Contraction analysis of non-linear distributed systems

International Journal of Control

Volumn 78, Issue 9, 2005, Pages 678-688

  Lohmiller, W ^a   Slotine, J J E ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL EQUIPMENT; HAMILTONIANS; STABILITY; TIME VARYING SYSTEMS;

NON-LINEAR DISTRIBUTED SYSTEMS; STABILITY ANALYSIS;

NONLINEAR SYSTEMS;

EID: 27844596643     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170500130952     Document Type: Article

References (52)

1. N. Aghannan and P. Rouchon, "An intrinsic observer for a class of Lagrangian systems", IEEE Transactions on Automatic Control, 48, pp. 936-945, 2003.
2. D. Angeli, "A Lyapunov approach to incremental stability properties", IEEE Transactions on Automatic Control, 47, pp. 410-421, 2002.
3. R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Dover Publications, 1962.
4. G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, New York: Springer, 2002.
5. D.H. Ballard and R.P. Rao, "Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive field effects", Nature Neuroscience, 1, pp. 79-87, 1999.
6. M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image Inpainting, New Orleans: SIGGRAPH 2000, 2000.
7. D. Bertsekas and J. Tsitsiklis, Parallel and Distributed Computation, Englewood, NJ: Prentice-Hall, 1989.
8. A.E. Bryson and Y.C. Ho, Applied Optimal Control, Taylor and Francis, 1975.
9. B.P. Demidovich, "Dissipativity of a nonlinear system of differential equations", Ser. Matematika Mehanika, Part I N.6, pp. 19-27, 1961;
10. Ser. Matematika Mehanika, Part I N. Part II N.1, pp. 3-8, Vestnik Moscow State University, 1962.
11. P.G. Drazin and W.H. Reid, Hydrodynamic Stability, Cambridge University Press, 1981.
12. L.C. Evans, Partial Differential Equations, American Mathematical Society, 1998.
13. T. Evgeniou, M. Pontil and T. Poggio, "Statistical learning theory: a primer". International Journal of Computer Vision, 38, pp. 9-13, 2000.
14. V. Fromion, S. Monaco and D. Normand-Cyrot, "Asymptotic properties of incrementally stable systems", IEEE Transactions on Automatic Control, 41, pp. 721-723, 1996.
15. W. Hahn, Stability of Motion, New York: Springer Verlag, 1967.
16. J. de Halleux, C. Prieur, J.-M. Coron, B. d'andreéa-novel and G. Bastin, "Boundary feedback control in networks of open channels", Automatica, 39, pp. 1365-1376, 2003.
17. P. Hartmann, Ordinary Differential Equations, 2nd edn, Boston: Birkhauser, 1982.
18. L. Hormander, "Lectures on nonlinear hyperbolic differential equations". Springer Verlag, 1997.
19. A. Jawzwinski, Stochastic Processes and Filtering Theory, San Diego: Elsevier, 1970.
20. J. Jouffroy and J. Opderbecke, "Underwater vehicle trajectory estimation using contracting PDE-based observers", in American Control Conference, Boston, MA, 2004.
21. T. Kailath, Linear Systems, Englewood Cliffs, NJ: Prentice Hall, 1980.
22. T. Kato, Perturbation Theory for Linear Operators, Berlin: Springer Verlag, 1995.
23. N.N. Krasovskii, Problems of the Theory of Stability of Motion, Moskow: Mir, 1959.
24. D. Kristiansen, Doctoral thesis, Norwegian University of Science and Technology, Trondheim (2000).
25. D. Kristiansen and O. Egeland, "Time and spatial discretization methods that preserve passivity properties for systems described by partial differential equations", in American Control Conference Chicago, Illinois, 2000.
26. M. Krstic and D. Hua, "Output-feedback control of stochastic nonlinear systems-stabilization, disturbance attenuation and adaptation", in Lecture Notes in Control and Information Sciences 244, London: Springer Verlag, 1999.
27. G.A. Leonov, I.M. Burkin and A.I. Shepeljavyi, Frequency Methods in Oscillation Theory, Springer Science, Berlin: Kluwer, 1996.
