Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NECESSARY CONDITIONS FOR OPTIMAL CONTROL PROBLEM UNDER STATE CONSTRAINTS

  • KIM KYUNG-EUNG (Department of Mathematics School of the Liberal Arts Seoul National University of Technology)
  • Published : 2005.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

Keywords

References

  1. J.-P. Aubin and A. Cellina, Differential Inclusion, Aundlehren der Math. Wiss., Springer-Verlag, 1984
  2. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, Basel, Berlin, 1990
  3. J.-P. Aubin, H. Frankowska and C. Olech, Controllability of convex process, SIAM J. Control Optim. 24 (1986), 1192-1211 https://doi.org/10.1137/0324072
  4. L. Cesari, Optimization Theory and Application, Springer-Verlag, New-York, Hei- delberg, Berlin, 1983
  5. F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, 1983
  6. N. Dunford and J. T. Schwartz, Linear Operator I, Wiley, N.Y., 1957
  7. H. Frankowska, Contingent cones to reachable sets of control systems, SIAM J. Control Optim. 27 (1989), 170-198 https://doi.org/10.1137/0327010
  8. P. D. Loewen and R. T. Rockafellar, The adjoint arc in nonsmooth optimization, Trans. Amer. Math. Soc. 325 (1991), 39-72 https://doi.org/10.2307/2001658
  9. E. J. Mcshane, Integration, Princeton University Press, 1944
  10. R. T. Rockafellar, Integrals which are convex functionals, II, Pacific J. Math. 39 (1971), no. 2, 439-469 https://doi.org/10.2140/pjm.1971.39.439
  11. R. B. Vinter and G. Pappas, A Maximum Principle for Nonsmooth Optimal- Control Problems with State Constraints, J. Math. Anal. Appl. 89 (1982), 212- 232 https://doi.org/10.1016/0022-247X(82)90099-3