The linear programming approach to deterministic optimal control problems

Daniel Hernández-Hernández; Onésimo Hernández-Lerma; Michael Taksar

Applicationes Mathematicae (1996)

  • Volume: 24, Issue: 1, page 17-33
  • ISSN: 1233-7234

Abstract

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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 * ) ≤ inf ( P ) ≤ J * ( t , x ) . Then we give conditions under which (i) there is no duality gap

How to cite

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Hernández-Hernández, Daniel, Hernández-Lerma, Onésimo, and Taksar, Michael. "The linear programming approach to deterministic optimal control problems." Applicationes Mathematicae 24.1 (1996): 17-33. <http://eudml.org/doc/219148>.

@article{Hernández1996,
abstract = {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 $\sup (P^*) \le \inf (P)\le J^*(t,x)$. Then we give conditions under which (i) there is no duality gap},
author = {Hernández-Hernández, Daniel, Hernández-Lerma, Onésimo, Taksar, Michael},
journal = {Applicationes Mathematicae},
keywords = {linear programming (in infinite-dimensional spaces); duality theory; optimal control; optimal problem in infinite-dimensional spaces; linear programming},
language = {eng},
number = {1},
pages = {17-33},
title = {The linear programming approach to deterministic optimal control problems},
url = {http://eudml.org/doc/219148},
volume = {24},
year = {1996},
}

TY - JOUR
AU - Hernández-Hernández, Daniel
AU - Hernández-Lerma, Onésimo
AU - Taksar, Michael
TI - The linear programming approach to deterministic optimal control problems
JO - Applicationes Mathematicae
PY - 1996
VL - 24
IS - 1
SP - 17
EP - 33
AB - 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 $\sup (P^*) \le \inf (P)\le J^*(t,x)$. Then we give conditions under which (i) there is no duality gap
LA - eng
KW - linear programming (in infinite-dimensional spaces); duality theory; optimal control; optimal problem in infinite-dimensional spaces; linear programming
UR - http://eudml.org/doc/219148
ER -

References

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  1. [1] E. J. Anderson and P. Nash, Linear Programming in Infinite-Dimensional Spaces, Wiley, Chichester, 1989. 
  2. [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. [3] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975. 
  4. [4] W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, New York, 1992. Zbl0773.60070
  5. [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. [6] W. H. Fleming, Convex duality approach to the optimal control of diffusions, SIAM J. Control Optim. 27 (1989), 1136-1155. Zbl0693.93082
  7. [7] O. Hernández-Lerma, Existence of average optimal policies in Markov control processes with strictly unbounded costs, Kybernetika (Prague) 29 (1993), 1-17. Zbl0792.93120
  8. [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. Zbl0820.90124
  9. [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. Zbl0799.90120
  10. [10] J. L. Kelley, General Topology, Van Nostrand, New York, 1957. 
  11. [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. Zbl0443.49015
  12. [12] J. E. Rubio, Control and Optimization, Manchester Univ. Press, Manchester, 1986. Zbl1095.49500
  13. [13] R. H. Stockbridge, Time-average control of martingale problems: a linear programming formulation, Ann. Probab. 18 (1990), 206-217. Zbl0699.49019

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