Free Access
Issue
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
Page(s) 393 - 422
DOI https://doi.org/10.1051/cocv:2002045
Published online 15 August 2002
  1. D. Auckly, L. Kapitanski and W. White, Control of nonlinear underactuated systems. Comm. Pure Appl. Math. 53 (2000) 354-369. (See related papers at http://www.math.ksu.edu/dav/). [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Blankenstein, R. Ortega and A. van Der Schaft, The matching conditions of controlled Lagrangians and IDA passivity based control. Preprint (2001). [Google Scholar]
  3. A.M. Bloch, D.E. Chang, N.E. Leonard and J.E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems II: Potential shaping. IEEE Trans. Automat. Control 46 (2001) 1556-1571. [CrossRef] [MathSciNet] [Google Scholar]
  4. A.M. Bloch, D.E. Chang, N.E. Leonard, J.E. Marsden and C.A. Woolsey, Stabilization of Mechanical Systems with Structure-Modifying Feedback. Presented at the 2001 SIAM Conf. on Control and its Applications, http://www.aoe.vt.edu/~cwoolsey/Lectures/SIAM.7.01.html [Google Scholar]
  5. A.M. Bloch and P.E. Crouch, Representation of Dirac structures on vector space and nonlinear L-C circuits, in Proc. Symp. on Appl. Math., AMS 66 (1998) 103-118. [Google Scholar]
  6. A.M. Bloch and P.E. Crouch, Optimal control, optimization and analytical mechanics, in Mathematical Control Theory, edited by J. Baillieul and J. Willems Springer (1998) 268-321. [Google Scholar]
  7. A.M. Bloch, P.S. Krishnaprasad, J.E. Marsden and G. Sánchez De Alvarez, Stabilization of rigid body dynamics by internal and external torques. Automatica 28 (1992) 745-756. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.M. Bloch, N.E. Leonard and J.E. Marsden, Stabilization of mechanical systems using controlled Lagrangians, in Proc. IEEE CDC 36 (1997) 2356-2361. [Google Scholar]
  9. A.M. Bloch, N.E. Leonard and J.E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems I: The first matching theorem. IEEE Trans. Automat. Control 45 (2000) 2253-2270. [CrossRef] [MathSciNet] [Google Scholar]
  10. A.M. Bloch, N.E. Leonard and J.E. Marsden, Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems. Int. J. Robust Nonlinear Control 11 (2001) 191-214. [CrossRef] [Google Scholar]
  11. R.W. Brockett, Control theory and analytical mechanics, in 1976 Ames Research Center (NASA) Conference on Geometric Control Theory, edited by R. Hermann and C. Martin. Math Sci Press, Brookline, Massachusetts, Lie Groups: History, Frontiers, and Applications VII (1976) 1-46. [Google Scholar]
  12. A. Cannas Da Silva and A. Weinstein, Geometric Models for Noncommutative Algebras. Amer. Math. Soc., Berkeley Mathematics Lecture Notes (1999). [Google Scholar]
  13. H. Cendra, J.E. Marsden and T.S. Ratiu, Lagrangian Reduction by Stages. Memoirs of the Amer. Math. Soc. 152 (2001). [Google Scholar]
  14. H. Cendra, J.E. Marsden and T.S. Ratiu, Geometric mechanics, Lagrangian reduction and nonholonomic systems, in Mathematics Unlimited-2001 and Beyond, edited by B. Enquist and W. Schmid. Springer-Verlag, New York (2001) 221-273. [Google Scholar]
  15. T. Courant, Dirac manifolds. Trans. Amer. Math. Soc. 319 (1990) 631-661. [CrossRef] [MathSciNet] [Google Scholar]
  16. P.E. Crouch and A. J. van der Schaft, Variational and Hamiltonian Control Systems. Springer-Verlag, Berlin, Lecture Notes in Control and Inform. Sci. 101 (1987). [Google Scholar]
  17. I. Dorfman,Dirac Structures and Integrability of Nonlinear Evolution Equations. Chichester: John Wiley (1993). [Google Scholar]
  18. J. Hamberg, General matching conditions in the theory of controlled Lagrangians, in Proc. IEEE CDC (1999) 2519-2523. [Google Scholar]
  19. J. Hamberg, Controlled Lagrangians, symmetries and conditions for strong matching, in Lagrangian and Hamiltonian Methods for Nonlinear Control: A Proc. Volume from the IFAC Workshop, edited by N.E. Leonard and R. Ortega. Pergamon (2000) 57-62. [Google Scholar]
  20. A. Ibort, M. De Leon, J.C. Marrero and D. Martin De Diego, Dirac brackets in constrained dynamics. Fortschr. Phys. 30 (1999) 459-492. [CrossRef] [Google Scholar]
  21. S.M. Jalnapurkar and J.E. Marsden, Stabilization of relative equilibria II. Regul. Chaotic Dyn. 3 (1999) 161-179. [CrossRef] [Google Scholar]
