Differential inclusions with free time

Philip D. Loewen; Frank H. Clarke; Richard B. Vinter

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 6, page 573-593
  • ISSN: 0294-1449

How to cite

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Loewen, Philip D., Clarke, Frank H., and Vinter, Richard B.. "Differential inclusions with free time." Annales de l'I.H.P. Analyse non linéaire 5.6 (1988): 573-593. <http://eudml.org/doc/78165>.

@article{Loewen1988,
author = {Loewen, Philip D., Clarke, Frank H., Vinter, Richard B.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Mayer type; differential inclusion; state- and endpoints-constraints; Hamilton necessary optimality conditions},
language = {eng},
number = {6},
pages = {573-593},
publisher = {Gauthier-Villars},
title = {Differential inclusions with free time},
url = {http://eudml.org/doc/78165},
volume = {5},
year = {1988},
}

TY - JOUR
AU - Loewen, Philip D.
AU - Clarke, Frank H.
AU - Vinter, Richard B.
TI - Differential inclusions with free time
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 6
SP - 573
EP - 593
LA - eng
KW - Mayer type; differential inclusion; state- and endpoints-constraints; Hamilton necessary optimality conditions
UR - http://eudml.org/doc/78165
ER -

References

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  1. [1] L.D. Berkovitz, Optimal Control Theory, Springer Verlag, New York, 1974. Zbl0295.49001MR372707
  2. [2] F.H. Clarke, Optimization and Nonsmooth Analysis, New York, Wiley-Interscience, 1983. Zbl0582.49001MR709590
  3. [3] F.H. Clarke, Perturbed Optimal Control Probelms, I.E.E.E. Trans. Auto. Control, Vol. AC-31, 1986, pp. 535-542. Zbl0587.49026MR839082
  4. [4] F.H. Clarke and P.D. Loewen, The Value Function in Optimal Control: Sensitivity, Controllability, and Time-Optimality, S.I.A.M. J. Control Optim., Vol. 24, 1986, pp. 243-263. Zbl0601.49020MR826515
  5. [5] F.H. Clarke and P.D. Loewen, State Constraints in Optimal Control: a Case Study in Proximal Normal Analysis, S.I.A.M. J. Control Optim., Vol. 25, 1987, pp. 1440- 1456. Zbl0637.49007MR912450
  6. [6] F.H. Clarke and R.B. Vinter, Optimal Multiprocesses, S.I.A.M. J. Control Optim. (to appear). Zbl0684.49007MR1009338
  7. [7] F.H. Clarke and R.B. Vinter, Applications of Optimal Multiprocesses, S.I.A.M. J. Control Optim. (to appear). Zbl0695.49014MR1009337
  8. [8] R.V. Gamkrelidze, On Some Extremal Problems in the Theory of Differential Equations with Applications to the Theory of Optimal Control, S.I.A.M. J. Control, Vol. 3, 1965, pp. 106-128. Zbl0296.49009MR192937
  9. [9] A.D. Ioffe and V.M. Tikhomirov, Theory of Extremal Probelms, Amsterdam,North Holland, 1979. Zbl0407.90051
  10. [10] P.D. Loewen, The Proximal Subgradient Formula in Banach Space, Canadian Math. Bulletin, to appear. Zbl0622.46018MR956368
  11. [11] L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mischenko, The Mathematical Theory of Optimal Processes, Trans. K. N. TRIROGOFF and L. W. NEUSTADT Eds., Wiley, New York, 1962. Zbl0882.01027MR166037
  12. [12] R.T. Rockafellar, Proximal Subgradients, Marginal Values, and Augmented Lagrangians in Nonconvex Optimization, Math. of Oper. Res., Vol. 6, 1982, pp. 427-437. Zbl0492.90073MR629642
  13. [13] R.T. Rockafellar, Extensions of Subgradient Calculus with Applications to Optimization, Nonlinear Analysis, Vol. 9, 1985, pp. 665-698. Zbl0593.49013MR796082
  14. [14] R.B. Vinter and G. Pappas, A Maximum Principle for Non-Smooth Optimal Control Problems with State Constraints, J.M.A.A., Vol. 89, 1982, pp. 212-232. Zbl0519.49011MR672197
  15. [15] J. Warga, Optimal Control of Differential and Functional Equations, New York, Academic Press, 1972. Zbl0253.49001MR372708

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