Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control

  title={Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control},
  author={Olivier Alvarez and Martino Bardi},
  journal={SIAM J. Control and Optimization},
Viscosity solutions methods are used to pass to the limit in some penalization problems for rst order and second order, degenerate parabolic, Hamilton-Jacobi-Bellman equations. This characterizes the limit of the value functions of singularly perturbed optimal control problems for nonlinear deterministic systems and controlled degenerate diiusions, respectively. The results cover also cases where the usual order reduction method does not give the correct limit, and diiusion processes with fast… CONTINUE READING
Highly Cited
This paper has 146 citations. REVIEW CITATIONS


Publications citing this paper.
Showing 1-10 of 39 citations

147 Citations

Citations per Year
Semantic Scholar estimates that this publication has 147 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 37 references

On ergodic stochastic control

  • M. Arisawa, P.-L. Lions
  • Comm. Partial Di erential Equa- tions 23
  • 1998
Highly Influential
9 Excerpts

Singular perturbation of a nite horizon problem with state-space constraints

  • F. Bagagiolo, M. Bardi
  • SIAM J. Control Optim. 36
  • 1998
Highly Influential
10 Excerpts

Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations

  • M. Bardi, I. Capuzzo-Dolcetta
  • Birkhauser, Boston
  • 1997
Highly Influential
9 Excerpts

The perturbed test function method for viscosity solutions of nonlinear P.D.E

  • L. Evans
  • Proc. Roy. Soc. Edinburgh Sect. A
  • 1989
Highly Influential
8 Excerpts

Perturbation methods in optimal control, Wiley/Gauthier-Villars, Chichester

  • A. Bensoussan
  • 1988
Highly Influential
9 Excerpts

Homogeneization of Hamilton-Jacobi equa- tions

  • P.-L. Lions, G. Papanicolaou, S.R.S. Varadhan
  • Unpublished
  • 1986
Highly Influential
4 Excerpts

Invariant measures of di erential inclusions applied to singular perturbations

  • Z. Artstein
  • J. Di erential Equations 152
  • 1999
Highly Influential
6 Excerpts

Limits of singularly perturbed control problems with statistical dynamics of fast motions

  • A. Vigodner
  • SIAM J. Control Optim
  • 1997
Highly Influential
4 Excerpts