In this paper, multi-model estimation and fault detection using neural network is proposed for an unknown time continuous fractional order nonlinear system. Fractional differentiation is considered based on Caputo concept and the fractional order is considered to be between 0 and 1. In order to estimate a time continuous fractional order nonlinear system with unknown term in its dynamic, single-layer and double-layer RBF neural network is used. First, a parallel-series neural network observer is designed for state estimation. Weights of the neural network are updated adaptively and updating laws are presented in fractional order form. Using Lyapunov method, it is proved that state estimation error and weight estimation error of the neural network are bounded. Parameters of the neural estimator converge to ideal parameters which satisfy excitation condition stability. Then, multi-model estimation structure of fractional order nonlinear systems is presented and its application in fault detection is investigated. Finally, simulation results are presented to show efficiency of the proposed method.
AbdollahiFTalebiHAPatelRV (2006) A stable neural network-based observer with application to flexible-joint manipulators. IEEE Transactions on Neural Networks17(1): 118–129.
2.
Aguila-CamachoNDuarte-MermoudMAGallegosJA (2014) Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation19: 2951–2957.
3.
AlessandriABagliettoMBattistelliGGaggeroM (2011) Moving-horizon state estimation for nonlinear systems using neural networks. IEEE Transactions on Neural Networks22(5): 768–780.
4.
AribiAFargesCAounMMelchiorPNajarSAbdelkrimMN (2014) Fault detection based on fractional order models: Application to diagnosis of thermal systems. Communications in Nonlinear Science and Numerical Simulation19(10): 3679–3693.
5.
BaiJYuY (2018) Neural networks based adaptive consensus for a class of fractional-order uncertain nonlinear multiagent systems. Complexity2018: 1–10.
6.
BaruchIThomasFFloresJGortchevaE (2001) A multimodel recurrent neural network for systems identification and control. IEEE Transactions on Neural Networks2: 1291–1296.
7.
BaruchIThomasFGarridoRGortchevaE (1999) A hybrid multimodel neural network for nonlinear systems identification. IEEE Transactions on Neural Networks6: 4278–4283.
8.
ChaibSBoutatDBenaliAKratzF (2009) Failure detection and reconstruction in switched nonlinear systems. Nonlinear Analysis: Hybrid Systems3(3): 225–238.
9.
DibazarAYousefiABergerTW (2014) Large-scale parameter estimation for nonlinear dynamic systems: Application on spike-in, spike-out neural models. In: International Joint Conference on Neural Networks (IJCNN), Beijing, China, 6–11 July, 2422–2427.
10.
DingXCaoJ (2017) Global dissipativity of fractional-order delayed neural networks with coupling. In: International Workshop on Complex Systems and Networks, Doha, Qatar, 8–10 December, 218–223.
11.
DrakeKJCampbellSLAndjelkovicISweetinghamK (2007) Model-based failure detection on nonlinear systems: Theory and transition. Naval Engineers Journal119(2): 93–107.
12.
El-SayedAM (1996) Fractional-order diffusion-wave equation. International Journal of Theoretical Physics35(2): 311–322.
13.
EsfandiariKMehrabiEAbdollahiFTalebiHA (2016) Neural network-based adaptive control of uncertain multivariable systems: Theory and experiments. In: IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Banff, Canada, July 2016, 907–912.
14.
FausettL (1993) Fundamentals of Neural Networks: Architectures, Algorithms and Applications. London, UK: Pearson.
15.
HartleyTTLorenzoCF (2002) Dynamics and control of initialized fractional-order systems. Nonlinear Dynamics29(1–4): 201–233.
16.
HeWChenYYinZ (2016) Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Transactions on Cybernetics46(3): 620–629.
17.
HuangY (2016) Neuro-observer based online finite-horizon optimal control for uncertain non-linear continuous-time systems. IET Control Theory & Applications11(3): 401–410.
18.
HwangCLeuJTsayS (2002) A note on time-domain simulation of feedback fractional-order systems. IEEE Transactions on Automatic Control47(4): 625–631.
19.
KashiASZhugeQCartledgeJCEtemadSABorowiecACharltonDLaperleCO’SullivanM (2018) Nonlinear signal-to-noise ratio estimation in coherent optical fiber transmission systems using artificial neural networks. Journal of Lightwave Technology. 36(23): 5424–5431
20.
KilbasAASrivastavaHMTrujilloJJ (2006) Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier.
21.
LewisFLYesildirekALiuK (1996) Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Transactions on Neural Networks7(2): 1–11.
22.
LiYMTongSC (2016) Failure detection and adaptive fuzzy backstepping fault-tolerant control of faults nonlinear systems. In: 12th World Congress on Intelligent Control and Automation (WCICA), Guilin, China, 12–15 June, 749–752.
23.
NarendraKSBalakrishnanJ (1997) Adaptive control using multiple models. IEEE Transactions on Automatic Control42: 171–187.
24.
Perez-CruzJHRubioJJPachecoJSorianoE (2013) State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks. Neural Computing & Applications25(3–4): 693–701.
25.
PisanoARapaícMRUsaiE (2012) Discontinuous dynamical systems for fault detection: A unified approach including fractional and integer order dynamics. Mathematics and Computers in Simulation95: 111–125.
26.
PisanoARapaícMUsaiEJeliciZ (2011) Second order sliding mode approaches to disturbance estimation and fault detection in fractional-order systems. IFAC Proceedings Volumes44(1): 2436–2441.
27.
RahmaniMRFarrokhiM (2017) Nonlinear dynamic system identification using neuro-fractional order Hammerstein model. Transactions of the Institute of Measurement and Control. DOI: 10.1177/0142331217734301.
28.
RuanXLiuJ (2017) Mittag-Leffler stabilization of impulsive fractional-order neural networks with continuous and distributed delays. In: 4th International Conference on Information, Cybernetics and Computational Social Systems (ICCSS), Dalian, China, 383–388.
29.
SelmicRRLewisFL (2001) Multimodel neural networks identification and failure detection of nonlinear systems. In: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, USA, December 2001, 3128–3133.
30.
ShumskyAY (1995) Efficiency analysis and optimal design of observer-based failure detection procedures for nonlinear systems. In: Proceedings of the American Control Conference, Seattle, Washington, USA, June 1995, 107–108.
31.
VinagreBFeliuV (2002) Modeling and control of dynamic system using fractional calculus: Application to electrochemical processes and flexible structures. In: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, 214–239.
32.
YadaiahNSuresh KumarABapiRSRoopchandanM (2011) State estimation of nonlinear system through particle filter based recurrent neural networks. IEEE Transactions on Neural Networks: 307–310.
33.
ZaborovskyVMeylanovR (2001) Informational network traffic model based on fractional calculus. In: International Conferences on Info-Tech and Info-Net, Beijing, China, 29 October–1 November 2001, 58–63.
34.
ZareiJTabatabaeiM (2018) Fractional order unknown input filter design for fault detection of discrete fractional order linear systems. Transactions of the Institute of Measurement and Control48: 1–9.
ZhangSChenYYuY (2017) Robust: A survey of fractional-order neural networks. In: Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Cleveland, Ohio, USA, 6–9 August, pp. 1–10.
37.
ZhongWLuJMiaoY (2017) Fault detection observer design for fractional-order systems. In: 29th Chinese Control and Decision Conference (CCDC), Chongqing, China, 2796–2801.
