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Behrouz H, Mohammadzaman I, Mohammadi A. Robust State-Feedback Control of Uncertain LPV systems Using Integral Quadratic Constraints. JoC 2024; 18 (1) :45-53
URL: http://joc.kntu.ac.ir/article-1-1045-en.html
URL: http://joc.kntu.ac.ir/article-1-1045-en.html
1- Faculty of Electrical and computer Engineering, Malek Ashtar University of Technology, Tehran, Iran
Abstract: (317 Views)
A linear matrix inequality (LMI)-based algorithm is developed to design a robust state-feedback controller using integral quadratic constraints (IQCs) for an uncertain linear parameter varying system (LPVS). The uncertain LPVS is described by an interconnection of a nominal LPVS which is solely dependent on the measurable parameters and a block-structured uncertainty. The IQC approach is implemented to model the input/output behavior of the uncertainties. In general, the robust synthesis method and the IQC stability analysis for the uncertain LPVS lead to a non-convex problem and are solved by the iterative algorithms. However, in the proposed method, the problem is converted into a convex problem. Therefore, the LPV synthesis for the nominal LPVS and the IQC analysis for handling uncertainties are performed simultaneously. Consequently, without any constraints on nominal system matrices, the proposed method might achieve a better performance and less computational burden. Furthermore, the object is to minimize the
Keywords: gain-scheduled controller, integral quadratic constraints, polytopic system, uncertain linear parameter varying systems.
Type of Article: Research paper |
Subject:
Special
Received: 2022/10/24 | Accepted: 2023/12/27 | Published: 2024/06/20
Received: 2022/10/24 | Accepted: 2023/12/27 | Published: 2024/06/20
References
1. [1] J. Mohammadpour and C. W. Scherer, Control of linear parameter varying systems with applications. Springer New York Dordrecht Heidelberg London, 2012. [DOI:10.1007/978-1-4614-1833-7]
2. [2] H. Asrari, I. Mohammadzaman, and F. Allahverdizadeh, "Robust gain-scheduled control of linear parameter-varying systems with uncertain scheduling parameters in the presence of the time-invariant uncertainties," J. Control (Persian Edition)., vol. 15, no. 1, pp. 1-19, 2021. [DOI:10.52547/joc.15.1.1]
3. [3] S. Wang, H. Pfifer, and P. Seiler, "Robust synthesis for linear parameter varying systems using integral quadratic constraints," Automatica, vol. 68, pp. 111-118, 2016. [DOI:10.1016/j.automatica.2016.01.053]
4. [4] J. Veenman and C. W. Scherer, "A synthesis framework for robust gain-scheduling controllers," Automatica, vol. 50, no. 11, pp. 2799-2812, 2014. [DOI:10.1016/j.automatica.2014.10.002]
5. [5] A. Rantzer, A. Megretski, A. Rantzer, and A. Megretski, "System analysis via integral quadratic constraints," IEEE Trans. Autom. Control, vol. 42, no. 6, pp. 819-830, 1997. [DOI:10.1109/9.587335]
6. [6] P. Seiler, "Stability analysis with dissipation inequalities and integral quadratic constraints," IEEE Trans. Automat. Contr., vol. 60, no. 6, pp. 1704-1709, 2015. [DOI:10.1109/TAC.2014.2361004]
7. [7] M. Fetzer and C. W. Scherer, "Full-block multipliers for repeated, slope-restricted scalar nonlinearities," Int. J. Robust Nonlinear Control, vol. 27, no. 17, pp. 3376-3411, 2017. [DOI:10.1002/rnc.3751]
8. [8] P. Seiler, A. Packard, and G. J. Balas, "A dissipation inequality formulation for stability analysis with integral quadratic constraints," Proc. IEEE Conf. Decis. Control, pp. 2304-2309, 2010. [DOI:10.1109/CDC.2010.5717073]
9. [9] J. M. Fry, M. Farhood, and P. Seiler, "IQC-based robustness analysis of discrete-time linear time-varying systems," Int. J. Robust Nonlinear Control, vol. 27, no. 16, pp. 3135-3157, 2017. [DOI:10.1002/rnc.3731]
10. [10] H. Pfifer and P. Seiler, "Less conservative robustness analysis of linear parameter varying systems using integral quadratic constraints," Int. J. Robust Nonlinear Control, vol. 26, no. 16, pp. 3580-3594, 2016. [DOI:10.1002/rnc.3521]
11. [11] M. J. L. Bin Hu and P. Seiler, "Robustness analysis of uncertain discrete-time systems with dissipation inequalities and integral quadratic constraints," Int. J. Robust Nonlinear Control, 2016.
12. [12] J. Veenman and C. W.Scherer, "IQC-synthesis with general dynamic multipliers," Int. J. Robust Nonlinear Control, vol. 24, no. 17, pp. 3027-3056, 2014. [DOI:10.1002/rnc.3042]
13. [13] R. Venkataraman and P. Seiler, "Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints," Int. J. Robust Nonlinear Control, vol. 28, no. 3, pp. 953-975, 2017. [DOI:10.1002/rnc.3913]
14. [14] O. Martin, J., Wilcox, L. C., Burstedde, C., Ghattas, "Analysis and design of optimization algorithms via integral quadratic constraints," Siam J. Control Optim., vol. 34, no. 3, pp. 57-95, 2012.
