Exploiting optimal control for target-oriented manipulation of (bio)chemical systems: A model-based approach to specific modification of self-organized dynamics

International Journal of Modern Physics B

Volumn 19, Issue 25, 2005, Pages 3763-3798

  Lebiedz, D ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Cell biology and biomedicine; Control of self organization and pattern formation; External forcing; Nonlinear dynamics in chemistry; Optimal control; Optimization

Indexed keywords

EID: 27644457757     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979205032498     Document Type: Review

References (100)

1. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (John Wiley, New York, 1971).
2. G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (John Wiley, New York, 1977).
3. P. Ball, The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, Oxford, 1998).
4. A. Carbone, M. Gronov, M. Gronov and P. Prusinkiewicz, Pattern Formation in Biology, Vision and Dynamics (World Scientific, Singapore, 2000).
5. D. Walgraef, Spatio-Temporal Pattern Formation, With Examples from Physics, Chemistry, and Materials Science Springer-Verlag, New York, 1996).
6. S. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Chemistry, Biology and Engineering (Perseus Books Group, New York, 2001).
7. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
8. A. J. Koch and H. Meinhardt, Rev, Mod. Phys. 66, 1471 (1994).
9. J. D. Murray, Mathematical Biology I and II (Springer-Verlag, New York, 2002).
10. J. Keener and J. Sneyd, Mathematical Physiology (Springer-Verlag, New York, 1998).
11. C. P. Fall, E. S. Marland, J. M. Wagner and J. J. Tyson, Computational Cell Biology, (Springer-Verlag, New York, 2002).
12. I. R. Epstein and K. Showalter, J. Phys. Chem. 100, 13132 (1996).
13. F. Sagues and I. R. Epstein, Dalton Trans. 7, 1201 (2003).
14. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour (Cambridge University Press, Cambridge, 1996).
15. J. Walleczek, Self-organized Biological Dynamics and Nonlinear Control (Cambridge University Press, Cambridge, 2000).
16. A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 2001).
17. M. Morari and J. H. Lee, Comput. Chem. Eng. 23, 667 (1999).
18. F. Allgöwer and A. Zheng, Nonlinear Predictive Control (Birkhäuser, Basel, 2000).
19. E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
20. K. Pyragas, Phys. Lett. A170, 421 (1992).
21. T. Shinbrot, C. Grebogi, E. Ott and J. A. Yorke, Nature 363, 411 (1993).
22. T. Sakurai, E. Mihaliuk, F. Chirila and K. Showalter, Science 296, 2009 (2002).
23. E. Mihaliuk, T. Sakurai, F. Chirila and K. Showalter, Faraday Disc. 120, 383 (2001).
24. V. Vanag, L. Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, Nature, 406, 389 (2000).
25. M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. Mikhailov, H. H. Rotermund and G. Ertl, Science, 292, 1357 (2001).
26. S. Sinha and N. Gupte, Phys. Rev. E58, R5221 (1998).
27. S. Sinha and N. Gupte, Phys. Rev. E64, 015203(R) (2001).
28. G. V. Osipov, B. V. Shulgin and J. J. Collins, Phys Rev. E58, 6955 (1998).
29. J. H. Xiao, G. Hu and J. H. Gao, Int. J. Bifurcat. Chaos 10, 655 (2000).
30. A. M. Pertsov, J. M. Davidenko, R. Salomonsz, W. T. Baxter and J. Jalife, Circ. Res. 72, 631 (1993).
