{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:43Z","timestamp":1760240683371,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,8,17]],"date-time":"2019-08-17T00:00:00Z","timestamp":1566000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper presents an active control design for the synchronization of two identical Petrzela chaotic systems (Petrzela, J.; Gotthans, T. New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure. Applied Sciences. 2017, 7, 976) on master-slave configuration. For the active control, the parameters of both systems are assumed to be a priori known, the control law by means of the dynamic of the error synchronization is designed to guarantee the convergence to zero of error states and the synchronization process is verified by numerical simulation. By taking advantage of the execution and implementation facilities of microcontroller based chaotic systems in digital devices, the active controller is implemented in a 32 bits ARM microcontroller. The experimental results were obtained by using the fourth order Runge-Kutta numerical method to integrate the differential equations of the controller, where the results were measured with a digital oscilloscope.<\/jats:p>","DOI":"10.3390\/computation7030040","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T06:10:14Z","timestamp":1566195014000},"page":"40","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System"],"prefix":"10.3390","volume":"7","author":[{"given":"Ra\u00fal","family":"Rivera-Blas","sequence":"first","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, Escuela Superior de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica, Unidad Azcapotzalco, Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, Av. Granjas No. 682, Col. Santa Catarina, Ciudad de M\u00e9xico C.P. 02250, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salvador Antonio","family":"Rodr\u00edguez Paredes","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, Escuela Superior de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica, Unidad Azcapotzalco, Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, Av. Granjas No. 682, Col. Santa Catarina, Ciudad de M\u00e9xico C.P. 02250, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis Armando","family":"Flores-Herrera","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, Escuela Superior de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica, Unidad Azcapotzalco, Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, Av. Granjas No. 682, Col. Santa Catarina, Ciudad de M\u00e9xico C.P. 02250, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6243-7940","authenticated-orcid":false,"given":"Ignacio","family":"Adri\u00e1n Romero","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, Escuela Superior de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica, Unidad Azcapotzalco, Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, Av. Granjas No. 682, Col. Santa Catarina, Ciudad de M\u00e9xico C.P. 02250, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","article-title":"Synchronization in chaotic systems","volume":"64","author":"Pecora","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1063\/1.166278","article-title":"Fundamentals of synchronization in chaotic systems, concepts, and applications","volume":"7","author":"Pecora","year":"1997","journal-title":"Chaos Int. J. Nonlinear Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/S0960-0779(02)00585-4","article-title":"An adaptive chaos synchronization scheme applied to secure communication","volume":"18","author":"Feki","year":"2003","journal-title":"Chaos Solitons Fractals"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Tanougast, C., Dandache, A., Azzaz, M.S., and Sadoudi, S. (2012). Hardware design of embedded systems for security applications. Embedded Systems\u2014High Performance Systems, Applications and Projects, Intech.","DOI":"10.5772\/38649"},{"key":"ref_5","first-page":"123080","article-title":"An experimental realization of a chaos-based secure communication using arduino microcontrollers","volume":"2015","author":"Acho","year":"2015","journal-title":"Sci. World J."},{"key":"ref_6","first-page":"81","article-title":"A survey of chaotic secure communication systems","volume":"2","author":"Yang","year":"2004","journal-title":"Int. J. Comput. Cognit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1016\/j.sigpro.2012.11.008","article-title":"Image encryption process based on chaotic synchronization phenomena","volume":"93","author":"Volos","year":"2013","journal-title":"Signal Proc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/70.976022","article-title":"The chaotic mobile robot","volume":"17","author":"Nakamura","year":"2001","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"206","DOI":"10.5391\/IJFIS.2003.3.2.206","article-title":"Obstacle avoidance methods in the chaotic mobile robot with integrated some chaos equation","volume":"3","author":"Bae","year":"2003","journal-title":"Int. J. Fuzzy Logic Intell. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1142\/S021812741002548X","article-title":"A cooperative mobile robot task assignment and coverage planning based on chaos synchronization","volume":"20","author":"Fallahi","year":"2010","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_11","first-page":"145","article-title":"Performance evaluation of chaotic mobile robot controllers","volume":"3","author":"Fahmy","year":"2012","journal-title":"Int. Trans. J. Eng. Manag. Appl. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"60","DOI":"10.5772\/62796","article-title":"Applications of chaotic dynamics in robotics","volume":"13","author":"Zang","year":"2016","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_13","first-page":"125","article-title":"Cooperation of autonomous mobile robots for surveillance missions based on hyperchaos synchronization","volume":"6","author":"Volos","year":"2016","journal-title":"J. Appl. Math. Bioinf."