Yıl 2019,
, 47 - 53, 31.12.2019
Atike Reza Ahrabi
,
Hamidreza Kobravi
Kaynakça
- [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.
Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback
Yıl 2019,
, 47 - 53, 31.12.2019
Atike Reza Ahrabi
,
Hamidreza Kobravi
Öz
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.
Kaynakça
- [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.