The present work addresses chaos synchronization between two different general chaotic systems with parametric and structural uncertainties, subject to external disturbances and input dead-zone nonlinearities. In this regard, a novel robust controller has been designed that guarantees asymptotic stability of synchronization errors and boundedness of all closed-loop signals. One advantage of the proposed controller over the existing control algorithms is using only one update law for estimating the structural uncertainties, external disturbances, and unknown characteristics of the dead-zone nonlinearities, which reduces the computational burden considerably. The designed controller is singularity free, and a smooth projection algorithm has been used to make the controller more robust. In addition, a finite-time controller has been designed and its performance has been compared with the robustly designed controller.
AghababaMP (2014) Adaptive control for electromechanical systems considering dead-zone phenomenon. Nonlinear Dynamics75: 157–174.
2.
AghababaMPAghababaHP (2012) A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs. Nonlinear Dynamics69: 1903–1914.
3.
AghababaMPAghababaHP (2013) Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs. Nonlinear Dynamics73: 363–376.
4.
AghababaMPKhanmohammadiSAlizadehG (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Applied Mathematical Modelling35: 3080–3091.
5.
AkellaMRSubbaraoK (2005) A novel parameter projection mechanism for smooth and stable adaptive control. Systems & Control Letters54: 43–51.
6.
BagheriPShahrokhiMSalariehH (2017) Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters. Journal of Vibration and Control23: 389–399.
7.
BakkerRAnnaswamyAM (1996) Stability and robustness properties of a simple adaptive controller. IEEE Transactions on Automatic Control41: 1352–1358.
8.
BhatSPBernsteinDS (2000) Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization38: 751–766.
9.
ChoHBaiE-W (1998) Convergence results for an adaptive dead zone inverse. International Journal of Adaptive Control and Signal Processing12: 451–466.
10.
DingSLiSLiQ (2009) Stability analysis for a second-order continuous finite-time control system subject to a disturbance. Journal of Control Theory and Applications7: 271–276.
11.
DuHShiP (2016) A new robust adaptive control method for modified function projective synchronization with unknown bounded parametric uncertainties and external disturbances. Nonlinear Dynamics85: 355–363.
12.
FengYYuXHanF (2013) On nonsingular terminal sliding-mode control of nonlinear systems. Automatica49: 1715–1722.
13.
HamelSBoulkrouneA (2016) A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities. International Journal of General Systems45: 689–710.
14.
HungM-LYanJ-JLiaoT-L (2008) Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input. Chaos, Solitons & Fractals35: 181–187.
15.
HungYCHwangCCLiaoTL, et al. (2006) Generalized projective synchronization of chaotic systems with unknown dead-zone input: observer-based approach. Chaos: An Interdisciplinary Journal of Nonlinear Science16: 033125.
16.
ItkisU (1976) Control Systems of Variable Structure. New York: Wiley.
17.
KebriaeiHYazdanpanahMJ (2010) Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity. Communications in Nonlinear Science and Numerical Simulation15: 430–441.
18.
LiJLiWLiQ (2012) Sliding mode control for uncertain chaotic systems with input nonlinearity. Communications in Nonlinear Science and Numerical Simulation17: 341–348.
19.
LiSTianY-P (2003) Finite time synchronization of chaotic systems. Chaos, Solitons & Fractals15: 303–310.
20.
LiWChenX (2009) Projective synchronization of Chua’s chaotic system with dead-zone in the control input. Communications in Nonlinear Science and Numerical Simulation14: 3100–3107.
21.
LiuCLiuTLiuL, et al. (2004) A new chaotic attractor. Chaos, Solitons & Fractals22: 1031–1038.
22.
MohammadpourSBinazadehT (2018) Robust finite-time synchronization of uncertain chaotic systems: application on Duffing–Holmes system and chaos gyros. Systems Science & Control Engineering6: 28–36.
23.
NarendraKSAnnaswamyAM (2012) Stable Adaptive Systems. New York: Courier Corporation.
24.
ReckerDKokotovicPRhodeD, et al. (1991) Adaptive nonlinear control of systems containing a deadzone. In: Proceedings of the 30th IEEE conference on decision and control, Brighton, UK, 11–13 December 1991, pp. 2111–2115.Brighton, UK: IEEE.
25.
RoopaeiMZolghadri JahromiMJohnR, et al. (2010) Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input. Communications in Nonlinear Science and Numerical Simulation15: 2536–2545.
26.
SlotineJ-JECoetseeJA (1986) Adaptive sliding controller synthesis for non-linear systems. International Journal of Control43: 1631–1651.
27.
SunY-J (2009) Chaos synchronization of uncertain Genesio–Tesi chaotic systems with deadzone nonlinearity. Physics Letters A373: 3273–3276.
28.
TaoGKokotovicPV (1994) Adaptive control of plants with unknown dead-zones. IEEE Transactions on Automatic Control39: 59–68.
29.
TaoGKokotovićPV (1995) Discrete-time adaptive control of systems with unknown deadzones. International Journal of Control61: 1–17.
30.
UtkinVI (1978) Sliding Modes and Their Application in Variable Structure Systems. Moscow: Mir Publishers.
31.
VaidyanathanSAzarAT (2015) Anti-synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan–Madhavan chaotic systems. In: Advances and Applications in Sliding Mode Control Systems.Berlin: Springer, 527–547.
32.
WangHHanZ-zXieQ-y, et al. (2009) Finite-time chaos synchronization of unified chaotic system with uncertain parameters. Communications in Nonlinear Science and Numerical Simulation14: 2239–2247.
33.
WangX-SSuC-YHongH (2004) Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica40: 407–413.
34.
XiXMobayenSRenH, et al. (2018) Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control. Journal of Vibration and Control24: 3842–3854.
35.
YangC-COuC-J (2013) Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros. Communications in Nonlinear Science and Numerical Simulation18: 682–691.
36.
YauH-T (2008) Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs. Physics Letters A372: 2380–2385.
37.
ZhangZLuJGaoL, et al. (2013) Exponential synchronization of Genesio–Tesi chaotic systems with partially known uncertainties and completely unknown dead-zone nonlinearity. Journal of the Franklin Institute350: 347–357.