15. [15] J. Veenman, C. W. Scherer, and H. Köroğlu, "Robust stability and performance analysis based on integral quadratic constraints," Eur. J. Control, vol. 31, pp. 1-32, 2016. [DOI:10.1016/j.ejcon.2016.04.004]
16. [16] H. Pfifer and P. Seiler, "Robustness analysis of linear parameter varying systems using integral quadratic constraints," Am. Control Conf. USA, 2014. [DOI:10.1109/ACC.2014.6858751]
17. [17] F. Wu, X. H. Yang, A. Packard, and G. Becker, "Induced L2-norm control for LPV systems with bounded parameter variation rates," Int. J. Robust Nonlinear Control, vol. 6, no. 9-10, pp. 983-998, 1996.
https://doi.org/10.1002/(SICI)1099-1239(199611)6:9/10<983::AID-RNC263>3.0.CO;2-C [DOI:10.1002/(SICI)1099-1239(199611)6:9/103.0.CO;2-C]
18. [18] P. Apkarian and R. J. Adams, "Advanced gain-scheduling techniques for uncertain systems," IEEE Trans. Control Syst. Technol., vol. 6, no. 1, pp. 21-32, 1998. [DOI:10.1109/87.654874]
19. [19] F. Wu, "A generalized LPV system analysis and control synthesis framework," Int. J. Control, vol. 74, no. 7, pp. 745-759, 2001. [DOI:10.1080/00207170010031495]
20. [20] V. F. Montagner, R. C. L. F. Oliveira, P. L. D. Peres, and P. A. B. Abstract:, "Linear matrix inequality characterisation for H∞ and H2 guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems," IET Control Theory Appl., vol. 6, pp. 1726-1735, 2007. [DOI:10.1049/iet-cta:20070037]
21. [21] W. Xie, "Quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control," IET Control Theory Appl., vol. 6, no. 11, pp. 1577-1582, 2012. [DOI:10.1049/iet-cta.2011.0362]
22. [22] H. Pfifer and P. Seiler, "Robustness analysis of linear parameter varying systems using integral quadratic constraints," Int. J. Robust Nonlinear Control, vol. 25, no. 15, pp. 2843-2864, 2015. [DOI:10.1002/rnc.3240]
23. [23] K. Zhou, J. Doyle, and K. Glover, Robust and optimal control. Prentice-Hall, 1996.
24. [24] P. Apkarian and D. Noll, "IQC analysis and synthesis via nonsmooth optimization," Syst. Control Lett., vol. 55, no. 12, pp. 971-981, 2006. [DOI:10.1016/j.sysconle.2006.06.008]
25. [25] X.-H. Chang, J. H. Park, and J. Zhou, "Robust static output feedback H∞ control design for linear systems with polytopic uncertainties," Syst. Control Lett., vol. 85, pp. 23-32, 2015. [DOI:10.1016/j.sysconle.2015.08.007]
26. [26] R. A. Nichols, R. T. Reichert, W. J. Rugh, and S. Member, "Gain scheduling for H-Infinity controllers : a flight control example," IEEE Trans. Control Syst. Technol., vol. 1, no. 2, pp. 69-79, 1993. [DOI:10.1109/87.238400]
27. [27] P. Apkarian, P. Gahinets, and G. Becker, "Self-scheduled H∞ control of linear parameter-varying systems: a design example," Automatica, vol. 31, no. 9, pp. 1251-1261, 1995. [DOI:10.1016/0005-1098(95)00038-X]
28. [28] D. H. Lee, J. B. Park, Y. H. Joo, and K. C. Lin, "Lifted versions of robust D-stability and D-stabilisation conditions for uncertain polytopic linear systems," IET Control Theory Appl., vol. 6, no. 1, pp. 24-36, 2012. [DOI:10.1049/iet-cta.2010.0197]
29. [29] C. Scherer and S. Weiland, Linear matrix inequalities in control. 2000.
30. [30] J. Dong and G.-H. Yang, "Robust static output feedback control synthesis for linear continues systems with polytopic uncertainties," Automatica, vol. 49, no. 6, pp. 1821-1829, 2013. [DOI:10.1016/j.automatica.2013.02.047]
31. [31] J. M. Biannic and P. Apkarian, "Missile autopilot design via a modified LPV synthesis technique," Aerosp. Sci. Technol., vol. 3, pp. 153-160, 1999. [DOI:10.1016/S1270-9638(99)80039-X]
32. [32] D. Rotondo, F. Ejjari, and V. Puig, "Robust state-feedback control of uncertain LPV systems: An LMI-based approach," J. Franklin Inst., vol. 351, no. 5, pp. 2781-2803, 2014. [DOI:10.1016/j.jfranklin.2014.01.018]
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