Cascaded nonlinear time-varying systems: Analysis and design

Lecture Notes in Control and Information Sciences

Volumn 311, Issue , 2005, Pages 23-64

  Loría, Antonio ^a   Panteley, Elena ^a  

^a UNIV PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748881404     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/11334774_2     Document Type: Article

References (69)

1. M. Arcak, D. Angeli, and E. Sontag, "A unifying integral ISS framework for stability of nonlinear cascades," SIAM J. on Contr. and Opt., vol. 40, pp. 888-1904, 2002.
2. G. Bastin, B. Brogliato, G. Campion, C. Canudas, M. Khalil, B. d'Andra Novel, A. de Luca, R. Lozano, R. Ortega, C. Samson, B. Siciliano, and P. Tomei (1996) Theory of Robot Control. Texts in Applied Mathematics. Springer-Verlag.
3. S. Boyd and S. Sastry (1989) Adaptive control: stability, convergence, and robustness. Prentice Hall, USA.
4. R. Brockett (1983) Asymptotic stability and feedback stabilization. In R. S. Millman R. W. Brocket and H. J. Sussmann, editors, Differential geometric control theory, pages 181-191. Birkhäuser.
5. C.I. Byrnes and A. Isidori (1989) New results and examples in nonlinear feedback stabilization. Syst. & Contr. Letters, 12:437-442.
6. M. Corless and L. Gilelmo (1998) New converse Lyapunov theorems and related results on exponential stability. Math. of Cont. Sign. and Syst., 11(1):79-100.
7. R. Fierro and F.L. Lewis (1995) Control of a nonholonomic mobile robot: backstepping kinematics into dynamics. In Proc. 34th. IEEE Conf. Decision Contr., pages 3805-3810, New Orleans, LA.
8. T. I. Fossen (1994) Guidance and control of ocean vehicles. John Wiley & Sons Ltd.
9. T. I. Fossen and J. P. Strand (1999) Passive nonlinear observer design for ships using Lyapunov methods: Full-scale experiments with a supply vessel. Automatica, 35(1):3-16.
10. W. Hahn (1967) Stability of motion. Springer-Verlag, New York.
11. P. Ioannou and J. Sun (1996) Robust adaptive control. Prentice Hall, New Jersey, USA.
12. M. Janković, R. Sepulchre, and P. V. Kokotović (1996) Constructive Lyapunov stabilization of non linear cascaded systems. IEEE Trans. on Automat. Contr., 41:1723-1736.
13. R.H. Middleton J.H. Braslavsky (1996) Global and semi-global stabilizability in certain cascade nonlinear systems. IEEE Trans. on Automat. Contr., 41:876-880.
14. Z.-P. Jiang, E. Lefeber, and H. Nijmeijer. (1998) Stabilization and tracking of a nonholonomic mobile robot with saturating actuators. In Control'98, Portugal.
15. Z. P. Jiang and I. Mareels (1997) A small gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Trans. on Automat. Contr., 42(3): 1-17.
16. Z.-P. Jiang and H. Nijmeijer (1997) Backstepping based tracking control of nonholonomic chained systems. In Proc. 4th. European Contr. Conf., Brussels, Belgium. Paper no. 672.
17. Z.-P. Jiang and H. Nijmeijer (1997) Tracking control of mobile robots: A case study in backstepping. Automatica, 33(7):1393-1399.
18. Y. Kanayama, Y. Kimura, F. Miyazaki, and T. Naguchi (1990) A stable traking control scheme for an autonomous vehicle. In Proc. IEEE Conf. Robotics Automat., pages 384-389.
19. H. Khalil (1996) Nonlinear systems. Macmillan Publishing Co., 2nd ed., New York.
20. H. Khalil (2002) Nonlinear systems. Prentice Hall, 3rd ed., New York.
21. D.E. Koditschek (1987) Adaptive techniques for mechanical systems. In Proceedings 5th Yale Workshop on Adaptive Systems, pages 259-265, New Haven, CT.
22. I. Kolmanovsky and H. McClamroch (1995) Developments in nonholonomic control problems. Control systems magazine, pages 20-36.