  22. S.M. Jalnapurkar and J.E. Marsden, Stabilization of relative equilibria. IEEE Trans. Automat. Control 45 (2000) 1483-1491. [CrossRef] [MathSciNet] [Google Scholar]
  23. H.K. Khalil, Nonlinear Systems. Prentice-Hall, Inc. Second Edition (1996). [Google Scholar]
  24. W.S. Koon and J.E. Marsden, The Poisson reduction of nonholonomic mechanical systems. Reports on Math. Phys. 42 (1998) 101-134. [CrossRef] [Google Scholar]
  25. P.S. Krishnaprasad, Lie-Poisson structures, dual-spin spacecraft and asymptotic stability. Nonl. Anal. Th. Meth. and Appl. 9 (1985) 1011-1035. [CrossRef] [Google Scholar]
  26. J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry. Springer-Verlag, Texts in Appl. Math. 17 (1999) Second Edition. [Google Scholar]
  27. B.M. Maschke, A.J. van der Schaft and P.C. Breedveld, An Intrinsic Hamiltonian Formulation of the Dynamics of LC-Circuits. IEEE Trans. Circuits and Systems 42 (1995) 73-82. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Ortega, A. Loria, P.J. Nicklasson and H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems. Springer-Verlag. Communication & Control Engineering Series (1998). [Google Scholar]
  29. R. Ortega, M.W. Spong, F. Gómez-Estern and G. Blankenstein, Stabilization of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Aut. Control (to appear). [Google Scholar]
  30. G. Sánchez De Alvarez, Controllability of Poisson control systems with symmetry. Amer. Math. Soc., Providence, RI., Contemp. Math. 97 (1989) 399-412. [Google Scholar]
  31. M.W. Spong, Underactuated mechanical systems, in Control Problems in Robotics and Automation, edited by B. Siciliano and K.P. Valavanis. Spinger-Verlag, Lecture Notes in Control and Inform. Sci. 230. [Presented at the International Workshop on Control Problems in Robotics and Automation: Future Directions Hyatt Regency, San Diego, California (1997).] [Google Scholar]
  32. A.J. van der Schaft, Hamiltonian dynamics with external forces and observations. Math. Syst. Theory 15 (1982) 145-168. [CrossRef] [Google Scholar]
  33. A.J. van der Schaft, System Theoretic Descriptions of Physical Systems, Doct. Dissertation, University of Groningen; also CWI Tract #3, CWI, Amsterdam (1983). [Google Scholar]
  34. A.J. van der Schaft, Stabilization of Hamiltonian systems. Nonlinear Anal. Theor. Meth. Appl. 10 (1986) 1021-1035. [CrossRef] [Google Scholar]
  35. A.J. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control. Springer-Verlag, Commun. Control Engrg. Ser. (2000). [Google Scholar]
  36. A.J. van der Schaft and B. Maschke, On the Hamiltonian formulation of nonholonomic mechanical systems. Rep. Math. Phys. 34 (1994) 225-233. [CrossRef] [MathSciNet] [Google Scholar]
  37. J.C. Willems, System theoretic models for the analysis of physical systems. Ricerche di Automatica 10 (1979) 71-106. [MathSciNet] [Google Scholar]
  38. C.A. Woolsey, Energy Shaping and Dissipation: Underwater Vehicle Stabilization Using Internal Rotors, Ph.D. Thesis. Princeton University (2001). [Google Scholar]
  39. C.A. Woolsey, A.M. Bloch, N.E. Leonard and J.E. Marsden, Physical dissipation and the method of controlled Lagrangians, in Proc. of the European Control Conference (2001) 2570-2575. [Google Scholar]
  40. C.A. Woolsey, A.M. Bloch, N.E. Leonard and J.E. Marsden, Dissipation and controlled Euler-Poincaré systems, in Proc. IEEE CDC (2001) 3378-3383. [Google Scholar]
  41. C.A. Woolsey and N.E. Leonard, Modification of Hamiltonian structure to stabilize an underwater vehicle, in Lagrangian and Hamiltonian Methods for Nonlinear Control: A Proc. Volume from the IFAC Workshop edited by N.E. Leonard and R. Ortega. Pergamon (2000) 175-176. [Google Scholar]
  42. D.V. Zenkov, A.M. Bloch, N.E. Leonard and J.E. Marsden, Matching and stabilization of the unicycle with rider, Lagrangian and Hamiltonian Methods for Nonlinear Control: A Proc. Volume from the IFAC Workshop, edited by N.E. Leonard and R. Ortega. Pergamon (2000) 177-178. [Google Scholar]
  43. D.V. Zenkov, A.M. Bloch and J.E. Marsden, Flat nonholonomic matching, Proc ACC 2002 (to appear). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.