Yıl 2019, Cilt 03 , Sayı 2, Sayfalar 47 - 53 2019-12-31

Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback

Atike REZA AHRABİ [1] , Hamidreza KOBRAVİ [2]


The converting of an unwelcome chaotic behaviour of the brain activity into another chaotic behaviour can result in some disorders and their treatment as an epileptic seizure. Recently in some articles, energy-based feedback control is introduced only as an aim to omit the chaos. In other words, it is used only for anti-control of chaos. But in this study, the capability of changing chaotic dynamics to other ones with a feedback energy-based controller has been demonstrated. The converting of chaos dynamics to another chaos dynamics can be made possible by using energy feedback and Limiting to omit the chaos should not be occurred by using energy feedback. Some practical applications of chaos to chaos controllable related to the emphasis of this issue. A short glance at a well-known Lorenz chaotic system has been indicated that chaos to chaos control will be reachable by combining a self-regulating gain fuzzy system with an energy feedback control, as well.
Hamilton energy, Chaos control, Fuzzy logic system
  • [1] J. Ma, F. Wu, W. Jin, P. Zhou, T. Hayat, Calculation of Hamilton energy and control of dynamical systems with different types of attractors, Chaos, 27 (2017) 1-9. doi:10.1063/j.chaos. 2017.01.17.
  • [2] C. Barbara, C. Silvano, Hyperchaotic behavior of two bidirectional Chua’s circuits, Chaos, 27 (2002) 625–637. doi: 10.1002/cta.213 / Circuit Theory Appl. 2002.04.24.
  • [3] G. Grassi, S. Mascolo, Synchronizing high dimensional chaotic systems via eigenvalue placement with application to cellular neural networks, Int. J. Bifurc. Chaos. 9 (1999) 705–711. doi: 10.1142/S0218127499000493 / Chaos. 1999.01.04.
  • [4] R. Vicente, J. Daudén and R. Toral, Analysis and characterization of the hyperchaos generated by a semiconductor laser subject, IEEE. 41 (2005) 541–548. doi: 10.1109/JQE.2005.843606 / Quantum Electron. 2005.03.24.
  • [5] Shaohua Luo, Quanping Sun, and Wei Cheng, Chaos control of the micro-electro-mechanical resonator by using adaptive dynamic surface technology with extended state observer, AIP, 6 (2016) 5019. Doi: 10.1063/1.4946785/ AIP Advances. 2016.05.12
  • [6] P. Sriramalakshmi, A. Kavitha, P. Sanjeevikumar, Tole Sutikno, Pandav Kiran Maroti, Vigna K. Ramachandaramurthy, Control of Chaos in a Current Mode Controlled Buck Boost Converter Using Weak Periodic Perturbation Method, IJPEDS, 8(2017) 1467-1480. Doi: 10.11591/ijpeds.v8i4.pp1467-1480/ Power Electronics and Drive System. 2017.06.04
  • [7] M Fuhong, W Yaoda, G Peng, W Enrong, and J A. Auth, Bifurcations, chaos and adaptive backstepping sliding mode control of a power system with excitation limitation, AIP, 6(2016) 21. Doi: 10.1063/1.4961696/ AIP Advances/ 2016/08/12
  • [8] P Singh, M Kshetrimayum, B Roy, Chaos control in biological system using recursive backstepping sliding mode control, EPJST, 21 (2018) 731-746. Doi: 10.1140/epjst/e2018-800023-6/ 2018.07.18
  • [9] S Mobayen, F Tchier, Synchronization of a class of uncertain chaotic systems with Lipschitz nonlinearities using state-feedback control design: a matrix inequality approach, AJOF, 24(2018) 1-15/ doi: 10.1002/asjc.1512/ Asian Journal of Control. 2018.01.15
  • [10] A. N. Njah, V Uchechukwu, Control and synchronization of chaos in nonlinear gyros via backstepping design, JNS, 5(2008) 11-19/ doi: 10.1002/asjc.1512/ Nonlinear Science. 2008.08.05
  • [11] L Runzi, S Haipeng, Z Yanhui Zeng, Chaos Control and Synchronization via Switched Output Control Strategy, HINDAWI, 27 (2017) 1-11. doi: 10.1155/2017/6125102 / Complixity. 2017.11.03.
  • [12] C Wang, H Zhang, W Fan, M Ping, Adaptive control method for chaotic power systems based on finite-time stability theory and passivity-based control approach, Elsevier, 112 (2018) 159-167. 1doi: 0.1016/j.chaos.2018.05.005
  • [13] R Pérez, J Moreno, A novel Lyapunov-based trajectory tracking controller for a quadrotor: Experimental analysis by using two motion tasks, ELSEVIER, 61(2019)58-68, doi:10.1016/j.mechatronics.2019.05.006 / Decision and Control. 2019.11.04.
  • [14] C. Aguilar, J. Moreno, Model reference adaptive control for the trajectory tracking of a DC motor with pendular load, IASTED, 13(2013) 266-272 / doi: 10.2316/P.2013.807-038 / Intelligent Systems and Control. 2013.09.13.
  • [15] X Xiaojian, S Mobayen, H Ren, S Jafari, Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control, VIB, 24(2017) 3842-3854/ doi: 10.1177/1077546317713532/ Vibration and Control. 2017.05.06
  • [16] R Song, Q Wei, Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances, Elsevier, 26 (2017) 73-89 .doi: 10.1088/1674-1056/26/3/030505/ Chinese Physical Society.2017.05.05
  • [17] J Moreno, Lyapunov function-based adaptive chaos anti control of robot manipulators, IEEE, 23(2014) 41-53, doi: 10.1109/ISIE.2014.6864788/ International Symposium on Industrial Electronics. 2014.07.28.
  • [18] H. Zargarzadeh, M.R. Jahed Motlagh, Anti–control of chaos in rigid motion using an internal torque source, IFAC, 23(2009) 349-353, doi: 10.3182/20090622-3-UK-3004.00065/ Analysis and Control of Chaotic Systems. 2009.05.20.
  • [19] J. Moreno, Model reference adaptive control for the trajectory tracking of a DC motor with pendular load, IASTED, 18(2013)1-11 / doi: 10.1016/j.cnsns.2012.06.003/ Communications in Nonlinear Science and Numerical Simulation. 2013.01.23.
  • [20] Y Xinghuo, C Guanrong, S Yanxing, C Zhenwei, X Yang, A generalized OGY method for controlling higher order chaotic systems, IEEE, 39 (2002) 21-33, Doi: 10.1080/10260220290013507/ Decision and Control. 2002.04.01.
  • [21] J. Ma, F. Wu, W. Jin, P. Zhou, T. Hayat, Calculation of Hamilton energy and control of dynamical systems with different types of attractors, Chaos, 27 (2017) 1-9. doi:10.1063/j.chaos. 2017.01.17
  • [22] Sarasola C, Torrealdea FJ, D'Anjou A, Mouj-ahid A, Graña M, Ping Zhou and Tasawar H, Energy balance in feedback synchronization of chaotic systems, Physical Review. 69 (2004) 11606–116019. doi: 10.1103/PhysRevE. 2004.7.30.
  • [23] H.Kobravi, A.Erfanian, A decentralized adaptive robust method for chaos control, Chaos,19 (2009) 1-9. doi: 10.1063/1.3183806/ Chaos. 2009.04.27
  • [24] S Lashkari, A Sheikhani, M Hashemi Golpayegan, A Moghimi, H Kobravi, Detection and Prediction of Absence Seizures Based on Nonlinear Analysis of the EEG in Wag/Rij Animal Model, Int Clin Neurosci, 5 (2018) 21-27. doi: 10.15171/j. Int Clin Neurosci 2018.03.15.
  • [25] K Lehnertz, CE Elger, Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity, Physical Review Letter, 95 (1998) 5019. doi: 10.1103/PhysRevLett.1998.06.12.
  • [26] K Lehnertz, CE Elger, Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss, Electroencephalography and Clinical Neurophysiology, 80 (1995) 108-17. doi: 10.1103/ clinical Neurophysiology.1995.01.05.
  • [27] A.M. Lopez Jimineza, C. Camacho Martinez Vara De Rey, A.R. Garcia Toress, Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series, Discrete Dynamics in Nature and Society,7 (2002) 41-53, doi: 10.1080/10260220290013507/ Dynamics in Nature. 2002.04.21.
Birincil Dil en
Konular Matematik
Yayınlanma Tarihi Aralık
Bölüm Articles
Yazarlar

