Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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OPTIMAL CONDITIONS FOR ENDPOINT CONSTRAINED OPTIMAL CONTROL

  • Kim, Kyung-Eung (DEPARTMENT OF MATHEMATICS SCHOOL OF THE LIBERAL ARTS SEOUL NATIONAL UNIVERSITY OF TECHNOLOGY)
  • Published : 2008.08.31
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Abstract

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

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References

  1. L. Cesari, Optimization-Theory and Applications, Problems with ordinary differential equations. Applications of Mathematics (New York), 17. Springer-Verlag, New York, 1983
  2. H. Frankowska, Contingent cones to reachable sets of control systems, SIAM J. Control Optim. 27 (1989), no. 1, 170-198 https://doi.org/10.1137/0327010
  3. K. E. Kim, Necessary conditions for optimal control problem under state constraints, J. Korean Math. Soc. 42 (2005), no. 1, 17-35 https://doi.org/10.4134/JKMS.2005.42.1.017
  4. P. D. Loewen, Optimal Control via Nonsmooth Analysis, CRM Proceeding & Lecture Notes, American Mathematical Society, 1993
  5. R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Grundlehren der Mathematischen Wissenschaften, 317. Springer-Verlag, Berlin, 1998
  6. R. B. Vinter, Optimal Control Birkhauser, Boston, 2000