Exponential stabilization for a class of nonlinear parabolic PDE systems via fuzzy control approach

IEEE Transactions on Fuzzy Systems

Volumn 20, Issue 2, 2012, Pages 318-329

  Wu, Huai Ning ^a   Wang, Jun Wei ^a   Li, Han Xiong ^b  

^a BEIHANG UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Exponential stability; fuzzy control; linear matrix inequalities (LMIs); spatially distributed processes; Takagi Sugeno (T S) fuzzy model

Indexed keywords

CLOSED-LOOP; CONTROL APPROACH; CONTROL TECHNIQUES; DECAY RATE; DESIGN METHOD; EXPONENTIAL STABILIZATION; EXPONENTIALLY STABLE; FINITE NUMBER; FUZZY CONTROL DESIGNS; FUZZY STATE FEEDBACK CONTROLLERS; LINEAR MATRIX INEQUALITY (LMIS); LINEAR MATRIX INEQUALITY OPTIMIZATIONS; LYAPUNOV TECHNIQUES; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS; PARABOLIC PDES; RECURSIVE ALGORITHMS; SEMI-LINEAR PARABOLIC PDE; SEMILINEAR; SPATIALLY DISTRIBUTED PROCESS; T-S FUZZY; T-S FUZZY MODELS; TAKAGI SUGENO FUZZY MODELS; TAKAGI-SUGENO; TEMPERATURE PROFILE CONTROL;

ASYMPTOTIC STABILITY; DECAY (ORGANIC); FUZZY CONTROL; NONLINEAR CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; SPATIAL DISTRIBUTION; STABILIZATION; STATE FEEDBACK;

LINEAR MATRIX INEQUALITIES;

EID: 84859712922     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2011.2173694     Document Type: Article

References (52)