Orcid: 0000-0002-8889-3290
Yazar: Atike REZA AHRABİ (Sorumlu Yazar)
Kurum: IAUM
Ülke: Iran


Yazar: Hamidreza KOBRAVİ
Kurum: Islamic Azad University
Ülke: Iran


Tarihler

Yayımlanma Tarihi : 31 Aralık 2019

Bibtex @araştırma makalesi { forecasting653493, journal = {Turkish Journal of Forecasting}, issn = {}, eissn = {2618-6594}, address = {Giresun Üniversitesi Fen Edebiyat Fakültesi İstatistik Bölümü, Güre Yerleşkesi, 28100 Merkez, Giresun}, publisher = {Giresun Üniversitesi}, year = {2019}, volume = {03}, pages = {47 - 53}, doi = {10.34110/forecasting.653493}, title = {Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback}, key = {cite}, author = {Reza Ahrabi̇, Atike and Kobravi̇, Hamidreza} }
APA Reza Ahrabi̇, A , Kobravi̇, H . (2019). Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback . Turkish Journal of Forecasting , 03 (2) , 47-53 . DOI: 10.34110/forecasting.653493
MLA Reza Ahrabi̇, A , Kobravi̇, H . "Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback" . Turkish Journal of Forecasting 03 (2019 ): 47-53 <https://dergipark.org.tr/tr/pub/forecasting/issue/51702/653493>
Chicago Reza Ahrabi̇, A , Kobravi̇, H . "Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback". Turkish Journal of Forecasting 03 (2019 ): 47-53
RIS TY - JOUR T1 - Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback AU - Atike Reza Ahrabi̇ , Hamidreza Kobravi̇ Y1 - 2019 PY - 2019 N1 - doi: 10.34110/forecasting.653493 DO - 10.34110/forecasting.653493 T2 - Turkish Journal of Forecasting JF - Journal JO - JOR SP - 47 EP - 53 VL - 03 IS - 2 SN - -2618-6594 M3 - doi: 10.34110/forecasting.653493 UR - https://doi.org/10.34110/forecasting.653493 Y2 - 2019 ER -
EndNote %0 Turkish Journal of Forecasting Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback %A Atike Reza Ahrabi̇ , Hamidreza Kobravi̇ %T Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback %D 2019 %J Turkish Journal of Forecasting %P -2618-6594 %V 03 %N 2 %R doi: 10.34110/forecasting.653493 %U 10.34110/forecasting.653493
ISNAD Reza Ahrabi̇, Atike , Kobravi̇, Hamidreza . "Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback". Turkish Journal of Forecasting 03 / 2 (Aralık 2020): 47-53 . https://doi.org/10.34110/forecasting.653493
AMA Reza Ahrabi̇ A , Kobravi̇ H . Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback. TJF. 2019; 03(2): 47-53.
Vancouver Reza Ahrabi̇ A , Kobravi̇ H . Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback. Turkish Journal of Forecasting. 2019; 03(2): 47-53.