23. M. Krstić, I. Kanellakopoulos, and P. Kokotović (1995) Nonlinear and Adaptive control design. John Wiley & Sons, Inc., New York.
24. J. Kurzweil (1956) On the inversion of Ljapunov's second theorem on stability of motion. Amer. Math. Soc. Translations, 24:19-77.
25. A. A. J. Lefeber (2000) Tracking control of nonlinear mechanical systems. PhD thesis, University of Twente, Enschede, The Netherlands.
26. Y. Lin, E. D. Sontag, and Y. Wang (1996) A smooth converse Lyapunov theorem for robust stability. SIAM J. on Contr. and Opt., 34:124-160.
27. A. Loría T. I. Fossen, and E. Panteley (2000) A separation principle for dynamic positioning of ships: theoretical and experimental results. IEEE Trans. Contr. Syst. Technol., 8(2):332-344.
28. A. Loría H. Nijmeijer, and O. Egeland (1998) Controlled synchronization of two pendula: cascaded structure approach. In Proc. American Control Conference, Philadelphia, PA.
29. I. J. Malkin (1958) Theory of stability of motion. Technical report, U.S. Atomic energy commission.
30. F. Mazene and L. Praly (1996) Adding integrators, saturated controls and global asymptotic stabilization of feedforward systems. IEEE Trans. on Automat. Contr., 41(11):1559-1579.
31. F. Mazene and L. Praly (1997) Asymptotic tracking of a state reference for systems with a feedforward structure. In Proc. 4th. European Contr. Conf., Brussels, Belgium, paper no. 954.
32. To appear in Automatica.
33. F. Mazene, R. Sepulchre, and M. Janković (1997) Lyapunov functions for stable cascades and applications to global stabilization. In Proc. 36th. IEEE Conf. Decision Contr.
34. A. Micaelli and C. Samson (1993) Trajectory tracking for unicycle-type and two-steering-wheels mobile robots. Technical Report 2097, INRIA.
35. P. Moraal, M. Van Nieuwstadt, and M. Jankovich (1997) Robust geometric control: An automotive application. In Proc. 4th. European Contr. Conf., Brussels.
36. A. P. Morgan and K. S. Narendra (1977) On the stability of nonautonomous differential equations x = [A+B(t)]x with skew-symmetric matrix B(t). SIAM J. on Contr. and Opt., 15(1):163-176.
37. R.M. Murray, G. Walsh, and S.S. Sastry (1992) Stabilization and tracking for nonholonomic control systems using time-varying state feedback. In M. Fliess, editor, IFAC Nonlinear control systems design, pages 109-114, Bordeaux.
38. W. Oelen and J. van Amerongen (1994) Robust tracking control of two-degreesof-freedom mobile robots. Control Engineering Practice, pages 333-340.
39. R. Ortega, (1991) Passivity properties for stabilization of nonlinear cascaded systems. Automatica, 29:423-424.
40. R. Ortega, A. Loría P. J. Nicklasson, and H. Sira-Ramírez (1998) Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. Comunications and Control Engineering. Springer Verlag, London. ISBN 1-85233-016-3.
41. E. Panteley, E. Lefeber, A. Loría and H. Nijmeijer (1998) Exponential tracking of a mobile car using a cascaded approach. In IFAC Workshop on Motion Control, pages 221-226, Grenoble, France.
42. E. Panteley and A. Loría(1997) Global uniform asymptotic stability of cascaded non autonomous nonlinear systems. In Proc. 4th. European Contr. Conf., Louvain-La,-Neuve, Belgium. Paper no. 259.
43. E. Panteley and A. Loría(1998) On global uniform asymptotic stability of non linear time-varying non autonomous systems in cascade. Syst. & Contr. Letters, 33(2):131-138.
44. E. Panteley, A. Loría and A. Sokolov (1999) Global uniform asymptotic stability of nonlinear nonautonomous systems: Application to a turbo-diesel engine. European J. of Contr., 5:107-115.