1. W. H. Ray, Advanced Process Control. New York:McGraw-Hill, 1981.
2. M. J. Balas, "Feedback control of linear diffusion processes," Int. J. Control, vol. 29, no. 3, pp. 523-534, 1979.
3. R. F. Curtain, "Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input," IEEE Trans. Automat. Control, vol. AC-27, no. 1, pp. 98-104, Feb. 1982.
4. M. J. Balas, "The Galerkin method and feedback control of linear distributed parameter systems," J. Math. Anal. Appl., vol. 91, no. 2, pp. 527-546, 1983.
5. M. J. Balas, "Reduced-order feedback control of distributed parameter systems via singular perturbation methods," J. Math. Anal. Appl., vol. 87, no. 1, pp. 281-294, 1982.
6. S. Dubljevic and P. D. Christofides, "Predictive control of parabolic PDEs with boundary control actuation," Comput. Chem. Eng., vol. 61, no. 18, pp. 6239-6248, 2006. (Pubitemid 44107900)
7. P. D. Christofides, Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes. Boston, MA: Birkḧauser, 2001.
8. S. Dubljevic, P. D. Christofides, and I. G. Kevrekidis, "Distributed nonlinear control of diffusion-reaction processes," Int. J. Robust Nonlinear Control, vol. 14, no. 2, pp. 133-156, 2004.
9. G. Hagen and I. Mezic, "Spillover stabilization in finite-dimensional control and observer design for dissipative evolution equations," SIAM J. Control Optim., vol. 42, no. 2, pp. 746-768, 2003.
10. M. J. Balas, "Feedback control of flexible systems," IEEE Trans. Automat. Control, vol. AC-23, no. 4, pp. 673-679, Aug. 1978.
11. M. A. Demetriou, "Model reference adaptive control of slowly timevarying parabolic distributed parameter systems," in Proc. 33rd Conf. Decision Control, Lake Buena Vista, FL, Dec. 14-16, 1994, pp. 775-780.
12. B. Bamieh, F. Paganini, and M. A. Dahleh, "Distributed control of spatially invariant systems," IEEE Trans. Automat. Control, vol. 47, no. 7, pp. 1091-1107, Jul. 2002. (Pubitemid 34835332)
13. Y. Orlov and D. Dochain, "Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor," IEEE Trans. Automat. Control, vol. 47, no. 8, pp. 1293-1304, Aug. 2002. (Pubitemid 34959762)
14. G. Hagen, I. Mezic, and B. Bamieh, "Distributed control design for parabolic evolution equations: Application to compressor stall control," IEEE Trans. Automat. Control, vol. 49, no. 8, pp. 1247-1258, Aug. 2004.
15. W. J. Liu, "Boundary feedback stabilization of an unstable heat equation," SIAM J. Control Optim., vol. 42, no. 3, pp. 1033-1043, 2003.
16. E. Fridman and Y. Orlov, "An LMI approach to H∞ boundary control of semilinear parabolic and hyperbolic systems," Automatica, vol. 45, no. 9, pp. 2060-2066, 2009.
17. A. Smyshlyaev and M. Krstic, Adaptive Control of Parabolic PDEs. Princeton, NJ: Princeton Univ. Press, 2010.
18. 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, Feb. 1985.
19. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001.
20. G. Feng, Analysis and Synthesis of Fuzzy Control Systems: AModel Based Approach. Boca Raton, FL: CRC, 2010.
21. H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, "Parameterized linear matrix inequality techniques in fuzzy control system design," IEEE Trans. Fuzzy Syst., vol. 9, no. 2, pp. 324-332, Apr. 2001. (Pubitemid 32505588)
22. K. Tanaka, T. Hori, and H. O. Wang, "A multiple Lyapunov function approach to stabilization of fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 582-589, Aug. 2003.
23. T. M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form," Automatica, vol. 40, no. 5, pp. 823-829, 2004.
24. B. Chen, X. P. Liu, and S. C. Tong, "Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay," Fuzzy Sets Syst., vol. 157, no. 16, pp. 2224-2240, 2006. (Pubitemid 44080319)
25. B.Yang, D.Yu,G. Feng, and C. Chen, "Stabilisation of a class of nonlinear continuous time systems by a fuzzy control approach," Proc. Inst. Elect. Eng., Control Theory Appl., vol. 153, no. 4, pp. 427-436, 2006. (Pubitemid 43781896)
26. H. Gao and T. Chen, "Stabilization of nonlinear systems under variable sampling: A fuzzy control approach," IEEE Trans. Fuzzy Syst., vol. 15, no. 5, pp. 972-983, Oct. 2007. (Pubitemid 47578002)
27. H. G. Zhang, Y. Wang, and D. Liu, "Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays," IEEE Trans. Syst.,Man, Cybern. B, vol. 38, no. 1, pp. 126-140, Feb. 2008. (Pubitemid 351285020)
28. D. Yue, E. Tian, Y. Zhang, and C. Peng, "Delay-distributed-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay," IEEE Trans. Syst., Man, Cybern. B, vol. 39, no. 2, pp. 503-516, Apr. 2009.
29. K. Zhang, B. Jiang, andM. Staroswiecki, "Dynamic output feedback-fault tolerant controller design for Takagi-Sugeno fuzzy systems with actuator faults," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 194-201, Feb. 2010.
30. D. H. Lee, J. B. Park, and Y. H. Joo, "Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems: Multipleparameterization approach," IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 425-429, Apr. 2010.
31. H. K. Lam, "LMI-based stability analysis for fuzzy-model-based control systems using artificial T-S fuzzy model," IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 505-513, Jun. 2011.
32. E. Tian, D. Yue, T. C. Yang, Z. Gu, and G. Liu, "T-S fuzzy modelbased robust stabilization for networked control systemswith probabilistic sensor and actuator failure," IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 553-561, Jun. 2011.
33. H.-N. Wu and H.-X. Li, "Finite-dimensional constrained fuzzy control of a class of nonlinear distributed process systems," IEEE Trans. Syst.,Man, Cybern. B, vol. 37, no. 5, pp. 1422-1430, Oct. 2007. (Pubitemid 47534606)
34. H.-N. Wu and H.-X. Li, "H∞ fuzzy observer-based control for a class of nonlinear distributed parameter systems with control constraints," IEEE Trans. Fuzzy Syst., vol. 16, no. 2, pp. 502-516, Apr. 2008. (Pubitemid 351586048)
35. B.-S. Chen and Y.-T. Chang, "Fuzzy state-space modeling and robust observer-based control design for nonlinear partial differential systems," IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 1025-1043, Oct. 2009.
36. H. K. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
37. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
38. P. Gahinet, A. Nemirovskii, A. J. Laub, and M. Chilali, LMI Control Toolbox for Use With MATLAB. Natick, MA: The MathWorks Inc., 1995.
39. J.-W. Wang, H.-N. Wu, and H.-X. Li, "Distributed fuzzy control design of nonlinear hyperbolic PDE systems with application to nonisothermal plug-flow reactor," IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 514-526, Jun. 2011.
40. J. Robinson, Infinite-Dimensional Dynamical Systems. Cambridge, UK: Cambridge Univ. Press, 2001.
41. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. New York: Springer-Verlag, 1983.
42. R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory. New York: Springer-Verlag, 1995.
43. J. Smoller, Shock Waves and Reaction-Diffusion Equations. Berlin, Germany: Springer-Verlag, 1983.
44. C. Ho andY. Tai, "REVIEW:MEMSand its applications for flowcontrol," ASME J. Fluid Eng., vol. 118, no. 3, pp. 437-447, 1996.
45. H. T. Banks, R. S. Smith, and Y. Wang, Smart Material Structures: Modeling, Estimation and Control. New York: Wiley, 1996.
46. J. Wolff, A. G. Papathanasiou, H. H. Rotermund, G. Ertl, X. Li, and I. G. Kevrekidis, "Local manipulation of catalytic surface reactivity," J. Catal., vol. 216, no. 1-2, pp. 246-256, 2003.
47. T. X. Wang, "Stability in abstract functional-differential equations. II. Applications," J. Math. Anal. Appl., vol. 186, no. 3, pp. 835-861, 1994.
48. K. M. Abadir and J. R. Magnus, Matrix Algebra. Cambridge, U.K.: Cambridge Univ. Press, 2005.
49. E. D. Sontag, "A universal construction of Artstein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, no. 2, pp. 117-123, 1989.
50. S. G. Krantz and H. R. Parks, The Implicit Function Theorem: History, Theory, and Application. Boston, MA: Birkḧauser, 2002.
51. U. Shaked and V. Suplin, "A new bounded real lemma representation for the continuous-time case," IEEE Trans. Automat. Control, vol. 46, no. 9, pp. 1420-1426, Sep. 2001. (Pubitemid 32981646)
52. R. L. Burden and J. D. Faires, Numerical Analysis, 7th ed. New York: Brooks/Cole, 2000.