Research Article Adaptive Integral-Based Robust Q-S Synchronization and Parameter Identification of Nonlinear Hyperchaotic Complex Systems Sami Ud Din , 1 Muhammad Rafiq Mufti , 2 Humaira Afzal , 3 Majid Ali , 1 and Muhammad Abdul Moiz Zia 4 1 Department of Electrical Engineering, NAMAL Institute Mianwali, Mianwali 42250, Pakistan 2 Department of Computer Science, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan 3 Department of Computer Science, Bahauddin Zakariya University, Multan 60800, Pakistan 4 Department of Computer Science, University of Central Punjab, Lahore 54000, Pakistan Correspondence should be addressed to Sami Ud Din; sami.uddin@namal.edu.pk Received 20 December 2020; Revised 24 March 2021; Accepted 8 April 2021; Published 30 April 2021 Academic Editor: Xianggui Guo Copyright©2021SamiUdDinetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. iscommuniquepresentstheQ-Ssynchronizationoftwononidenticalcomplexnonlinearhyperchaoticsystemswithunknown parameters. An adaptive controller based on adaptive integral sliding mode control and parameter update laws are designed to realize the synchronization and parameter identification to a given map vector. e aforementioned strategy’s employment demandsthetransformationofasystemintoaspecificstructurecontaininganominalpartandsomeunknownterms(lateron, these unknown terms will be computed adaptively). An integral sliding mode controller is used to stabilize the error system by designing nominal control accompanied by compensator control. For chattering suppression, a continuous compensator of smoothnatureisusedinsteadofconventionalcontrol.estabilityoftheproposedalgorithmisestablishedinanimpressiveway, using Lyapunov criteria. A numerical simulation is performed to illustrate the validity of the proposed synchronization scheme. 1.Introduction Synchronization is considered to be a fundamental phe- nomenon that enables coherent behavior in the coupled systems.Chaossynchronizationhasbeenofgreatinterestto researchers in recent years. e hyperchaotic systems are very sensitive towards initial conditions and possess at least two positive Lyapunov exponents. ey have bounded trajectories in the phase space, exhibit more complex nonlinear behavior, and so on. Hyperchaos was first for- malized in 1979 by Rossler [1]. Many other hyperchaotic systemswerereportedlateron[2–4].In[5],theWien-bridge coupled oscillator system was also indicated to be hyper- chaotic. In 1990, Pecora and Carroll [6] introduced the synchronization of two identical chaotic systems with dif- ferentinitialconditions.efieldofchaoticsynchronization flourishedextensivelyinthelasttwodecades,andmanynew strategies are also proposed in this regard, including com- plete synchronization [7, 8], lag synchronization [9, 10], inverse lag synchronization [11], inverse π-lag synchroni- zation [12], generalized synchronization [13–15], multiple chaotic systems’ synchronization [16, 17], phase synchro- nization [18], antisynchronization [19, 20], partial syn- chronization [21, 22], Q-S synchronization [23, 24], projective synchronization [25, 26], and fractional chaos synchronization [27, 28]. In recent years, generalized syn- chronization (GS) of chaotic systems was widely investi- gated. e researchers in the control community are still exploring the new dimensions of inverse generalized syn- chronization (IGS), which is also considered an attractive idea of this era regarding secure communication. e sliding mode control (SMC) has attracted re- searchers’attentioninrecentyearsduetoitsrobustresponse to model insensitivity towards nonlinearities, ease of Hindawi Complexity Volume 2021, Article ID 6678978, 17 pages https://doi.org/10.1155/2021/6678978