Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems

Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems We consider an optimal stochastic control problem for which the payoff is the average of a given cost function. In a non ergodic setting, but under a suitable nonexpansivity condition, we obtain the existence of the limit value when the averaging parameter converges (namely the discount factor tends to zero for Abel mean or the horizon tends to infinity for the Cesàro mean). The main novelty of our result lies on the fact that this limit may depend on initial conditions of the control system (in contrast to what is usually obtained by other approaches). We also prove that the limit does not depend of the chosen average (Abel or Cesàro mean). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-013-9230-4
Publisher site
See Article on Publisher Site

Abstract

We consider an optimal stochastic control problem for which the payoff is the average of a given cost function. In a non ergodic setting, but under a suitable nonexpansivity condition, we obtain the existence of the limit value when the averaging parameter converges (namely the discount factor tends to zero for Abel mean or the horizon tends to infinity for the Cesàro mean). The main novelty of our result lies on the fact that this limit may depend on initial conditions of the control system (in contrast to what is usually obtained by other approaches). We also prove that the limit does not depend of the chosen average (Abel or Cesàro mean).

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2014

References

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