), 277–280.
• [5] Zulakmal, Narwen, R. Budi, I. B. Ahmad, and Muhafzan: On the LQ optimization subject to descriptor system under disturbance. Asian Journal of Scientific Research, 11(4) (2018), 540–543.
• [6] P. Benigno and M. Woodford: Optimal taxation in an RBC model: a LQR approach. Journal of Economic Dynamics & Control, 30 (2006), 1445–1489.
• [7] J. Y. Ishihara and M. H. Terra: Impulse controllability and observability of rectangular descriptor systems. IEEE Trans. Aut. Cont., 46(6) (2001), 991–994.
• [8] Z. Yan: Geometric analysis of impulse controllability for descriptor system. Systems & Control Letters, 56 (2007), 1–6.
• [9] Muhafzan: Use of semidefinite programming for solving the LQR problem subject to descriptor systems. Int. J. Math. Computh. Sci., 20 (2010), 655–664.
• [10] C. Wu, X. Wang, K. L. Teo, and L. Jiang: Robust optimal control of continuous LQR system subject to disturbances. In: Intelligent Systems, Control and Automation: Science and Engineering, 2014, Springer, pp. 11–34.

Uwagi

EN

1. The work was supported by Universitas Andalas under Grant KRP1GB-PDU-Unand-2018 No. 04/UN.16.17/PP.RGB/LPPM/2018.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).