Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown quantized input and control directions subject to actuator failures
Restricted accessResearch articleFirst published online October, 2022
Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown quantized input and control directions subject to actuator failures
This article addresses an adaptive backstepping control design for uncertain fractional-order nonlinear systems in the strict-feedback form subject to unknown input quantization, unknown state-dependent control directions, and unknown actuator failure. The system order can be commensurate or noncommensurate. The total number of failures is allowed to be infinite. The Nussbaum function is used to deal with the problem of unknown control directions. Compared with the existing results, the control gains can be functions of states and the knowledge of quantization parameters and characteristics of the actuator failure are unknown. By applying the backstepping control approach based on the frequency-distributed model, it is proved that all the closed-loop signals remain bounded and the output tracking error converges to the origin asymptotically. Finally, the effectiveness of the proposed controller is demonstrated by two simulation examples.
Aguila-CamachoNDuarte-MermoudMAGallegosJA (2014) Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation19(9): 2951–2957.
2.
AhmadIShafiqM (2020a) Oscillation free robust adaptive synchronization of chaotic systems with parametric uncertainties. Transactions of the Institute of Measurement and Control42(11): 1977–1996.
3.
AhmadIShafiqM (2020b) Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders. Automatika61(3): 396–414.
4.
AhmadISaabanABIbrahimAB, et al. (2016) Reduced-order synchronization of time-delay chaotic systems with known and unknown parameters. Optik127(13): 5506–5514.
5.
AhmedSLochanKRoyBK (2019) Fractional-order Adaptive Sliding Mode Control for a Two-Link Flexible Manipulator. Singapore: Springer.
6.
Alaviyan ShahriESAlfiATenreiro MachadoJ (2018) Robust stability and stabilization of uncertain fractional order systems subject to input saturation. Journal of Vibration and Control24(16): 3676–3683.
7.
AskariMRShahrokhiMKhajeh TalkhonchehM (2017) Observer-based adaptive fuzzy controller for nonlinear systems with unknown control directions and input saturation. Fuzzy Sets and Systems314: 24–45.
8.
AxtellMBiseME (1990). Fractional calculus application in control systems. In: IEEE conference on aerospace and electronics, Dayton, OH, USA, pp. 563–566. May 1990: IEEE.
9.
CaponettoRDongolaGFortunaL (2010) Fractional Order Systems: Modeling and Control Applications. Singapore: World Scientific.
10.
CeragioliFDe PersisCFrascaP (2011) Discontinuities and hysteresis in quantized average consensus. Automatica47(9): 1916–1928.
11.
ChenWDaiHSongY, et al. (2017) Convex Lyapunov functions for stability analysis of fractional order systems. IET Control Theory & Applications11(7): 1070–1074.
12.
ChoiYHYooSJ (2017) Approximation-based adaptive tracking of uncertain input-quantized nonlinear systems in the presence of unknown quantization parameters and control directions. International Journal of Control, Automation and Systems15(3): 1414–1424.
13.
De PersisCMazencF (2010) Stability of quantized time-delay nonlinear systems: a Lyapunov-Krasowskii-functional approach. Mathematics of Control, Signals, and Systems21(4): 337–370.
14.
DebnathL (2003) Recent applications of fractional calculus to science and engineering. International Journal of Mathematics and Mathematical Sciences2003(54): 3413–3442.
15.
Duarte-MermoudMAAguila-CamachoNGallegosJA, et al. (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Communications in Nonlinear Science and Numerical Simulation22(1–3): 650–659.
16.
GeSSHongFLeeTH (2004) Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics)34(1): 499–516.
17.
HabibiHRahimi NohoojiHHowardI (2018) Adaptive PID control of wind turbines for power regulation with unknown control direction and actuator faults. IEEE Access6: 37464–37479.
18.
HanJ (2009) From PID to active disturbance rejection control. IEEE transactions on Industrial Electronics56(3): 900–906.