31. R. Martin, G.-L. Oppo, G. K. Harkness, A. J. Scroggie and W. J. Firth, Opt. Express 1, 39 (1997).
32. E. Schöll, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors (Cambridge University Press, Cambridge, 2001).
33. I. Z. Kiss and J. L. Hudson, AIChE J. 49, 2234 (2003).
34. L. T. Biegler and I. E. Grossmann, Comput. Chem. Eng. 28, 1169 (2004).
35. I. E. Grossmann and L. T. Biegler, Comput. Chem. Eng. 28, 1193 (2004).
36. 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, eds. M. Grötschel, S. Krumke and J. Rambau, (Springer-Verlang, Berlin, Heidelberg, 2001), p. 295.
37. L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze and E. F. Miscenko, The Mathematical Theory of Optimal Processes (John Wiley, New York, 1962).
38. E. R. Pinch, Optimal Control and the Calculus of Variations (Oxford University Press, Oxford, 1993).
39. L. N. Hand and J. D. Finch, Analytical Mechanics (Cambridge University Press, New York, 1998).
40. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999).
41. R. Fletcher, Practical Optimization (John Wiley, New York, 2000).
42. H. G. Bock and K. J. Plitt, in Proc. Ninth IFAC World Congress (Budapest. Pergamon Press, New York, 1984).
43. D. B. Leineweber, I. Bauer, H. G. Bock and J. P. Schlöder, Comput. Chem. Eng. 27, 157 (2003).
44. I. Bauer, F. Finocchi, W. J. Duschl, H.-P. Gail and J. P. Schlöder, Astron. Astrophys. 317, 273 (1997).
45. G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization (John Wiley, New York, 1999).
46. C. A. Floudas, Nonlinear and Mixed-Integer Optimization (Oxford University Press, Oxford, 1995).
47. S. Qin and T. Badgwell, Nonlinear Model Predictive Control: Theory and Application, eds. B. Kouvaritakis and M. Cannon (The Institute of Electrical Engineers, London, 2001), pp. 3-32.
48. M. Henson, Comp. & Chem. Eng. 23, 187 (1998).
49. D. Mayne, J. Rawlings, C. Rao and P. Scokaert, Automatica 26(6), 789 (2000).
50. L. Biegler, Progress in systems theory, in Nonlinear Predictive Control, eds. F. Allgöwer and A. Zheng, Vol. 26 (Birkhäuser, Basel, 2000), p. 219.
51. M. Diehl, H. Bock, J. Schlöder, R. Findeisen, Z. Nagy and F. Allgöwer, J. Proc. Contr. 12(4), 577 (2002).
52. M. Diehl, Real-Time Optimization for Large Scale Nonlinear Processes, Vol. 920 of Fortschr.-Ber. VDI Reihe 8, Meß-, Steuerungs- und Regelungstechnik (VDI Verlag, Düsseldorf, 2002).
53. M. Diehl, H. G. Bock and J. P. Schlöder, SIAM J. Control Optim. 43, 1714 (2005).
54. U. Brandt-Pollmann, D. Lebiedz, M. Diehl, S. Sager and J. P. Schlöder, Chaos 15, 033901 (2005).
55. D. Lebiedz and U. Brandt-Pollmann, Phys. Rev. Lett., 91, 208301 (2003).
56. D. Lebiedz and U. Brandt-Pollmann, Chaos 15, 023901 (2005).
57. M. Diehl, I. Uslu, R. Findeisen, S. Schwarzkopf, F. Allgöwer, H. Bock, T. Bürner, E. Gilles, A. Kienle, J. Schlöder and E. Stein, in Online Optimization of Large Scale Systems: State of the Art, eds. M. Grötschel, S. O. Krumke and J. Rambau, (Springer-Verlag, Berlin, Heidelberg, 2001), p. 363.
58. R. Tyson, S. R. Lubkin and J. D. Murray, J. Math. Biol. 38, 359 (1999).
59. R. Tyson, L. G. Stern and R. J. LeVeque, J. Math. Biol. 41, 455 (2000).
60. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter, Molecular Biology of the Cell (Garland Science, New York, 2002).
61. H. G. Othmer and T. Hillen, SIAM J. Appl. Math. 62, 1222 (2002).
