Linear control and estimation of nonlinear chaotic convection: Harnessing the butterfly effect

Physics of Fluids

Volumn 11, Issue 5, 1999, Pages 1169-1186

  Bewley, Thomas R ^a,b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000163062     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869986     Document Type: Article

References (43)

1. E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141 (1963).
2. B. Saltzman, "Finite amplitude free convection as an initial value problem - I," J. Atmos. Sci. 19, 329-341 (1962).
3. Y. Z. Wang, J. Singer, and H. H. Bau, "Controlling chaos in a thermal convection loop," J. Fluid Mech. 237, 479-498 (1992).
4. J. Gleick, Chaos: Making a New Science (Viking, New York, 1987).
5. J. A. Yorke, and E. E. Yorke, "Chaotic behavior and fluid dynamics," in Hydrodynamic Stability and the Transition to Turbulence, edited by H. L. Swinney and J. Gollub, Topics in Applied Physics, Vol. 45 (Springer, New York, 1982), pp. 77-95.
6. M. Gorman, P. J. Widmann, and K. A. Robins, "Nonlinear dynamics of a convection loop: A quantitative comparison of experiment with theory," Physica 19D, 255-267 (1986).
7. P. J. Widmann, M. Gorman, and K. A. Robins, "Nonlinear dynamics of a convection loop ii. Chaos in laminar and turbulent flows," Physica D 36, 157-166 (1989).
8. J. E. Hart, "A new analysis of the closed loop thermosyphon," Int. J. Heat Mass Transf. 27, 125-136 (1984).
9. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors (Springer, New York, 1982).
10. E. N. Lorenz, The Essence of Chaos (University of Washington Press, Seattle, 1993).
11. T. Shinbrot, C. Grebogi, E. Ott, and J. A. Yorke, "Using small perturbations to control chaos," Nature (London) 363, 411-417 (1993).
12. J. M. Nese, "Quantifying local predictability in phase space," Physica D 35, 237-250 (1989).
13. B. Eckhardt, and D. Yau, "Local Lyapunov exponents in chaotic systems," Physica D 65, 100-108 (1989).
14. B. F. Farrell, and P. J. Ioannou, "Generalized stability theory. Part II: Nonautonomous operators," J. Atmos. Sci. 53, 2041-2053 (1996).
15. T. L. Vincent, "Control using chaos," IEEE Control Syst. Mag. 17, 65-76 (1997).
16. P. K. Yuen, and H. H. Bau, "Optimal and adaptive control of chaotic convection - Theory and experiments," Phys. Fluids (submitted).
17. T. L. Vincent, and J. Yu, "Control of a chaotic system," Dynamics and Control 1, 35-52 (1991).
18. H. H. Bau and Y. Z. Wang, "Chaos: A heat transfer perspective," in Annual Review of Heat Transfer, edited by C. L. Tien, Vol. 4, pp. 1-50 (1991).
19. H. Wang and E. H. Abed, "Bifurcation control of chaotic dynamical systems," University of Maryland Institute for Systems Research, Technical Research Report 92-67 (1992).
20. C.-J. Wan and D. S. Bernstein, "Nonlinear feedback control with global stabilization," Dynamics and Control 5, 321-346 (1995).
21. P. K. Yuen and H. H. Bau, "Rendering a subcritical Hopf bifurcation supercritical," J. Fluid Mech. 317, 91-109 (1996).
22. T. R. Bewley and S. Liu, "Optimal and robust control and estimation of linear paths to transition," J. Fluid Mech. 365, 305-349 (1998).
23. A. J. Laub, "Invariant subspace methods for the numerical solution of Riccati equations," in The Riccati Equation, edited by Bittaini, Laub, and Willems (Springer, New York, 1991), pp. 163-196.
24. ∞ control problems," IEEE Trans. Autom. Control. 34, 831-847 (1989).
25. F. L. Lewis and V. L. Syrmos, Optimal Control (Wiley, New York, 1995).
26. M. Green and D. J. N. Limebeer, Linear Robust Control (Prentice-Hall, New York, 1995).
27. S. Skogestad and I. Postlethwaite, Multivariable Feedback Control (Wiley, New York, 1996).
28. J. Malmborg, B. Bernhardsson, and K. J. Åström, "A stabilizing switching scheme for multi controller systems," Proceedings of the 13th World Congress of IFAC, F, San Francisco, pp. 229-234 (1996).
29. K. Ezal, Z. Pan, and P. V. Kokotović, "Locally optimal backstepping design," Proceedings of the 36th IEEE Conference on Decision and Control, San Diego (1997).
30. M. Janković, R. Sepulchre, and P. V. Kokotović, "Constructive Lyapunov stabilization of nonlinear cascade systems," IEEE Trans. Autom. Control. 41, 1723-1735 (1996).
31. M. Janković, private communication (1997).
32. P. K. Kokotović, "The joy of feedback: Nonlinear and adaptive," IEEE Control Syst. Mag. 12, 7-17 (1992).
33. P. Moin and T. R. Bewley, "Application of control theory to turbulence," Twelfth Australasian Fluid Mechanics Conference, December 10-15, 1995, Sydney, pp. 109-117.
34. S. K. Robinson, "Coherent motions in the turbulent boundary layer," Annu. Rev. Fluid Mech. 23, 601-639 (1991).
35. J. Jeong, F. Hussain, W. Schoppa, and J. Kim, "Coherent structures near the wall in a turbulent channel flow," J. Fluid Mech. 332, 185-214 (1997).
36. T. R. Bewley, P. Moin, and R. Temam, "DNS-based predictive control of turbulence: an optimal target for feedback algorithms," J. Fluid Mech. (submitted).
37. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University Press, Cambridge, 1996).
38. T. R. Bewley, P. Moin, and R. Temam, "A method for optimizing feedback control rules for wall-bounded turbulent flows based on control theory," Proceedings of the ASME Fluids Engineering Summer Meeting, ASME FED Vol. 237, p. 279-285 (1996).
39. T. R. Bewley, R. Temam, and M. Ziane, "A general framework for robust control in fluid mechanics," Physica D (submitted).
40. C. Lee, J. Kim, D. Babcock, and R. Goodman, "Application of neural network to turbulence control for drag reduction," Phys. Fluids 9, 1740-1747 (1997).
41. 2-Gain and Passivity Techniques in Nonlinear Control (Springer, New York, 1996).
42. A. Isidori, Nonlinear Control Systems (Springer, New York, 1995).
43. D. Graham and D. McRuer, Analysis of Nonlinear Control Systems (Wiley, New York, 1961).