Research Article Mamdani-Type Fuzzy-Based Adaptive Nonhomogeneous Synchronization J. R. Pulido–Luna , 1 J.A.L´ opez–Renter´ ıa , 2 and N. R. Cazarez–Castro 1 1 Departamento de Ingenier´ ıa El´ ectrica y Electr´ onica, Tecnol´ ogico Nacional de M´ exico, Instituto Tecnol´ ogico de Tijuana, Calzada Tecnol´ ogico S/N, Fracc, Tom´ as Aquino, Tijuana, Baja California, CP 22414, Mexico 2 CONACyT-Tecnol´ ogicoNacionaldeM´ exico,InstitutoTecnol´ ogicodeTijuana,CalzadaTecnol´ ogicoS/N,Fracc,Tom´ as Aquino, Tijuana, Baja California, CP 22414, Mexico CorrespondenceshouldbeaddressedtoJ.A.L´ opez–Renter´ ıa;jorge.lopez@tectijuana.edu.mxandN.R.Cazarez–Castro;nohe@ ieee.org Received 26 March 2021; Accepted 28 July 2021; Published 24 August 2021 AcademicEditor:ZakiaHammouch Copyright © 2021 J. R. Pulido–Luna et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. eaimofthisworkisthedesignofanadaptivecontrollerbasedonMamdani-typefuzzyinferencesystems.einputcontrolis constructedwithsaturationfunctions’fuzzy-equivalents,whichworksastheadaptiveschemeofthecontroller.iscontrollawis designedtostabilizetheerrorsystemtosynchronizeapairofchaoticnonhomogeneouspiecewisesystems.Finally,anillustrative example as numerical evidence is developed. 1. Introduction esynchronizationphenomenaamongdynamicalsystems areawidelystudiedtopicinthelastdecadesduetothevast amountofapplicationsinscienceandengineering[1–3].In the related literature, dynamical systems and synchroniza- tionapplicationsinmanyfieldscanbefound,frombiology [4, 5], mechanical systems [6–9], chemistry [10], physics [11,12],fuzzymodeling[13–16]tosecurecommunications [17–19],amongmanyothers.Ingeneral,itissaidthatasetof dynamicalsystemsachievesynchronizationiftrajectoriesin each system approach a common trajectory. Amongthesystemsstudiedinsynchronization,theones that stand out are the chaotic systems; chaotic systems exhibit more complex dynamics, and they must satisfy the next conditions according to Devaney’s definition of chaos [20]: (i) sensitivedependencetoinitialconditions, (ii) dense periodic orbits, and (iii) must be transitive. Many works consider the problem of chaos synchronization; in [21], the authors synchronize chaotic systems by linking them with common signals. Chua et al. [22] explore the synchroni- zation phenomena in Chua’s circuit, proven to be the simplest electronic circuit to exhibit chaotic behaviour; on the contrary, Femat and Sol´ ıs-Perales [23] discuss several phenomena involved with chaos synchronization, and a feedback controller is implemented to illustrate such syn- chronization. In [24], chaos synchronization between two coupledchaoticdynamicalsystemsispresented.Conditions for global asymptotic synchronization are presented and a new method for the analysis of the stability of the syn- chronization is reported, but different techniques and ap- plicationsarestilldevelopedforthistypeofsysteminthelast years.In[25],theauthorspresentthedesignofarule-based controllerforaclassofmaster-slavechaossynchronization, and unlike traditional methods, the control law obtained from this method has less maximum magnitude of the control signal and reduces the actuator saturation phe- nomenon in mechanical systems. AL-Azzawi and Aziz [26] presentthesynchronizationbetweentwononhomogeneous hyperchaoticsystems.Anonlinearcontrolisusedtoachieve synchronization and also report a stability analysis of the error dynamics system using Lyapunov’s second method and Cardano’s method. In [27], higher-order adaptive PID controllersasanewgenerationofPIDcontrollersforchaos Hindawi Complexity Volume 2021, Article ID 9913114, 11 pages https://doi.org/10.1155/2021/9913114