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Decentralized static output feedback controller design for linear interconnected systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Many interconnected systems in the real world, such as power systems and chemical processes, are often composed of subsystems. A decentralized controller is suitable for an interconnected system because of its more practical and accessible implementation. We use the homotopy method to compute a decentralized controller. Since the centralized controller constitutes the starting point for the method, its existence becomes very important. This paper introduces a non-singular matrix and a design parameter to generate a centralized controller. If the initial centralized controller fails, we can change the value of the design parameter to generate a new centralized controller. A sufficient condition for a decentralized controller is given as a bilinear matrix inequality with three matrix variables: a controller gain matrix and a pair of other matrix variables. Finally, we present numerical examples to validate the proposed decentralized controller design method.
Rocznik
Strony
83--96
Opis fizyczny
Bibliogr. 32 poz., rys., wykr.
Twórcy
  • Department of Mathematics, Sepuluh Nopember Institute of Technology, Sukolilo ITS Campus, Surabaya, 60111, Indonesia
  • Department of Data Science, Telkom Surabaya Institute of Technology, 156 Ketintang Street, Gayungan, Surabaya, 60231, Indonesia
  • Department of Mathematics, Sepuluh Nopember Institute of Technology, Sukolilo ITS Campus, Surabaya, 60111, Indonesia
  • Department of Mathematics, Sepuluh Nopember Institute of Technology, Sukolilo ITS Campus, Surabaya, 60111, Indonesia
  • Department of Mathematical Sciences, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama City, Saitama, 337-8570, Japan
autor
  • Department of Mathematics, Sepuluh Nopember Institute of Technology, Sukolilo ITS Campus, Surabaya, 60111, Indonesia
Bibliografia
  • [1] Ben Amor, R. and Elloumi, S. (2018). Decentralized control approaches of large-scale interconnected systems, Advances in Science, Technology and Engineering Systems Journal 3(1): 394-403.
  • [2] Benlatreche, A., Knittel, D. and Ostertag, E. (2008). Robust decentralised control strategies for large-scale web handling systems, Control Engineering Practice 16(6): 736-750.
  • [3] Burke, J.V., Lewis, A.S. and Overton, M.L. (2002). Two numerical methods for optimizing matrix stability, Linear Algebra and Its Applications 351: 117-145.
  • [4] Cai, J., Wen, C., Xing, L. and Yan, Q. (2022). Decentralized backstepping control for interconnected systems with non-triangular structural uncertainties, IEEE Transactions on Automatic Control, DOI: 10.1109/TAC.2022.3152083, (early access).
  • [5] Chang, X.-H. (2014). Robust Output Feedback H∞ Control and Filtering for Uncertain Linear Systems, Springer, Berlin/Heidelberg.
  • [6] Chang, X.-H. and Yang, G.-H. (2014). New results on output feedback H∞ control for linear discrete-time systems, IEEE Transactions on Automatic Control 59(5): 1355-1359.
  • [7] Chen, N., Ikeda, M. and Gui, W. (2005). Design of robust H∞ control for interconnected systems: A homotopy method, International Journal of Control, Automation and Systems 3(2): 143-151.
  • [8] Chiu, W.-Y. (2017). Method of reduction of variables for bilinear matrix inequality problems in system and control designs, IEEE Transactions on Systems, Man, and Cybernetics: Systems 47(7): 1241-1256.
  • [9] De Oliveira, M.C., Bernussou, J. and Geromel, J.C. (1999). A new discrete-time robust stability condition, Systems & Control Letters 37(4): 261-265.
  • [10] Gahinet, P. and Apkarian, P. (1994). A linear matrix inequality approach to H∞ control, International Journal of Robust and Nonlinear Control 4(4): 421-448.
  • [11] Harno, H.G. and Petersen, I.R. (2014). Robust H∞ control via a stable decentralized nonlinear output feedback controller, International Journal of Robust and Nonlinear Control 24(2): 191-213.
  • [12] Hassibi, A., How, J. and Boyd, S. (1999). A path-following method for solving BMI problems in control, Proceedings of the 1999 American Control Conference, San Diego, USA, Vol. 2, pp. 1385-1389.
  • [13] Huo, X., Karimi, H.R., Zhao, X., Wang, B. and Zong, G. (2021). Adaptive-critic design for decentralized event-triggered control of constrained nonlinear interconnected systems within an identifier-critic framework, IEEE Transactions on Cybernetics 52(8): 7478-7491, DOI: 10.1109/TCYB.2020.3037321.