},{"key":"ref_14","unstructured":"Campos, J.M.S. (2019). Inducci\u00f3n de trayectorias ca\u00f3ticas mediante acoplamiento de robots m\u00f3viles para la cobertura de \u00e1reas espec\u00edficas de forma s\u00edncrona. [Ph.D. Thesis, Manufactura avanzada\u2014CIATEQ]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/j.chaos.2018.12.002","article-title":"A multi-scroll chaotic system for a higher coverage path planning of a mobile robot using flatness controller","volume":"118","author":"Nasr","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.physleta.2004.07.024","article-title":"Adaptive feedback synchronization of a unified chaotic system","volume":"329","author":"Lu","year":"2004","journal-title":"Phys. Lett. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.chaos.2003.12.103","article-title":"Adaptive feedback synchronization of L\u00fc system","volume":"22","author":"Han","year":"2004","journal-title":"Chaos Solitons Fractals"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s11071-010-9893-1","article-title":"Adaptive control for synchronization of a four-dimensional chaotic system via a single variable","volume":"65","author":"Wang","year":"2011","journal-title":"Nonlinear Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/s11071-010-9814-3","article-title":"Adaptive synchronization of L\u00fc hyperchaotic system with uncertain parameters based on single-input controller","volume":"63","author":"Yang","year":"2011","journal-title":"Nonlinear Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.physleta.2006.08.037","article-title":"A new criterion for chaos and hyperchaos synchronization using linear feedback control","volume":"360","author":"Wang","year":"2006","journal-title":"Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.chaos.2005.12.059","article-title":"Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems","volume":"33","author":"Yan","year":"2007","journal-title":"Chaos Solitons Fractals"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.1016\/j.cnsns.2006.12.011","article-title":"On control and synchronization in chaotic and hyperchaotic systems via linear feedback control","volume":"13","author":"Rafikov","year":"2008","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.chaos.2007.07.098","article-title":"Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control","volume":"40","author":"Chen","year":"2009","journal-title":"Chaos Solitons Fractals"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.physleta.2003.11.027","article-title":"Synchronization of chaotic systems via nonlinear control","volume":"320","author":"Huang","year":"2004","journal-title":"Phys. Lett. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.ijleo.2016.10.140","article-title":"Design of a nonlinear controller and its intelligent optimization for exponential synchronization of a new chaotic system","volume":"130","year":"2017","journal-title":"Optik"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/S0375-9601(03)00573-5","article-title":"Feedback and adaptive control for the synchronization of Chen system via a single variable","volume":"312","author":"Wang","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_27","first-page":"4989520","article-title":"Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control","volume":"2018","year":"2018","journal-title":"Complexity"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1142\/S0218127403008004","article-title":"A new criterion for chaos synchronization using linear state feedback control","volume":"13","author":"Jiang","year":"2003","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.jsv.2006.01.038","article-title":"Master-slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control","volume":"295","author":"Wu","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.physd.2007.03.014","article-title":"Chaos synchronization of the master\u2013slave generalized Lorenz systems via linear state error feedback control","volume":"229","author":"Wu","year":"2007","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4161","DOI":"10.1016\/j.apm.2010.04.013","article-title":"Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control","volume":"34","author":"Chen","year":"2010","journal-title":"Appl. Math Modell."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1016\/j.nonrwa.2010.10.009","article-title":"The sufficient criteria for global synchronization of chaotic power systems under linear state-error feedback control","volume":"12","author":"Lin","year":"2011","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"025007","DOI":"10.1088\/0031-8949\/85\/02\/025007","article-title":"Robust control for a class of chaotic and hyperchaotic systems via linear state feedback","volume":"85","author":"Li","year":"2012","journal-title":"Phys. Scr."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/TLA.2017.7854619","article-title":"Synchronization of chaotic Akgul system by means of feedback linearization and pole placement","volume":"15","author":"Cruz","year":"2017","journal-title":"IEEE Latin Am. Trans."