Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: A model study

Chaos

Volumn 15, Issue 3, 2005, Pages

  Brandt Pollmann, U ^a   Lebiedz, D ^a   Diehl, M ^a   Sager, S ^a   Schloder J ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31144459859     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1955387     Document Type: Article

References (58)

1. I. Kiss and J. Hudson, AIChE J. 49, 2234 (2003).
2. S. Qin and T. Badgwell, in Nonlinear Model Predictive Control: Theory and Application, edited by, B. Kouvaritakis, and, M. Cannon, (The Institute of Electrical Engineers, London, 2001), pp. 3-32.
3. M. Henson, Comput. Chem. Eng. 23, 187 (1998).
4. D. Mayne, J. Rawlings, C. Rao, and P. Scokaert, Automatica 26, 789 (2000).
5. L. Biegler, in Nonlinear Predictive Control, edited by, F. Allgöwer, and, A. Zheng, (Birkhäuser, Basel, 2000), Vol. 26 of Progress in Systems Theory, pp. 219-244.
6. D. Leineweber, A. Schäfer, H. Bock, and J. Schlöder, Comput. Chem. Eng. 27, 167 (2003).
7. H. Bock, M. Diehl, D. Leineweber, and J. Schlöder, in Nonlinear Predictive Control, edited by, F. Allgöwer, and, A. Zheng, (Birkhäuser, Basel, 2000), Vol. 26 of Progress in Systems Theory, pp. 246-267.
8. M. Diehl, H. Bock, J. Schlöder, R. Findeisen, Z. Nagy, and F. Allgöwer, J. Process Control 12, 577 (2002).
9. M. Diehl, Real-Time Optimization for Large Scale Nonlinear Processes, Vol. 920 of Fortschr.-Ber. VDI Reihe 8, MeΒ-, Steuerungs- und Regelungstechnik (VDI Verlag, Düsseldorf, 2002), download also at: http://www.ub.uni-heidelberg.de/archiv/1659/.
10. M. Diehl, R. Findeisen, S. Schwarzkopf, I. Uslu, F. Allgöwer, H. Bock, E. Gilles, and J. Schlöder, Automatisierungstechnik 50, 557 (2002).
11. D. Lebiedz and U. Brandt-Pollmann, Phys. Rev. Lett. 91, 208301 (2003).
12. D. Lebiedz and U. Brandt-Pollmann, Chaos 15, 023901 (2005).
13. H. Bock and K. Plitt, in Proc. 9th IFAC World Congress Budapest (Pergamon Press, Budapest, 1984).
14. D. Leineweber, Efficient Reduced SQP Methods for the Optimization of Chemical Processes Described by Large Sparse DAE Models, Vol. 613 of Fortschr.-Ber. VDI Reihe 3, Verfahrenstechnik (VDI Verlag, Düsseldorf, 1999).
15. M. Diehl, I. Uslu, R. Findeisen, S. Schwarzkopf, F. Allgöwer, H. Bock, T. Bürner, E. Gilles, A. Kienle, J. Schlöder, et al., in Online Optimization of Large Scale Systems: State of the Art, edited by, M. Grötschel, S. O. Krumke, and, J. Rambau, (Springer, Berlin, Heidelberg, 2001), pp. 363-384.
16. M. Diehl, R. Findeisen, S. Schwarzkopf, I. Uslu, F. Allgöwer, H. Bock, E. Gilles, and J. Schlöder, Automatisierungstechnik 51, 22 (2003).
17. P. Ball, The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, Oxford, 1998).
18. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).
19. D. Walgraef, Spatio-Temporal Pattern Formation, With Examples from Physics, Chemistry, and Materials Science (Springer-Verlag, New York, 1996).
20. J. Wolff, A. Papathanasiou, I. Kevrekidis, H. Rotermund, and G. Ertl, Science 294, 134 (2001).
21. M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. Mikhailov, H. Rotermund, and G. Ertl, Science 292, 1357 (2001).
