Abstract
In the present paper, the problem of robust H∞ filtering for continuous-time affine nonlinear singular systems (ANSSs) with norm-bounded uncertainty is studied. Employing Luenberger-like and certainty equivalent structures, and based on the differential game theory, sufficient conditions for the existence of such filters are derived. These conditions are in the form of a generalized Hamilton–Jacobi–Isaacs (GHJI) inequality and the output injection gain of each filter is obtained as a function of the corresponding GHJI inequality solution. Numerical simulations are provided to demonstrate the applicability of the proposed approach. The results show that the adopted method not only perfectly achieves the estimation goals in the presence of model uncertainties but also outperforms some existing results for known (certain) systems.
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References
Abbaszadeh M, Marquez HJ (2012) A generalized framework for robust nonlinear H∞ filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties. Automatica 48(5):894–900
Aliyu MDS (2011) Nonlinear H∞ control, Hamiltonian systems and Hamilton–Jacobi equations. CRC Press, Boca Raton
Aliyu MDS, Boukas EK (2012) H∞ filtering for nonlinear singular systems. IEEE T Circuits I 59(10):2395–2404
Barbosa KA, Cipriano A (2011) Robust H∞ filter design for singular systems with time-varying uncertainties. IET Control Theory Appl 5(9):1085–1091
Basar T, Olsder GJ (1998) Dynamic noncooperative game theory. Society for Industrial and Applied Mathematics, Philadelphia
Berman N, Shaked U (1996) H∞ nonlinear filtering. Int J Robust Nonlinear Control 6(4):281–296
Brenan KE, Campbell SL, Petzold LR (1996) Numerical solution of initial-value problems in differential-algebraic equations. Society for Industrial and Applied Mathematics, Philadelphia
Darouach M (2009) H∞ unbiased filtering for linear descriptor systems via LMI. IEEE Trans Autom Control 54(8):1966–1972
Darouach M, Boutat-Baddas L, Zerrougui M (2011) H∞ observers design for a class of nonlinear singular systems. Automatica 47(11):2517–2525
Duan GR (2010) Analysis and design of descriptor linear systems, vol 23. Springer, New York
Feng Y, Yagoubi M (2017) Robust control of linear descriptor systems. Springer, Singapore
Fridman E, Shaked U (1997) On regional nonlinear H∞-filtering. Syst Control Lett 29(4):233–240
Hassan L, Zemouche A, Boutayeb M (2011) H∞ observers design for a class of nonlinear time-delay systems in descriptor form. Int J Control 84(10):1653–1663
Hassanabadi A, Shafiee M, Puig V (2016a) UIO design for singular delayed LPV systems with application to actuator fault detection and isolation. Int J Syst Sci 47(1):107–121
Hassanabadi A, Shafiee M, Puig V (2016b) Robust fault detection of singular LPV systems with multiple time-varying delays. Int J Appl Math Comput Pol 26(1):45–61
Isidori A (1994) H∞ control via measurement feedback for affine nonlinear systems. Int J Robust Nonlinear Control 4(4):553–574
Kunkel P, Mehrmann V (2006) Differential-algebraic equations: analysis and numerical solution. European Mathematical Society, Berlin
Lee CM, Fong IK (2007) H∞ optimal singular and normal filter design for uncertain singular systems. IET Control Theory Appl 1(1):119–126
Li YF, Yung CF, Tseng CS (2008) Reduced-order filtering design for non-linear systems with H∞ setting. Int J Syst Sci 39(10):985–994
Limebeer DJN, Green M (1995) Linear robust control. Prentice-Hall, Englewood Cliffs
Lu R, Xu Y, Zhao X, Peng D, Xue A (2009) Delay-dependent H∞ filtering for nonlinear singular systems with network-induced delays. In: Proceedings of 7th Asian control conference, pp 600–604
Nagpal KM, Khargonekar PP (1991) Filtering and smoothing in an H∞ setting. IEEE Trans Autom Control 36(2):152–166
Nguang SK, Fu M (1996) Robust nonlinear H∞ filtering. Automatica 32(8):1195–1199
Qiu J, Xing Z, Li L, Yang M, Li Y (2013) Robust H∞ filtering for a class of nonlinear uncertain singular systems with time-varying delay. Int J Wavelets Multiresolut 11(05):1350035
Riaza R (2008) Differential-algebraic systems: analytical aspects and circuit applications. World Scientific, Singapore
Shaked U, Theodor Y (1992) H∞-optimal estimation: a tutorial. In: Proceedings of the 31st IEEE conference on decision and control, pp 2278–2286
Shergei M, Shaked U, De Souza CE (1996) Robust H∞ non-linear estimation. Int J Adapt Control Signal Process 10(4–5):395–408
Shojaee V, Shafiee M (2015) Singular systems: reasons and the importance of singular modeling. In: Proceedings of the 23rd Iranian conference on electrical engineering, pp 1024–1029 (In Persian)
Xu S, Lam J (2006) Robust control and filtering of singular systems. Springer, New York
Xu S, Lam J (2007) Reduced-order H∞ filtering for singular systems. Syst Control Lett 56(1):48–57
Xu S, Lam J, Zou Y (2003) H∞ filtering for singular systems. IEEE Trans Autom Control 48(12):2217–2222
Xue A, Ge M, Wang J, Lu R (2006) Robust H∞ filtering for a class of uncertain nonlinear singular delay systems. In: Proceedings of the American control conference, pp 2221–2226
Yung CF, Li YF, Sheu HT (2001) H∞ filtering and solution bound for non-linear systems. Int J Control 74(6):565–570
Zamani I, Shafiee M (2015) Stability analysis of uncertain switched singular time-delay systems with discrete and distributed delays. Optim Control Appl Methods 36:1–28
Zamani I, Shafiee M, Ibeas A (2015) Switched nonlinear singular systems with time-delay: stability analysis. Int J Robust Nonlinear Control 25:1497–1513
Zulfiqar A, Rehan M, Abid M (2016) Observer design for one-sided Lipschitz descriptor systems. Appl Math Model 40(3):2301–2311
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Shojaee, V., Shafiee, M. A Robust H∞ Filter for Uncertain Continuous-Time Affine Nonlinear Singular Systems. Iran J Sci Technol Trans Electr Eng 43 (Suppl 1), 247–258 (2019). https://doi.org/10.1007/s40998-018-0114-0
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DOI: https://doi.org/10.1007/s40998-018-0114-0