Advertisement

Minimal trajectories of nonconvex differential inclusions

  • H. Frankowska
  • B. Kaskosz
Contributed Papers
  • 52 Downloads

Abstract

We consider an optimization problem with endpoint constraints associated with a nonconvex differential inclusion. We give a necessary condition of the maximum principle type for a solution of the problem. Following the approach from Ref. 1, the condition is stated in terms of single-valued selections of the convexified right-hand side of the inclusion.

Key Words

Optimal control nonconvex differential inclusions endpoint constraints maximum principle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kaskosz, B., andŁojasiewicz, S.,A Maximum Principle for Generalized Control Systems, Nonlinear Analysis, Theory, Methods, and Applications, Vol. 9, pp. 109–130, 1985.Google Scholar
  2. 2.
    Rockafellar, R. T.,Existence and Duality Theorems for Convex Problems of Bolza, Transactions of the American Mathematical Society, Vol. 159, pp. 1–40, 1971.Google Scholar
  3. 3.
    Clarke, F. H.,Optimization and Nonsmooth Analysis, Wiley Interscience, New York, New York, 1983.Google Scholar
  4. 4.
    Clarke, F. H., andLoewen, P. D.,The Value Function in Optimal Control: Sensitivity, Controllability, and Time Optimality, SIAM Journal on Control and Optimization, Vol. 24, pp. 243–263, 1986.Google Scholar
  5. 5.
    Frankowska, H.,The Maximum Principle for an Optimal Solution to a Differential Inclusion with Endpoint Constraints, SIAM Journal on Control and Optimization, Vol. 25, pp. 145–157, 1987.Google Scholar
  6. 6.
    Aubin, J. P., andEkeland, I.,Applied Nonlinear Analysis, Wiley-Interscience, New York, New York, 1984.Google Scholar
  7. 7.
    Dubovickii, A. I., andMiljutin, A. M.,Extremum Problems with Constraints, Soviet Mathematics, Vol. 4, pp. 452–455, 1963.Google Scholar
  8. 8.
    Kaskosz, B., andŁojasiewicz, S.,On a Nonconvex, Nonsmooth Control System, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 39–53, 1988.Google Scholar
  9. 9.
    Ekeland, I.,On the Variational Principle, Journal of Mathematical Analysis and Applications, Vol. 47, pp. 324–353, 1974.Google Scholar
  10. 10.
    Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • H. Frankowska
    • 1
  • B. Kaskosz
    • 2
  1. 1.CEREMADE, Université de Paris-DauphineParisFrance
  2. 2.Department of MathematicsUniversity of Rhode IslandKingston

Personalised recommendations