22. T. Shinbrot, C. Grebogi, E. Ott, and J. Yorke, Nature (London) 363, 411 (1993).
23. T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, Science 296, 2009 (2002).
24. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Faraday Discuss. 120, 383 (2001).
25. V. Vanag, L. Yang, M. Dolnik, A. Zhabotinsky, and I. Epstein, Nature (London) 406, 389 (2000).
26. S. Sinha and N. Gupte, Phys. Rev. E 58, R5221 (1998).
27. S. Sinha and N. Gupte, Phys. Rev. E 64, 015203 (R) (2001).
28. G. Osipov, B. Shulgin, and J. Collins, Phys. Rev. E 58, 6955 (1998).
29. J. Xiao, G. H. Gu, and J. Gao, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 655 (2000).
30. A. Pertsov, J. Davidenko, R. Salomonsz, W. Baxter, and J. Jalife, Circ. Res. 72, 631 (1993).
31. R. Martin, G.-L. Oppo, G. Harkness, A. Scroggie, and W. Firth, Opt. Express 1, 39 (1997).
32. R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996).
33. A. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998).
34. S. Jensen, M. Schwab, and C. Denz, Phys. Rev. Lett. 81, 1614 (1998).
35. R. Neubecker, E. Benkler, R. Martin, and G.-L. Oppo, Phys. Rev. Lett. 91, 113903 (2003).
36. A. Boiteux and B. Hess, Ber. Bunsenges. Phys. Chem. 84, 392 (1980).
37. H. Petty, R. Worth, and A. Kindzelskii, Phys. Rev. Lett. 84, 2754 (2000).
38. H. Petty and A. Kindzelskii, Proc. Natl. Acad. Sci. U.S.A. 98, 3145 (2001).
39. A. Kindzelskii and H. Petty, Proc. Natl. Acad. Sci. U.S.A. 99, 9207 (2002).
40. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, New York, 2002).
41. H. Berg and L. Turner, Biophys. J. 58, 919 (1990).
42. E. Budrene and H. Berg, Nature (London) 349, 630 (1991).
43. E. Budrene and H. Berg, Nature (London) 376, 49 (1995).
44. R. Tyson, S. Lubkin, and J. Murray, J. Math. Biol. 38, 359 (1999).
45. R. Tyson, L. Stern, and R. LeVeque, J. Math. Biol. 41, 455 (2000).
46. H. Othmer and T. Hillen, SIAM J. Appl. Math. 62, 1222 (2002).
47. R. Bellman, Dynamic Programming (Princeton University Press, 1957).
48. I. Bauer, F. Finocchi, W. Duschl, H.-P. Gail, and J. Schlöder, Astron. Astrophys. 317, 273 (1997).
49. D. Leineweber, I. Bauer, H. Bock, and J. Schlöder, Comput. Chem. Eng. 27, 157 (2003).
50. T. Binder, L. Blank, H. Bock, R. Bulirsch, W. Dahmen, M. Diehl, T. Kronseder, W. Marquardt, J. Schlöder, and O. Stryk, in Online Optimization of Large Scale Systems: State of the Art, edited by, M. Grötschel, S. Krumke, and, J. Rambau, (Springer, Berlin, Heidelberg, 2001), pp. 295-340.
51. M. Diehl, L. Magni, and G. D. Nicolao, Annu. Rev. Control 28, 37 (2004).
52. M. Diehl, R. Findeisen, F. Allgöwer, H. Bock, and J. Schlöder, IEE Proc.: Control Theory Appl. 152, 296 (2005).
53. M. Diehl, H. Bock, and J. Schlöder, SIAM J. Control Optim. 43, 1714 (2005).
54. J. Tyson and J. Keener, Physica D 32, 327 (1988).
55. D. Lebiedz and H. Maurer, IEE Syst. Biol. 2, 222 (2004).
56. D. Lebiedz and U. Brandt-Pollmann, Chaos 14, 611 (2004).
57. D. Lebiedz and U. Brandt-Pollmann, Phys. Rev. E 70, 051609 (2004).
58. H. Petty, ChemBioChem 5, 1359 (2004).