Simulation and Control of Turbulence at Tokamaks with Artificial Intelligence Methods
Danilo Rastovic
Control Systems Group, Zagreb, Croatia.
DOI: 10.4236/jmp.2012.312234   PDF    HTML     4,785 Downloads   9,168 Views   Citations

Abstract

The control of turbulence at tokamaks is very complex problem.The idea is to apply the fuzzy Markovian processes and fuzzy Brownian motions as good approximation of general robust drift kinetic equation. It is obtained by using the artificial neural networks for solving of appropriate advanced control problem. The proof of the appropriate theorem is shown.

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D. Rastovic, "Simulation and Control of Turbulence at Tokamaks with Artificial Intelligence Methods," Journal of Modern Physics, Vol. 3 No. 12, 2012, pp. 1858-1869. doi: 10.4236/jmp.2012.312234.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] G. Zaslavsky, R. Z. Sagdeev, D. A. Usikov and A. A. Chernikov, “Weak Chaos and Quasi-Regular Patterns,” Cambridge University Press, Cambridge, 1991. doi:10.1017/CBO9780511599996
[2] X. Gao, S. Zhong and F. Gao, “Exponential Synchronization of Neural Networks with Time-Varying Delays,” Nonlinear Analysis, Vol. 71, No. 5, 2009, pp. 2003-2011. doi:10.1016/j.na.2009.01.243
[3] X. D. Li, “Existence and Global Exponential Stability of Periodic Solution for Delayed Neural Networks with Impulsive and Stochastic Effects,” Neurocomputing, Vol. 73, No. 4-6, 2010, pp. 749-758. doi:10.1016/j.neucom.2009.10.016
[4] L. Frassinetti, K. E. J. Olofsson, P. R. Brunsell and J. R. Drake, “Resonant Magnetic Perturbation Effect on Tearing Mode Dynamics,” Nuclear Fusion, Vol. 50, No. 3, 2010, Article ID: 035005. doi:10.1088/0029-5515/50/3/035005
[5] E. Minardi, “Thermodynamics of High Temperature Plasmas,” Entropy, Vol. 11, No. 1, 2009, pp. 124-221. doi:10.3390/e11010124
[6] E. Schuster, J. Dalessio, M. L. Walker, Y. In and J. S. Kim, “Extending the RWM Stability Region by Optimal Feedback Control,” 47th IEEE Conference on Decision and Control, Cancun, 9-11 December 2008, pp. 3145-3150.
[7] X. Garbet, Y. Idomura, L. Villard and T. H. Watanabe, “Gyrokinetic Simulations of Turbulent Transport,” Nuclear Fusion, Vol. 50, No. 4, 2010, Article ID: 043002. doi:10.1088/0029-5515/50/4/043002
[8] G. Van Oost, V. V. Bulanin, A. J. H. Donne, et al., “Multi-Machine Studies of the Role of Turbulence and Electric Fields in the Establishment of Improved Confinement in Tokamak Plasmas,” Plasma Physics and Controlled Fusion, Vol. 49, 2007, pp. A29-A44. doi:10.1088/0741-3335/49/5A/S03
[9] B. P. Milligen, B. A. Carreras, V. Antono, et al., “Long-Range Correlation Analysis of Plasma Turbulence,” 26th EPS Conference on Controlled Fusion and Plasma Physics, Vol. 23J, 1999, pp. 49-52.
[10] D. Rastovic, “Fixed Point Theorem and Infinite Fuzzy Logic Controllers,” Cybernetica, Vol. 39, No. 1, 1996, pp. 49-51.
[11] H. Emamirad, “Scattering Theory for Linearized Boltzmann Equation,” Transport Theory and Statistical Physics, Vol. 16, 1987, pp. 503-528. doi:10.1080/00411458708204304
[12] D. Rastovic, “Feedback Stabilization of Some Classes of Nonlinear Transport Systems,” Rendiconti del Circolo Matematico di Palermo, Vol. 51, No. 2, 2002, pp. 325-332. doi:10.1007/BF02871658
[13] D. Rastovic, “Vlasov-Poisson-Fokker-Planck Equations and Stabilization System,” Analele Universitatii de Vest din Timisoara, Vol. 42, No. 1, 2004, pp. 141-148.