  • [14] Jabri, D., Guelton, K., Belkhiat, D.E.C. and Manamanni, N. (2020). Decentralized static output tracking control of interconnected and disturbed Takagi-Sugeno systems, International Journal of Applied Mathematics and Computer Science 30(2): 225-238, DOI: 10.34768/amcs-2020-0018.
  • [15] Javanmardi, H., Dehghani, M., Mohammadi, M., Siamak, S. and Hesamzadeh, M.R. (2022). BMI-based load frequency control in microgrids under false data injection attacks, IEEE Systems Journal 16(1): 1021-1031.
  • [16] Javanmardi, H., Dehghani, M., Mohammadi, M., Vafamand, N. and Dragicevic, T. (2021). Optimal frequency regulation in AC mobile power grids exploiting bilinear matrix inequalities, IEEE Transactions on Transportation Electrification 7(4): 2464-2473.
  • [17] Kiriakidis, K. (2001). Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities, IEEE Transactions on Fuzzy Systems 9(2): 269-277.
  • [18] Lavaei, J. (2009). A new decentralization technique for interconnected systems, Proceedings of the 48h IEEE Conference on Decision and Control, CDC/2009 28th Chinese Control Conference, Shanghai, China, pp. 958-965.
  • [19] Li, P., Lam, J., Wang, Z. and Date, P. (2011). Positivity-preserving H∞ model reduction for positive systems, Automatica 47(7): 1504-1511.
  • [20] Liu, H. and Yu, H. (2018). Decentralized state estimation for a large-scale spatially interconnected system, ISA Transactions 74: 67-76.
  • [21] Liu, J.J., Lam, J. and Kwok, K.-W. (2021). Further improvements on non-negative edge consensus of networked systems, IEEE Transactions on Cybernetics 52(9): 9111-9119, DOI: 10.1109/TCYB.2021.3052833.
  • [22] Ojaghi, P. and Rahmani, M. (2017). LMI-based robust predictive load frequency control for power systems with communication delays, IEEE Transactions on Power Systems 32(5): 4091-4100.
  • [23] Qu, C., Huo, L., Li, H. and Wang, Y. (2014). A double homotopy approach for decentralized control of civil structures, Structural Control and Health Monitoring 21(3): 269-281.
  • [24] Siljak, D. (1991). Decentralized Control of Complex Systems, Academic Press, Boston.
  • [25] Straka, O. and Punčochář, I. (2020). Decentralized and distributed active fault diagnosis: Multiple model estimation algorithms, International Journal of Applied Mathematics and Computer Science 30(2): 239-249, DOI: 10.34768/amcs-2020-0019.
  • [26] Tuan, H. and Apkarian, P. (2000). Low nonconvexity-rank bilinear matrix inequalities: Algorithms and applications in robust controller and structure designs, IEEE Transactions on Automatic Control 45(11): 2111-2117.
  • [27] Vesely, V. and Thuan, N.Q. (2011). Robust decentralized controller design for large scale systems, 2011 12th International Carpathian Control Conference (ICCC), Velke Karlovice, Czech Republic, pp. 425-428.
  • [28] Wang, Y., Lynch, J.P. and Law, K.H. (2009). Decentralized H∞ controller design for large-scale civil structures, Earthquake Engineering & Structural Dynamics 38(3): 377-401.
  • [29] Wang, Y., Rajamani, R. and Zemouche, A. (2018). Sequential LMI approach for the design of a BMI-based robust observer state feedback controller with nonlinear uncertainties, International Journal of Robust and Nonlinear Control 28(4): 1246-1260.
  • [30] Zhai, G., Chen, N. and Gui, W. (2013). Decentralized design of interconnected H∞ feedback control systems with quantized signals, International Journal of Applied Mathematics and Computer Science 23(2): 317-325, DOI: 10.2478/amcs-2013-0024.
  • [31] Zhai, G., Ikeda, M. and Fujisaki, Y. (2001). Decentralized H∞ controller design: A matrix inequality approach using a homotopy method, Automatica 37(4): 565-572.
  • [32] Zhou, K. and Khargonekar, P.P. (1988). Robust stabilization of linear systems with norm-bounded time-varying uncertainty, Systems and Control Letters 10(1): 17–20.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c1baa9e1-2543-4428-bba6-609df9cdbe75
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