Fuzzy solutions to partial differential equations: Adaptive approach

IEEE Transactions on Fuzzy Systems

Volumn 17, Issue 1, 2009, Pages 116-127

  Chen, Yung Yue ^a   Chang, Yu Te ^a   Chen, Bor Sen ^a  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Adaptive fuzzy algorithm; Finite element method; Fuzzy approximation; Partial differential equation (PDE)

Indexed keywords

ADAPTIVE ALGORITHMS; AIRCRAFT ENGINES; APPROXIMATION ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; FUZZY LOGIC; FUZZY SETS; IMAGE SEGMENTATION; REAL TIME SYSTEMS;

ADAPTIVE APPROACHES; ADAPTIVE FUZZY ALGORITHM; ADAPTIVE LAWS; ADAPTIVE SCHEMES; ADJUSTABLE PARAMETERS; DESIGN OBJECTIVES; ENERGY PERSPECTIVES; ERROR BOUNDS; ERROR EQUATIONS; ERROR FUNCTIONS; EXACT SOLUTIONS; FREE PARAMETERS; FUZZY APPROXIMATION; FUZZY LOGIC SYSTEMS; MESH POINTS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 60549112223     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2008.2005010     Document Type: Article

References (29)

1. A. Kharab and R. Kharab, "Spreadsheet solution of hyperbolic partial differential equation," IEEE Trans. Educ., vol. 40, no. 1, pp. 103-110, Feb. 1997.
2. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing. Pacific Grove, CA: Brooks/Cole, 1991.
3. O. Bíró and K. Preis, "Finite element analysis of 3-D eddy currents," IEEE Trans. Magn., vol. 26, no. 2, pp. 418-423, Mar. 1990.
4. B. H. McDonald and A. Wexler, "Finite-element solution of unbounded field problems," IEEE Trans. Microw. Theory Tech., vol. MIT-20, no. 12, pp. 841-847, Dec. 1972.
5. S. Gratkowski, L. Pichon, and A. Razek, "New infinite elements for a finite element analysis of 2-D scattering problems," IEEE Trans. Magn., vol. 32, no. 3, pp. 882-885, May 1996.
6. H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, Feb. 1996.
7. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst. Man, Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan. 1985.
8. ∞ control theory, and linear matrix inequalities," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 1-13, Feb. 1996.
9. J.-S.R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence Upper saddle River, NJ: Prentice-Hall, 1997.
10. B. Kosko, Fuzzy Engineering. Upper saddle River, NJ: Prentice-Hall, 1997.
11. B. S. Chen, C. T. Tseng, and H. J. Uang, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 571-585, Oct. 1999.
12. ∞ tracking design of uncertain nonlinear SISO systems: Adaptive fuzzy approach," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 32-43, Feb. 1996.
13. S. P. Banks, Control Systems Engineering: Modelling and Simulation, Control Theory, and Microprocessor Implementation. Upper Saddle River, NJ: Prentice-Hall, 1986.
14. T. Leephakpreeda, "Novel determination of differential-equation solutions: Universal approximation method," J. Comput. Appl. Math. vol. 146, pp. 443-457, 2002.
15. R. Fletcher, Practical Methods of Optimization, 2nd ed. New York: Wiley, 1987.
16. G. Rudolph, "Convergence analysis of canonical genetic algorithms," IEEE Trans. Neural Netw., vol. 5, no. 1, pp. 96-101, Jan. 1994.
17. H. G. Kaper and M. Garbey, Asymptotic Analysis and the Numerical Solution of Partial Differential Equations. New York: Marcel Dekker, 1991.
18. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 4th ed. vol. 1, New York: McGraw-Hill, 1989.
19. D. H. Norrie and G. de Vries, An Introduction to Finite Element Analysis. New York: Academic, 1978.
20. T. M. Apostol, Mathematical Analysis. Reading, MA: Addison-Wesley, 1974.
21. S. Saatry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness. Englewood Cliffs, NJ: Prentice-Hall, 1989.
22. J. J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
23. S. H. Zak, Systems and Control. Oxford, U.K.: Oxford Univ. Press, 2003.
24. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001.
25. T.-H. S. Li and K.-J. Lin, "Composite fuzzy control of nonlinear singularly perturbed systems," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 176-187, Apr. 2007.
26. C. S. Tseng, "Robust fuzzy filter design for a class of nonlinear stochastic systems," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 261-274, Apr. 2007.
27. A. Shmilovici and O. Maimon, "On the solution of differential equations with fuzzy spline wavelets," Fuzzy Sets Syst., vol. 96, pp. 77-99, 1998.
28. I. Perfilieva, "Fuzzy transforms theory and applications," Fuzzy Sets Syst., vol. 157, pp. 993-1023, 2006.
29. M. Stepnicka and R. Valasek, "Numerical Solution of PDE with help of fuzzy transform," in Proc. 14th IEEE Int. Conf. Fuzzy Syst., May 25, 2005, pp. 1104-1109.