45. E. Panteley, A. Loría and A. Teel (1999) UGAS of NLTV systems: Applications to adaptive control. Technical Report 99-160, Lab. d'Automatique de Grenoble, UMR 5528, CNRS, France.
46. Related publications: see IEEE Trans. Aut. Contr. 46(12),
47. Syst. Contr. Lett. 2002.
48. E. Panteley and R. Ortega (1997) Cascaded control of feedback interconnected systems: Application to robots with AC drives. Automation, 33(11):1935-1947.
49. E. Panteley, R. Ortega, and P. Aquino (1997) Cascaded Control of Feedback Interconnected Systems: Application to Robots with AC Drives. In Proc. 4th. European Contr. Conf., Louvain-La-Neuve, Belgium.
50. L. Praly (2002) An introduction to lyapunov designs of global asymptotic stabilizers. Technical report, Banach Center Summer School on Mathematical control theory, Poland.
51. L. Praly and Y. Wang (1996) Stabilization in spite of matched unmodelled dynamics and an equivalent definition of input-to-state stability. Math. of Cont. Sign. and Syst., 9:1-33.
52. N. Rouche and J. Mawhin (1980) Ordinary differential, equations II: Stability and periodical solutions. Pitman publishing Ltd., London.
53. C. Rui and N.H. McClamroch (1995) Stabilization and asymptotic path tracking of a rolling disk. In Proc. 34th. IEEE Conf. Decision Contr., pages 4294-4299, New Orleans, LA.
54. A. Saberi, P. V. Kokotović, and H. J. Sussmann (1990) Global stabilization of partially linear systems. SIAM J. Contr. and Optimization, 28:1491-1503.
55. C. Samson and K. Ait-Abderrahim (1991) Feedback control of a nonholonomic wheeled cart in cartesian space. In Proc. IEEE Conf. Robotics Automat., pages 1136-1141, Sacramento.
56. G. Sansone and R. Conti (1964) Nonlinear Differential equations. Pergamon Press, Oxford, England.
57. S. Sastry and M. Bodson (1989) Adaptive control: Stability, convergence and robustness. Prentice Hall Intl.
58. P. Seibert and R. Suárez (1990) Global stabilization of nonlinear cascaded systems. Syst. & Contr. Letters, 14:347-352.
59. R. Sepulchre and M. Arcak abd A. R. Teel (2002) Trading the stability of finite zeros for global stabilization of nonlinear cascade systems. IEEE Trans. on Automat. Contr., 47(3):521-525.
60. R. Sepulchre, M. Janković, and P. Kokotović (1997) Constructive nonlinear control. Springer Verlag.
61. E. Sontag (1989) Smooth stabilization implies coprime factorization. IEEE Trans. on Automat. Contr., 34(4):435-443.
62. E. D. Sontag (1989) Remarks on stabilization and Input-to-State stability. In Proc. 28th. IEEE Conf. Decision Contr., pages 1376-1378, Tampa, Fl.
63. E. D. Sontag (1995) On the input-to-state stability property. European J. Control, 1:24-36.
64. E. D. Sontag, "Comments on integral variants of ISS," Syst. & Contr. Letters, vol. 34, pp. 93-100, 1998.
65. E.D. Sontag and Y. Wang (1995) On characterizations of the input-to-state stability property. Syst. & Contr. Letters, 24:351-359.
66. H. J. Sussman and P. V. Kokotović (1991) The peaking phenomenon and the global stabilization of nonlinear systems. IEEE Trans. on Automat. Contr., 36(4):424-439.
67. A. Teel. Converse Lyapunov function theorems: statements and constructions. Notes from Advanced nonlinear systems theory. Course no. ECE 594D, University of California, Santa Barbara, CA, USA, Summer 1998.
68. J. Tsinias (1989) Sufficient Lyapunov-like conditions for stabilization. Math. Control Signals Systems, pages 343-357.
69. M. Vidyasagar (1993) Nonlinear systems analysis. Prentice Hall, New Jersey.