28. D.C. Lewis, "Metric properties of differential equations", American Journal of Mathematics, 71, pp. 294-312, 1949.
29. P.L. Lions, Mathematical Topics in Fluid Mechanics, Gloucestershire, UK: Clarendon Press, 1996.
30. W. Lohmiller and J.J.E. Slotine, "Metric analysis for nonlinear systems", in I.E.E.E. Int. Conf. Control Applications, Dearborn, Michigan, 1996.
31. W. Lohmiller and J.J.E. Slotine, "On contraction analysis for nonlinear systems", Automatica, 34(6), pp. 683-696, 1998.
32. W. Lohmiller and J.J.E. Slotine, "Global convergence rates of nonlinear diffusion for time-varying images, scale-space theories in computer vision", in Lecture Notes in Computer Science 1682, Berlin: Springer Verlag, 1999a.
33. W. Lohmiller and J.J.E. Slotine, "Stability analysis and nonlinear observer design for nonlinear diffusion processes", in Lecture Notes in Control and Information Sciences 244, Berlin: Springer Verlag, 1999b.
34. W. Lohmiller and J.J.E. Slotine, "Contraction analysis of nonlinear reaction-diffusion processes", in European Control Conference, Karlsruhe, Germany, 1999c.
35. W. Lohmiller and J.J.E. Slotine, "Nonlinear process control using contraction theory", A. I. Che. Journal, 46(3), pp. 588-596, March 2000.
36. W. Lohmiller and J.J.E. Slotine, "Nonlinear PDE observers for machine vision", in I.E.E.E. M.M.A.R., Poland, 2001a.
37. W. Lohmiller and J.J.E. Slotine, "Analysis of nonlinear infinite dimensional systems using contraction theory", in I.E.E.E. M.M.A.R., Poland, 2001b.
38. D. Lovelock and H. Rund, Tensors, Differential Forms, and Variational Principles, Dover Publications, 1989.
39. Millennium Prize Problems, Clay Mathematics Institute, 2000.
40. T.D. Nguyen and O. Egeland, "Observer design for a towed seismic cable", in American Control Conference, Boston, 2004.
41. Z. Opial, "Sur la stabilité asymptotique des solutions d'un système d'équations différentielles", Ann. Polinici Math, 7, pp. 259-267, 1960.
42. A. Pavlov, A.Y. Pogromsky, N. van de Wouw and H. Nijmeijer, "Convergent dynamics, a tribute to Boris Pavlovich Demidovich", Systems & Control Letters, 52, pp. 257-261, 2004.
43. T. Poggio and S. Smale, "The mathematics of learning: dealing with data", Notices of the American Mathematical Society (AMS), 50(5), pp. 537-544, 2003.
44. G. Seifert, "On stability in the large for periodic solution of differential systems", Annals of Math, 67, pp. 83-89, 1958.
45. G. Sussman and I. Wisdom, "Chaotic evolution of the solar system", Science, No5066(257), pp. 56-62, 1992.
46. J.J.E. Slotine and W. Lohmiller, "Modularity, evolution, and the binding problem: a view from stability theory", Neural Networks, 14(2), pp. 137-145, 2001.
47. J.J.E. Slotine, "Modular stability tools for distributed computation and control", Int. J. Adaptive Control and Signal Processing, 17(6), pp. 397-416, 2003.
48. A. Smyshlyaev and M. Krstic, "Closed form boundary state feedbacks for a class of partial integro-differential equations", IEEE Transactions on Automatic Control, 49, pp. 2185-2202, 2004.
49. W. Wang and J.J.E. Slotine, "On partial contraction analysis for coupled nonlinear oscillators". Biological Cybernetics, 92(1), pp. 38-53, 2004.
50. V.A. Yakubovich, "Matrix inequalities method in stability theory for nonlinear control systems: I. Absolute stability of forced vibrations", Automation and Remote Control, 7, pp. 905-917, 1964.
51. T. Yoshizawa, "Stability theory by Lyapunov's second method", Math. Society of Japan, 1966.
52. Y. Zhao and J.J.E. Slotine, "Discrete nonlinear observers for inertial navigation", Systems and Control Letters, 54(7), 2005.