Two nonlinear state observers are proposed to reconstruct the system states for a class of uncertain nonlinear systems. Both state observers are designed based on continuous higher order sliding mode and terminal sliding mode concepts. The proposed observers are chattering-free and constructed without any detailed model knowledge of the system. Desirable features of the proposed observers include that they are immune to noise and can be designed separately from a controller. Lyapunov stability theory is employed to prove the finite-time convergent and uniformly ultimately bounded observation. Simulation results are provided to demonstrate the effectiveness and improved performance of the developed observers.
Ahmed-AliTLamnabhi-LagarrigueF (1999) Sliding observer-controller design for uncertain triangular nonlinear systems. IEEE Transaction on Automatic Control44(6): 1244–1249.
2.
AlmeidaDRAlvarezJFridmanL (2007) Robust observation and identification of nDOF Lagrangian systems. International Journal of Robust and Nonlinear Control17(9): 842–861.
3.
AlvarezJRosasDPenaJ (2009) Analog implementation of a robust control strategy for mechanical systems. IEEE Transactions on Industrial Electronics56(9): 3377–3385.
4.
AndrieuVPralyLAstolfiA (2009) High gain observers with updated gain and homogeneous correction terms. Automatica45(2): 422–428.
5.
AstolfiAOrtegaRVenkatramanA (2010) A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica46(1): 182–189.
6.
BascettaLMagnaniGRoccoP (2009) Velocity estimation: assessing the performance of non-model-based techniques. IEEE Transactions on Control Systems Technology17(2): 424–433.
7.
BhasinSKamalapurkarRDinhHDixonW (2013) Robust identification-based state derivative estimation for nonlinear systems. IEEE Transactions on Automatic Control58(1): 187–192.
8.
BhatSBemsteinD (2005) Finite-time stability of continuous autonomous system. SIAM Journal on Control and Optimization38(3): 751–766.
9.
ChoiJMisawaEYoungG (1999) A study on sliding mode state estimation. ASME Journal of Dynamic Systems, Measurement, and Control121(2): 225–260.
10.
DavilaJFridmanLLevantA (2005) Second-order sliding-mode observer for mechanical systems. IEEE Transactions on Automatic Control50(11): 1785–1789.
11.
DavilaJFridmanLPoznyakA (2006) Observation and identification of mechanical systems via second order sliding modes. International Journal of Control79(10): 1251–1262.
12.
DelshadSGustafssonT (2011) Nonlinear observer design for a class of Lipschitz time-delay systems with unknown inputs: LMI approach. In: 2011 XXIII international symposium on information, communication and automation technologies (ICAT), Sarajevo, Bosnia and Herzegovina, 27–29 Oct. 2011, pp. 1–5. Piscataway: IEEE Press.
13.
EdwardsCSpurgeonSPattonR (2000) Sliding mode observers for fault detection and isolation. Automatica36(4): 541–553.
14.
FernandezBHedrickJ (1987) Control of multivariable non-linear systems by the sliding mode method. International Journal of Control46(3): 1019–1040.
15.
HuangXLinWYangB (2005) Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica41(5): 881–888.
16.
IncremonaGPRubagottiMFerraraA (2017) Sliding mode control of constrained nonlinear systems. IEEE Transactions on Automatic Control62(6): 2965–2972.
LevantA (2003) Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control76(9–10): 924–941.
19.
LiuY (2009) Robust adaptive observer for nonlinear systems with unmodeled dynamics. Automatica45(8): 1891–1895.
20.
MarinoRSantosuossoGTomeiP (2001) Robust adaptive observers for nonlinear system with bounded disturbances. IEEE Transactions on Automatic Control46(6): 967–972.
21.
OuederMFarzaMBenAbdennourRM’SaadM (2012) A high gain observer with updated gain for a class of MIMO non-triangular systems. Systems & Control Letters61(2): 298–308.
22.
PertewAMarquezHZhaoQ (2006) H∞ observer design for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control51(7): 1211–1216.
23.
SabanovicAElitasMOhnishiK (2008) Sliding modes in constrained systems control. IEEE Transactions on Industrial Electronics55(9): 3332–3339.
24.
SanfeliceRPralyL (2011) On the performance of high-gain observers with gain adaption under measurement noise. Automatica47(10): 2165–2176.
25.
ShtesselYBBuffingtonJ (1998) Continuous sliding mode control. In: 1998 american control conference, Philadelphia, PA, USA, 26–26 June 1998, pp. 562–563. Piscataway: IEEE Press.
26.
SlotineELiW (1991) Applied Nonlinear Control. New Jersey: Prentice-Hall, Englewood Cliffs.
27.
SpurgeonS (2008) Sliding mode observers: a survey. International Journal of Systems Science39(8): 751–764.
28.
TanCEdwardsC (2002) Sliding mode observers for detection and reconstruction of sensor faults. Automatica38(10): 1815–1821.
29.
TanCEdwardsC (2009) Robust fault reconstruction using multiple sliding mode observers in cascade: development and design. In: 2009 american control conference (ACC‘09), St. Louis, MO, USA, 10–12 June 2009, pp. 3411–3416. Piscataway: IEEE Press.
30.
VeluvoluKLeeD (2011) Sliding mode high-gain observers for a class of uncertain nonlinear systems. Applied Mathematics Letters24(3): 329–334.
31.
XiaYZhuZFuMWangS (2011) Attitude tracking of rigid spacecraft with bounded disturbances. IEEE Transactions on Industrial Electronics58(2): 647–659.
32.
XinhuaWBijanS (2014) High-order nonlinear differentiator and application to aircraft control. Mechanical Systems and Signal Processing46(2): 227–252.
33.
XiongYSaifM (2001) Sliding mode observer for nonlinear uncertain systems. IEEE Transactions on Automatic Control46(12): 2012–2017.
34.
YanXGEdwardsC (2007) Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica43(9): 1605–1614.
35.
YandJZhuFZhangW (2015) Sliding-mode observers for nonlinear systems with unknown inputs and measurement noise. International Journal of Control, Automation and Systems11(5): 903–910.
36.
YuSYuXShirinzadehBManZ (2005) Non-singular terminal sliding mode control of rigid manipulators. Automatica41(11): 1957–1964.
37.
ZemoucheABoutayebM (2009) A unified H∞ adaptive observer synthesis method for a class of system with both Lipschitz and monotone nonlinearities. Systems & Control Letters58(4): 282–288.
38.
ZemoucheABoutayebMBaraG (2008) Observers for a class of Lipschitz systems with extension to H∞ performance analysis. Systems & Control Letters57(1): 18–27.
