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1996-1997 | 24 | 1 | 17-33
Tytuł artykułu

The linear programming approach to deterministic optimal control problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a deterministic optimal control problem (OCP) with value function, say $J^*$, we introduce a linear program $(P)$ and its dual $(P^*)$ whose values satisfy $\sup(P^*) \leq\inf(P)\leq J^*(t,x)$. Then we give conditions under which (i) there is no duality gap
Rocznik
Tom
24
Numer
1
Strony
17-33
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-02-09
poprawiono
1995-08-29
Twórcy
  • Departamento de Matemáticas, UAM-I, Apartado Postal 55-534, México D.F., Mexico
  • Departamento de Matemáticas, CINVESTAV-IPN, Apartado Postal 14-740, 07000 México D.F., Mexico
  • Department of Applied Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794, U.S.A.
Bibliografia
  • [1] E. J. Anderson and P. Nash, Linear Programming in Infinite-Dimensional Spaces, Wiley, Chichester, 1989.
  • [2] W. H. Fleming, Generalized solutions and convex duality in optimal control, in: Partial Differential Equations and the Calculus of Variations, Vol. I, F. Colombini et al. (eds.), Birkhäuser, Boston, 1989, 461-471.
  • [3] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975.
  • [4] W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, New York, 1992.
  • [5] W. H. Fleming and D. Vermes, Generalized solutions in the optimal control of diffusions, IMA Vol. Math. Appl. 10, W. H. Fleming and P. L. Lions (eds.), Springer, New York, 1988, 119-127.
  • [6] W. H. Fleming, Convex duality approach to the optimal control of diffusions, SIAM J. Control Optim. 27 (1989), 1136-1155.
  • [7] O. Hernández-Lerma, Existence of average optimal policies in Markov control processes with strictly unbounded costs, Kybernetika (Prague) 29 (1993), 1-17.
  • [8] O. Hernández-Lerma and D. Hernández-Hernández, Discounted cost Markov decision processes on Borel spaces: The linear programming formulation, J. Math. Anal. Appl. 183 (1994), 335-351.
  • [9] O. Hernández-Lerma and J. B. Lasserre, Linear programming and average optimality of Markov control processes on Borel spaces-unbounded costs, SIAM J. Control Optim. 32 (1994), 480-500.
  • [10] J. L. Kelley, General Topology, Van Nostrand, New York, 1957.
  • [11] R. M. Lewis and R. B. Vinter, Relaxation of optimal control problems to equivalent convex programs, J. Math. Anal. Appl. 74 (1980), 475-493.
  • [12] J. E. Rubio, Control and Optimization, Manchester Univ. Press, Manchester, 1986.
  • [13] R. H. Stockbridge, Time-average control of martingale problems: a linear programming formulation, Ann. Probab. 18 (1990), 206-217.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i1p17bwm
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