19.
HuaC-CWangQ-GGuanX-P (2008) Adaptive backstepping control for a class of time delay systems with nonlinear perturbations. International Journal of Adaptive Control and Signal Processing22(3): 289–305.
20.
HuaCNingJZhaoG, et al. (2018) Output feedback NN tracking control for fractional-order nonlinear systems with time-delay and input quantization. Neurocomputing290: 229–237.
JingY-HYangG-H (2017) Adaptive quantised fault-tolerant tracking control of uncertain nonlinear systems with unknown control direction and the prescribed accuracy. International Journal of Systems Science48(13): 2826–2837.
23.
KhettabKLadaciSBensafiaY (2016) Fuzzy adaptive control of fractional order chaotic systems with unknown control gain sign using a fractional order Nussbaum gain. IEEE/CAA Journal of Automatica Sinica6(3): 816–823.
24.
LaiGLiuZZhangY, et al. (2016) Quantisation‐based robust control of uncertain non‐strict‐feedback non‐linear systems under arbitrary switching. IET Control Theory & Applications10(5): 582–589.
25.
LenkaBKBanerjeeS (2018) Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems. Communications in Nonlinear Science and Numerical Simulation56: 365–379.
26.
LiL (2016) Fault Detection and Fault-Tolerant Control for Nonlinear Systems. Duisburg, Germany: Spring Vieweg.
27.
LiY-XWangQ-YTongS (2019) Fuzzy adaptive fault-tolerant control of fractional-order nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems51(3): 1372–1379.
28.
LiY-XYangG-H (2016) Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults. Automatica72: 177–185.
29.
LiYChenYPodlubnyI (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Computers & Mathematics with Applications59(5): 1810–1821.
30.
LiuZWangFZhangY, et al. (2015) Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems. IEEE Transactions on Cybernetics46(2): 524–534.
31.
LiuHPanYLiS, et al. (2017) Adaptive fuzzy backstepping control of fractional-order nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems47(8): 2209–2217.
32.
LiuZChenBLinC, et al. (2019) Adaptive neural constraint output control for a class of quantized input switched nonlinear system. IEEE Access7: 121493–121500.
33.
LunzeJNixdorfBSchröderJ (1999) Deterministic discrete-event representations of linear continuous-variable systems. Automatica35(3): 395–406.
34.
MonjeCAChenYVinagreBM, et al. (2010) Fractional-order Systems and Controls: Fundamentals and Applications. London, UK: Springer Science & Business Media.
35.
MoradvandiAShahrokhiMMalekSA (2019) Adaptive fuzzy decentralized control for a class of MIMO large-scale nonlinear state delay systems with unmodeled dynamics subject to unknown input saturation and infinite number of actuator failures. Information Sciences475: 121–141.
36.
MujumdarATamhaneBKurodeS (2015) Observer-based sliding mode control for a class of noncommensurate fractional-order systems. IEEE/ASME Transactions on Mechatronics20(5): 2504–2512.
37.
MuresanCIDulfEHProdanO (2016) A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers. Journal of Vibration and Control22(8): 1980–1992.
38.
NaJ (2013) Adaptive prescribed performance control of nonlinear systems with unknown dead zone. International Journal of Adaptive Control and Signal Processing27(5): 426–446.
39.
NikdelNBadamchizadehMA (2019) Fractional-order adaptive backstepping control of a class of uncertain systems with external disturbances. International Journal of Control92(6): 1344–1353.
40.
NiuBLiHQinT, et al. (2017) Adaptive NN dynamic surface controller design for nonlinear pure-feedback switched systems with time-delays and quantized input. IEEE Transactions on Systems, Man, and Cybernetics: Systems48(10): 1676–1688.
41.
NussbaumRD (1983) Some remarks on a conjecture in parameter adaptive control. Systems & Control Letters3(5): 243–246.
42.
