Robust fault-tolerant full-order and reduced-order observer synchronization for differential inclusion chaotic systems with unknown disturbances and parameters
Restricted accessResearch articleFirst published online August, 2015
Robust fault-tolerant full-order and reduced-order observer synchronization for differential inclusion chaotic systems with unknown disturbances and parameters
Within the drive-response configuration, this paper deals with the problem of fault-tolerant full-order and reduced-order observer synchronization for differential inclusion chaotic systems with unknown disturbances and parameters. Even if there are unknown disturbances and parameters in the drive system, a robust fault-tolerant adaptive full-order observer can be used to realize chaos synchronization with the response system for some assumptions whether or not fault occurs. What’s more, a reduced-order observer differential inclusion response system which can synchronize part states of the drive system is developed for the same assumptions. Finally, some numerical simulations for Lorenz chaotic systems with differential inclusion are designed and the simulation results are analyzed in detail.
Boulkroune A and M'saad M (2012) Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity. Journal of Vibration and Control 18: 437–450.
3.
BoutayebMDarouachMRafaralahyH (2002) Generalized state-space observers for chaotic synchronization and secure communication. IEEE Transactions on Circuits and Systems I49: 345–349.
4.
BrogliatoBHeemelsW (2009) Observer design for Lur’e systems with multivalued mappings: A passivity approach. IEEE Transactions on Automatic Control54: 1996–2001.
5.
BrogliatoBLozanoRMaschkeB (2007) Dissipative Systems Analysis and Control, London: Springer Verlag.
6.
BruinJDorisAWouwN (2012) Control of mechanical motion systems with non-collocation of actuation and friction: A Popov criterion approach for input-to-state stability and set-valued nonlinearities. Automatica45: 405–415.
7.
ChenC (1984) Linear System Theory and Design, Philadelphia: Saunders College Publishing.
8.
ChenC (2012) Delay independent criterion for multiple time-delay systems and its application in building structure control systems. Journal of Vibration and Control19(3): 395–414.
9.
ChenWSaifM (2006) An iterative learning observer for fault detection and accommodation in nonlinear time-delay systems. International Journal of Robust and Nonlinear Control16: 1–19.
10.
ChoYRajamaniR (1997) A systematic approach to adaptive observer synthesis for nonlinear systems. Physics Letters A42: 534–537.
DorisAAleksandarJuloskiL (2008) Observer designs for experimental non-smooth and discontinuous systems. IEEE Transactions on Control Systems Technology16: 1323–1332.
13.
GuoLWangH (2005) Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications52: 1644–1652.
14.
JiangBStaroswieckiMCocquempotV (2004) Fault diagnosis based on adaptive observer for a class of non-linear systems with unknown parameters. International Journal of Control77: 367–383.
15.
KristicMModestinoJDengH (1998) Stabilization of Nonlinear Uncertain Systems, New York: Springer Verlag.
16.
LiuBXuCLiuD (2011) Input-to-state-stability-type comparison principles and input-to-state stability for discrete-time dynamical networks with time delays. International Journal of Robust and Nonlinear Control23(4): 450–472.
17.
Louodop P, Fotsin H, Bowong S, et al. (2012) Adaptive time-delay synchronization of chaotic systems with uncertainties using a nonlinear feedback coupling. Journal of Vibration and Control, in press. DOI: 10.1177/1077546312467811.
18.
LuoRZWangYLDengSC (2010) Combination synchronization of three classic chaotic systems using active backstepping design. Chaos21: 043114–043114.
19.
Osorio M and Moreno J (2006) Dissipative design of observers for multivalued nonlinear systems. In: Proceedings of the IEEE conference on decision and control, San Diego, CA, 13–15 December, pp. 5400–5405.
20.
PecoraLCarrollT (1990) Bifurcation and chaos of an axially accelerating viscoelastic beam. Chaos, Solition and Fractals64: 821–824.
21.
RoydenH (1988) Real Analysis, London: Prentice Hall.
22.
ShiXWangZ (2012) Hybrid synchronization phenomenon in two coupled delay hyperchaotic Lorenz systems with unknown parameters via a single linear controller. Journal of Vibration and Control19(7): 1051–1060.
23.
SunJShenYZhangG (2012) Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control. Chaos22: 043107–043107.
24.
SunJShenYYinQ (2013a) Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos23: 013140–013140.
25.
SunJShenYZhangG (2013b) General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameters identification in several chaotic and hyperchaotic systems. Chinese Physics B22: 040508–040508.
26.
SunJShenYZhangG (2013c) Combination-combination synchronization among four identical or different chaotic systems. Nonlinear Dynamics73: 1211–1222.
27.
SunY (2009) On the state reconstructor design for a class of chaotic systems. Chaos, Solition and Fractals40: 815–820.
28.
WangCCPaiNSYauHT (2010) Chaos control in AFM system using sliding mode control by backstepping design. Communications in Nonlinear Science and Numerical Simulation15(3): 741–751.
29.
WangHOWangYWGuanZH (2003) Feedback and adaptive control for the synchronization of Chen system via a single variable. Physics Letters A31: 34–40.
YangYSLiaoTLYanJJ (2012) Sliding mode control design for generalized projective synchronization of unified chaotic systems containing nonlinear inputs. Journal of Vibration and Control18(6): 808–816.
32.
Zhao JK, Zhou D and Li YW (2012) A new impulsive synchronization of Chen hyper-chaotic system and Lv hyper-chaotic system. Journal of Vibration and Control, in press.
33.
ZhuF (2008) Full-order and reduced-order observer-based synchronization for chaotic systems with unknown disturbances and parameters. Physics Letters A372: 223–232.