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.chaos.2004.08.009","article-title":"Parameter mismatches, variable delay times and synchronization in time-delayed systems","volume":"25","author":"Shahverdiev","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.chaos.2004.05.023","article-title":"A novel criterion for delayed feedback control of time-delay chaotic systems","volume":"23","author":"Park","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3778","DOI":"10.1016\/j.cnsns.2014.03.031","article-title":"Synchronization of two coupled multimode oscillators with time-delayed feedback","volume":"19","author":"Emelianova","year":"2014","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5679","DOI":"10.1002\/mma.5106","article-title":"Multiswitching dual combination synchronization of time-delay chaotic systems","volume":"41","author":"Khan","year":"2018","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1007\/s12043-018-1546-9","article-title":"Control and synchronisation of a novel seven-dimensional hyperchaotic system with active control","volume":"90","author":"Varan","year":"2018","journal-title":"Pramana"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.arcontrol.2018.03.003","article-title":"Comparative performances of synchronisation between different classes of chaotic systems using three control techniques","volume":"45","author":"Singh","year":"2018","journal-title":"Ann. Rev. Control"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Vaidyanathan, S. (2016). Generalized projective synchronization of vaidyanathan chaotic system via active and adaptive control. Advances and Applications in Nonlinear Control Systems, Springer.","DOI":"10.1007\/978-3-319-30169-3_6"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4024","DOI":"10.1016\/j.ijleo.2016.01.069","article-title":"A new 3D chaotic system: Dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application","volume":"127","author":"Cicek","year":"2016","journal-title":"Optik"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3560","DOI":"10.1109\/TLA.2016.7786335","article-title":"Neural control for synchronization of a chaotic Chua-Chen system","volume":"14","year":"2016","journal-title":"IEEE Latin Am. Trans."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.chaos.2013.08.018","article-title":"Simple chaotic flows with a line equilibrium","volume":"57","author":"Jafari","year":"2013","journal-title":"Chaos Solitons Fractals"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"9111","DOI":"10.1016\/j.ijleo.2016.06.111","article-title":"A chaotic system with infinite equilibria located on a piecewise linear curve","volume":"127","author":"Pham","year":"2016","journal-title":"Optik"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1007\/s11071-016-2968-x","article-title":"Simple chaotic 3D flows with surfaces of equilibria","volume":"86","author":"Jafari","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1007\/s11071-015-2056-7","article-title":"New class of chaotic systems with circular equilibrium","volume":"81","author":"Gotthans","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.9734\/PSIJ\/2017\/38497","article-title":"Realization and implementation of polynomial chaotic sun system","volume":"16","author":"Nwachioma","year":"2017","journal-title":"Phys. Sci. Int. J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"7510","DOI":"10.1109\/ACCESS.2018.2889964","article-title":"A new chaotic oscillator-properties, analog implementation, and secure communication application","volume":"7","author":"Nwachioma","year":"2019","journal-title":"IEEE Access"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1140\/epjp\/i2018-12053-7","article-title":"A novel class of chaotic systems with different shapes of equilibrium and microcontroller-based cost-effective design for digital applications","volume":"133","author":"Rajagopal","year":"2018","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_51","unstructured":"Giakoumis, A.E., Volos, C.K., Stouboulos, I.N., and Kyprianidis, I.K. (2016, January 14\u201317). Implementation of a hyperchaotic system with hidden attractors into a microcontroller. Proceedings of the 20th International Conference on Circuits, Systems, Communications and Computers (CSCC 2016), Corfu Island, Greece."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.chaos.2018.12.030","article-title":"Discrete-time neural synchronization between an Arduino microcontroller and a compact development system using multiscroll chaotic signals","volume":"119","author":"Chiu","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.micpro.2017.10.013","article-title":"Lightweight chaotic image encryption algorithm for real-time embedded system: Implementation and analysis on 32-bit microcontroller","volume":"56","author":"Janakiraman","year":"2018","journal-title":"Microprocess. Microsyst."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.cnsns.2015.03.003","article-title":"FPGA realization of multi-scroll chaotic oscillators","volume":"27","year":"2015","journal-title":"Commun. Nonlinear Sci. Numer. Simulat."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"075217","DOI":"10.1063\/1.5038583","article-title":"FPGA-based implementation of chaotic oscillators by applying the numerical method based on trigonometric polynomials","volume":"8","year":"2018","journal-title":"AIP Adv."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"11786","DOI":"10.1016\/j.ijleo.2016.09.087","article-title":"Electronic circuit design, implementation and FPGA-based realization of a new 3D chaotic system with single equilibrium point","volume":"127","author":"Tuna","year":"2016","journal-title":"Optik"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Muthuswamy, B., and Banerjee, S. (2015). A Route to Chaos Using FPGAs, Springer.","DOI":"10.1007\/978-3-319-18105-9"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/7\/3\/40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:11:55Z","timestamp":1760188315000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/7\/3\/40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,17]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["computation7030040"],"URL":"https:\/\/doi.org\/10.3390\/computation7030040","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2019,8,17]]}}}