The field of chaotic systems control and synchronization has garnered considerable attention in light of its promising applications across various domains like secure communication, vibration suppression, and image processing. The paper investigates the problem of practical fixed-time master-slave synchronization for dissimilar fractional-order chaotic systems. Two novel adaptive fuzzy sliding-mode controllers employing non-singular fixed-time sliding surfaces are proposed to achieve practical fixed-time synchronization. Fuzzy logic systems, known for their ability to handle complex uncertainties, are used in our synchronization schemes to estimate continuous functional uncertainties. The effectiveness of the proposed synchronization schemes is validated through a simulation study.
AghababaMP (2012) Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional non-singular terminal sliding mode technique. Nonlinear Dynamics69(1–2): 247–261.
2.
AlikhanovAAAslMSHuangC (2024a) Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation. Fractional Calculus and Applied Analysis27(1): 102–123.
3.
AlikhanovAAAslMSLiD (2024b) A novel explicit fast numerical scheme for the Cauchy problem for integro-differential equations with a difference kernel and its application. Computers & Mathematics with Applications175: 330–344.
4.
AndrieuVPralyLAstolfiA (2008) A homogeneous approximation, recursive observer design and output feedback. SIAM Journal on Control and Optimization47(4): 1814C1850.
5.
AsadollahiMGhiasiARBadamchizadehMA (2020) Adaptive synchronization of chaotic systems with hysteresis quantizer input. ISA Transactions98: 137–148.
6.
BhalekarS (2014) Synchronization of incommensurate non-identical fractional order chaotic systems using active control. European Physical Journal: Special Topics223(8): 1495–1508.
7.
BoubelloutaAZouariFBoulkrouneA (2019) Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities. International Journal of General Systems48(3): 211–234.
8.
BoulkrouneALadaciS (2018) Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems. Hershey, PA: IGI Global.
9.
BounarNBoulkrouneALabdaiS, et al. (2024) Fixed-time fuzzy adaptive control scheme for doubly fed induction generator–based wind turbine. Transactions of the Institute of Measurement and Control46(8): 1579–1589.
10.
ChenGDongX (1998) From Chaos to Order: Methodologies, Perspectives and Applications. Singapore: World Scientific.
11.
DostiMMatinfarM (2023) Finite-time sliding mode control methods for a class of non-integer-order systems with input saturations and its application. Physica Scripta98(8): 085227.
12.
DuttaMRoyBK (2021) A new memductance-based fractional-order chaotic system and its fixed-time synchronisation. Chaos, Solitons & Fractals145: 110782.
13.
GholipourSAlfiADelavariH (2011) Chaos synchronization of fractional-order chaotic lorenz-stenflo system via fractional sliding mode control. In: 5th symposium on advances in science and technology, Mashhad, Iran, 12–17 May 2011, pp. 12–17.
14.
HaghighatniaSToossian ShandizHAlfiA (2019) Conformable fractional order sliding mode control for a class of fractional order chaotic systems. International Journal of Industrial Electronics Control and Optimization2(3): 177–188.
15.
HamelSBoulkrouneABouzeribaA (2016) Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead-zone nonlinearities. Complexity21(S1): 234–249.
16.
LinLXWangQHeBW, et al. (2021) Adaptive predefined-time synchronization of two different fractional-order chaotic systems with time-delay. IEEE Access9: 31908–31920.
17.
LorenzEN (1963) Deterministic nonperiodic flow. Journal of the Atmospheric Sciences20(2): 130–141.
18.
MaRRWuJWuK, et al. (2022) Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems. Nonlinear Dynamics109(4): 3145–3156.
19.
MaoB (2021) Two methods for terminal sliding-mode synchronization of fractional-order nonlinear chaotic systems. Asian Journal of Control23(4): 1720–1727.
20.
MichalakANowakowskiA (2017) Finite-time stability and finite-time synchronization of neural network-dual approach. Journal of the Franklin Institute354: 8513–8528.
21.
MofidOMomeniMMobayenS, et al. (2021) A disturbance observer-based sliding mode control for the robust synchronization of uncertain delayed chaotic systems: application to data security. IEEE Access9: 16546–16555.
22.
NiJKLiuLLiuCX, et al. (2017) Fractional order fixed-time nonsingular terminal sliding mode synchronization and control of fractional order chaotic systems. Nonlinear Dynamics89: 2065–2083.
23.
PahnehkolaeiSMAAlfiAMachadoJT (2017) Chaos suppression in fractional systems using adaptive fractional state feedback control. Chaos, Solitons & Fractals103: 488–503.
24.
PahnehkolaeiSMAAlfiAMachadoJT (2020) Fuzzy logic embedding of fractional order sliding mode and state feedback controllers for synchronization of uncertain fractional chaotic systems. Computational and Applied Mathematics39: 182.
25.
PecoraLMCarrollTL (1990) Synchronization in chaotic systems. Physical Review Letters64(8): 821–824.
26.
PodlubnyI (1999) Fractional Differential Equations. New York, NY: Academic Press.
27.
PolyakovA (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control57(8): 2106–2110.
28.
RoohiMMirzajaniSHaghighiAR, et al. (2024a) Robust design of two-level non-integer SMC based on deep soft actor-critic for synchronization of chaotic fractional order memristive neural networks. Fractal and Fractional8(9): 548.
29.
RoohiMMirzajaniSHaghighiAR, et al. (2024b) Robust stabilization of fractional-order hybrid optical system using a single-input TS-fuzzy sliding mode control strategy with input nonlinearities. AIMS Mathematics9: 25879–25907.
30.
RossikhinYShitikovaM (2004) Analysis of the viscoelastic rod dynamics via models involving fractional derivatives or operators of two different orders. The Shock and Vibration Digest36(1): 3–26.
31.
ShirkavandMPourgholiMYazdizadehA (2022) Robust global fixed-time synchronization of different dimensions fractional-order chaotic systems. Chaos, Solitons & Fractals154: 111616.
32.
SuHLuoRFuJ, et al. (2022) Fixed time control and synchronization of a class of uncertain chaotic systems with disturbances via passive control method. Mathematics and Computers in Simulation198: 474–493.
33.
WangLX (1994) Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Hoboken, NJ: Prentice-Hall.
34.
WangQZhangJDingD, et al. (2016) Adaptive Mittag-Leffler stabilization of a class of fractional order uncertain nonlinear systems. Asian Journal of Control18: 2343–2351.
35.
WuALZengZGSongXG (2016) Global Mittag-Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neurocomputing177: 489–496.
36.
ZhangRXYangSP (2011) Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller. Chinese Physics B20(11): 110506.
37.
ZhuHZhouSZhangJ (2009) Chaos and synchronization of the fractional order Chua’s system. Chaos, Solitons & Fractals39: 1595–1603.