PetrášI (2011) Fractional-order Nonlinear Systems: Modeling, Analysis and Simulation. Berlin, Germany: Springer Science & Business Media.
43.
PodlubnyI (1998) Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. California, USA: Elsevier.
44.
SabatierJAgrawalOPMachadoJT (eds) (2007) Advances in Fractional Calculus. Dordrecht, The Netherlands: Springer.
45.
SakthivelRAhnCKJobyM (2018) Fault-tolerant resilient control for fuzzy fractional order systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems49(9): 1797–1805.
46.
ShafiqMAhmadI (2019) Multi-switching combination anti-synchronization of unknown hyperchaotic systems. Arabian Journal for Science and Engineering44(8): 7335–7350.
47.
ShengDWeiYChengS, et al. (2017) Adaptive backstepping control for fractional order systems with input saturation. Journal of the Franklin Institute354(5): 2245–2268.
48.
SongSParkJHZhangB, et al. (2020) Adaptive command filtered neuro-fuzzy control design for fractional-order nonlinear systems with unknown control directions and input quantization. IEEE Transactions on Systems, Man, and Cybernetics: Systems1–12. DOI: 10.1109/TSMC.2020.2967425. in press
49.
TrigeassouJ-CMaamriNOustaloupA (2013) Lyapunov stability of linear fractional systems: Part 1—definition of fractional energy. In:ASME 2013 international design engineering technical conferences and computers and information in engineering conference, Portland, Oregon, August 2013. USA: ASME.
50.
WangF-YLiuD (2008) Networked Control Systems. London, UK: Springer.
51.
WangWWenC (2010) Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica46(12): 2082–2091.
52.
WangC-CYangG-H (2018) Prescribed performance adaptive fault-tolerant tracking control for nonlinear time-delay systems with input quantization and unknown control directions. Neurocomputing311: 333–343.
53.
WangMChenBShiP (2008) Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems. IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : A Publication of the IEEE Systems, Man, and Cybernetics Society38(3): 721–730.
54.
WangCWenCLinY (2015a) Decentralized adaptive backstepping control for a class of interconnected nonlinear systems with unknown actuator failures. Journal of the Franklin Institute352(3): 835–850.
55.
WangFYangYHuM (2015b) Asymptotic stability of delayed fractional-order neural networks with impulsive effects. Neurocomputing154: 239–244.
56.
WangWWangDPengZ, et al. (2015c) Prescribed performance consensus of uncertain nonlinear strict-feedback systems with unknown control directions. IEEE Transactions on Systems, Man, and Cybernetics: Systems46(9): 1279–1286.
57.
WangHXiaoping LiuPXieX, et al. (2018) Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator. Information Sciences. DOI: 10.1016/j.ins.2018.04.011.in press.
58.
WeiYDaiYChengS, et al. (2014) Study on fractional order tracking differentiator. In: The 5th conference on nonlinear science and complexity. Xian, China, August 2014. Springer. 04.
59.
WeiYChenYLiangS, et al. (2015) A novel algorithm on adaptive backstepping control of fractional order systems. Neurocomputing165: 395–402.
60.
WeiYTsePWYaoZ, et al. (2016) Adaptive backstepping output feedback control for a class of nonlinear fractional order systems. Nonlinear Dynamics86(2): 1047–1056.
61.
XudongYDingZ (2001) Robust tracking control of uncertain nonlinear systems with unknown control directions. Systems & Control Letters42(1): 1–10.
62.
YaoBTomizukaM (2001) Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms. Automatica37(9): 1305–1321.
63.
YuXLinY (2016) Adaptive backstepping quantized control for a class of nonlinear systems. IEEE Transactions on Automatic Control62(2): 981–985.
64.
ZhangZXieX-J (2014) Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs. International Journal of Control87(11): 2294–2311.
65.
ZouariFBoulkrouneAIbeasA, et al. (2017) Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation. Neural Computing and Applications28(1): 993–1010.
