Some optimal control applications of real-analytic stratifications and desingularization

Héctor Sussmann

Banach Center Publications (1998)

  • Volume: 44, Issue: 1, page 211-232
  • ISSN: 0137-6934

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Sussmann, Héctor. "Some optimal control applications of real-analytic stratifications and desingularization." Banach Center Publications 44.1 (1998): 211-232. <http://eudml.org/doc/208885>.

@article{Sussmann1998,
author = {Sussmann, Héctor},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {211-232},
title = {Some optimal control applications of real-analytic stratifications and desingularization},
url = {http://eudml.org/doc/208885},
volume = {44},
year = {1998},
}

TY - JOUR
AU - Sussmann, Héctor
TI - Some optimal control applications of real-analytic stratifications and desingularization
JO - Banach Center Publications
PY - 1998
VL - 44
IS - 1
SP - 211
EP - 232
LA - eng
UR - http://eudml.org/doc/208885
ER -

References

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  1. [1] P. Brunovsky, Every normal linear system has a regular synthesis, Math. Slovaca 28 (1978), 81-100. Zbl0369.49013
  2. [2] P. Brunovsky, Existence of regular synthesis for general problems, J. Differential Equations 38 (1980), 317-343. Zbl0417.49030
  3. [3] R. Hermann, On the accessibility problem in control theory, in: International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, J. P. LaSalle and S. Lefschetz (eds.), Academic Press, New York, 1963, 325-332. 
  4. [4] S. Łojasiewicz Jr., and H. J. Sussmann, Some examples of reachable sets and optimal cost functions that fail to be subanalytic, SIAM J. Control Optim. 23 (1985), 584-598. Zbl0569.49029
  5. [5] T. Nagano, Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan 18 (1966), 398-404. Zbl0147.23502
  6. [6] P. Stefan, Accessibility and Singular Foliations, Ph. D. Thesis, University of Warwick, 1973. 
  7. [7] H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188. Zbl0274.58002
  8. [8] H. J. Sussmann, Single-input observability of continuous-time systems, Math. Systems Theory 12 (1979), 371-393. Zbl0422.93019
  9. [9] H. J. Sussmann, A weak regularity theorem for real analytic optimal control problems, Rev. Mat. Iberoamericana 2 (1986), 307-317. Zbl0638.49018
  10. [10] H. J. Sussmann, Why real analyticity is important in control theory, in: Perspectives in Control Theory, Proceedings of the Sielpia Conference, Sielpia, Poland, 1988, B. Jakubczyk, K. Malanowski, and W. Respondek (eds.), Birkäuser, Boston, 1990, 315-340. 
  11. [11] H. J. Sussmann, A strong version of the Łojasiewicz Maximum Principle, in: Optimal Control of Differential Equations, N. H. Pavel (ed.), Lecture Notes in Pure and Appl. Math. 160, M. Dekker, New York, 1994, 293-309. Zbl0816.49018
  12. [12] H. J. Sussmann, A strong version of the Maximum Principle under weak hypotheses, in: Proc. 33rd IEEE Conf. Decision and Control, Orlando, FL, 1994, IEEE Publications, 1994, 1950-1956. 
  13. [13] H. J. Sussmann, A strong maximum principle for systems of differential inclusions, in: Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, Dec. 1996, IEEE Publications, 1996, 1809-1814. 
  14. [14] H. J. Sussmann, Multidifferential calculus: chain rule, open mapping and transversal intersection theorems, to appear in: Optimal Control: Theory, Algorithms, and Applications, W. W. Hager and P. M. Pardalos (eds.), Kluwer Academic Publishers, 1997. 
  15. [15] M. I. Zelikin and V. F. Borisov, Theory of Chattering Control, with Applications to Astronautics, Robotics, Economics and Engineering, Birkhäuser, Boston, 1994. Zbl0820.70003

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