[14] C. S. Rodrigues, A. P. S. Moura and C. Grebogi, “Random Fluctuation Leads to Forbidden Escape of Particles,” Physical Review E, Vol. 82, No. 2, 2010, Article ID: 026211. doi:10.1103/PhysRevE.82.026211
[15] D. Rastovic, “A Note on Stability Properties of Integrated Semigroups,” Acta Mathematica et Informatica Universitatis Ostraviensis, Vol. 3, No. 1, 1995, pp. 61-65.
[16] Y. Sarazin, V. Grandgirard, J. Abiteboul, et al., “Large Scale Dynamics in Flux Driven Gyrokinetic Turbulence,” Nuclear Fusion, Vol. 50, No. 5, 2010, Article ID: 054004. doi:10.1088/0029-5515/50/5/054004
[17] G. A. Ratta, J. Vega, A. Murari, et al., “An Advanced Disruption Predictor for JET Tested in a Simulated Real-Time Environment,” Nuclear Fusion, Vol. 50, No. 5, 2010, Article ID: 025005.
[18] D. Rastovic, “Fractional Fokker-Planck and Artificial Neural Networks,” Journal of Fusion Energy, Vol. 27, No. 3, 2008, pp. 182-187. doi:10.1007/s10894-007-9127-9
[19] K. C. Shaing, “Toroidal Momentum Confinement in Neoclassical Quasilinear Theory in Tokamaks,” Physics of Plasmas, Vol. 8, No. 1, 2001, pp. 193-200. doi:10.1063/1.1332986
[20] D. Yu and U. Parlitz, “Inferring Local Dynamics and Connectivity of Spatially Extended Systems with Long-Range Links Based on Steady-State Stabilization,” Physical Review E, Vol. 82, No. 2, 2010, Article ID: 026108.
[21] C. Bernardin and C. Landim, “Entropy of Stationary Nonequilibrium Measures of Boundary Driven Symmetric Simple Exclusion Processes,” Journal of Statistical Physics, Vol. 141, No. 6, 2010, pp. 1014-1038. doi:10.1007/s10955-010-0082-x
[22] C.-G. Liu and S.-J. Qian, “Poloidal Flow Destabilized by Electron Cyclotron Resonant Heating in Collision Tokamak Plasmas,” Chinese Physics Letters, Vol. 15, No. 1, 1998, p. 35. doi:10.1088/0256-307X/15/1/014
[23] R. L. Dewar, M. J. Hole, M. Mc Gann, et al., “Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles,” Entropy, Vol. 10, No. 4, 2008, pp. 621-634. doi:10.3390/e10040621
[24] D. Rastovic, “Fractional Variational Problems and Particle in Cell Gyrokinetic Simulations with Fuzzy Logic Approach for Tokamaks,” Nuclear Technology & Radiation Protection, Vol. 24, No. 2, 2009, pp. 138-144. doi:10.2298/NTRP0902138R
[25] D. Rastovic, “Optimal Control of Tokamak and Stellarator Plasma Behaviour,” Chaos, Solitons & Fractals, Vol. 32, No. 2, 2007, pp. 676-681. doi:10.1016/j.chaos.2005.11.016
[26] D. Rastovic, “Fuzzy Scaling and Stability of Tokamaks,” Journal of Fusion Energy, Vol. 28, No. 1, 2009, pp. 101-106. doi:10.1007/s10894-008-9154-1
[27] D. Rastovic, “Targeting and Synchronization at Tokamak with Recurrent Artificial Neural Networks,” Neural Computing & Applications, Vol. 21, No. 5, 2012, pp. 1065-1069. doi:10.1007/s00521-011-0527-4
[28] K. Wang and Z. D. Teng and H. J. Jiang, “Global Exponential Synchronization in Delayed Reaction-Diffusion Cellular Neural Networks with the Dirichlet Boundary Conditions,” Mathematical and Computer Modelling, Vol. 52, No. 1-2, 2010, pp. 12-24. doi:10.1016/j.mcm.2009.05.038
[29] D. Rastovic, “Applications of Artificial Intelligence and Multi-Variable Control of Chaos on Tokamak Equilibriums,” In: Glow Discharges and Tokamaks, Nova Science Publishers, Inc., 2011, pp. 407-418.
[30] M. Camplani, B. Cannas, A. Fanni, et al., “Tracking of the Plasma States in a Nuclear Fusion Device Using SOMs,” Neural Computing & Applications, Vol. 43, 2009, pp. 430-437.

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