62. H. C. Berg and L. Turner, Biophys. J. 58, 919 (1990).
63. E. O. Budrene and H. C. Berg, Nature 349, 630 (1991).
64. E. O. Budrene and H. C. Berg, Nature 376, 49 (1995).
65. D. Lebiedz and H. Maurer, Syst. Biol. 2, 222 (2004).
66. R. Bellman, Dynamic Programming (Princeton University Press, Princeton, 1957).
67. J. Tyson and J. Keener, Physica D 32, 327 (1988).
68. K. Christmann, Introduction to Surface Physical Chemistry (Springer-Verlag, New York, 1991).
69. D. Lebiedz and U. Brandt-Pollmann, Phys. Rev. E70, 051609 (2004).
70. K. Krischer, M. Eiswirth and G. Ertl, J. Chem. Phys. 96, 9161 (1992).
71. M. Bertram and A. S. Mikhailov, Phys. Rev. E67, 036207 (2003).
72. J. Wolff, A. G. Papathanasiou, I. G. Kevrekidis, H. H. Rotermund and G. Ertl, Science 294, 134 (2001).
73. J. Wolff, A. G. Papathanasiou, H. H. Rotermund, G. Ertl, X. Li and I. G. Kevrekidis, J. Catal. 216, 246 (2003).
74. J. Wolff, A. G. Papathanasiou, H. H. Rotermund, G. Ertl, M. A. Katsoulakis, X. Li and I. G. Kevrekidis, Phys. Rev. Lett. 90, 148301 (2003).
75. D. Lebiedz and U. Brandt-Pollmann, Chaos 14, 611 (2004).
76. D. Lebiedz, S. Sager, H. G. Bock and P. Lebiedz, Phys. Rev. Lett. 95, 108303 (2005).
77. E. N. Best, Biophys. J. 27, 87 (1979).
78. R. Guttman, S. Lewis and J. Rinzel, J. Physiol. 305, 377 (1980).
79. U. Kummer, L. F. Olsen, C. J. Dixon, A. K. Green, E. Bornberg-Bauer and G. Baier, Biophys. J. 79, 1188 (2000).
80. M. Berridge, Nature 386, 759 (1997).
81. H. Bisswanger, Enzyme Kinetics (John Wiley, Weinheim, 2002).
82. A. J. Morgan and R. Jacob, J. Physiol. 513, 8239 (1998).
83. X. Xu, W. Zeng, S. Popov, D. M. Berman, I. Davignon, K. Yu, D. Yowe, S. Offermanns, S. Muallem and T. M. Wilkie, J. Biol. Chem. 274, 3549 (1999).
84. E. J. Doedel, Congr. Num. 30, 265 (1981).
85. B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students (SIAM, Philadelphia, 2002).
86. C. Y. Kaya and J. L. Noakes, J. Optim. Theory and Appl. 117, 69 (2003).
87. S. Sager, H. G. Bock, M. Diehl, G. Reinelt and J. P. Schlöder, Lectures Notes in Economics and Mathematical Systems in Recent Advances in Optimization (Proc. 12th French-German-Spanish Conference on Optimization), ed. A. Seeger (Springer-Verlag, New York, y2005).
88. H. Maurer, C. Büskens, J. H. R. Kim and Y. Kaya, Optim. Control Appl. Meth. 26, 129 (2005).
89. H. R. Petty, Chem. Bio. Chem. 5, 1359 (2004).
90. A. Boiteux and B. Hess, Ber. Bunsenges. Phys. Chem. 84, 392 (1980).
91. H. R. Petty, R. G. Worth and A. L. Kindzelskii, Phys. Rev. Lett. 84, 2754 (2000).
92. H. R. Petty and A. L. Kindzelskii, Proc. Nat. Acad. Sci. USA 98, 3145 (2001).
93. A. L. Kindzelskii and H. R. Petty, Proc. Nat. Acad. Sci. USA 99, 9207 (2002).
94. A. Goldbeter, G. Dupont and M. J. Berridge, Proc. Nat. Acad. Sci. USA 87, 1461 (1990).
95. R. E. Dolmetsch, K. Xu and R. S. Lewis, Nature 392, 933 (1998).
96. W. H. Li, J. Llopis, M. Withney, G. Zlokarnik and R. Y. Tsien, Nature 392, 936 (1998).
97. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter, Molecular Biology of the Cell (Garland Science, New York, 2002).
98. J. J. Tyson, K. C. Chen and B. Novak, Curr. Opin. Cell Biol. 15, 221 (2003).
99. U. S. Bhalla and R. Iyengar, Science 283, 381 (1999).
100. G. Weng, U. S. Bhalla and R. Iyengar, Science 284, 92 (1999).