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A Hamilton-Jacobi-Bellman Approach for the Numerical Computation of Probabilistic State Constrained Reachable Sets

  • Mohamed Assellaou
  • Athena PicarelliEmail author
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 29)

Abstract

Aim of this work is to characterise and compute the set of initial conditions for a system of controlled diffusion processes which allow to reach a terminal target satisfying pointwise state constraints with a given probability of success. Defining a suitable auxiliary optimal control problem, the characterization of this set is related to the solution of a particular Hamilton-Jacobi-Bellman equation. A semi-Lagrangian numerical scheme is defined and its convergence to the unique viscosity solution of the equation is proved. The validity of the proposed approach is then tested on some numerical examples.

Keywords

Viscosity solutions Reachable set Discontinuous cost functions Neumann boundary conditions 

Notes

Acknowledgements

The authors are sincerely grateful to Olivier Bokanowski and Hasnaa Zidani for their guidance at the early stage of this paper.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.ENSTA ParisTechPalaiseau CedexFrance
  2. 2.Department of Economical SciencesUniversity of VeronaVeronaItaly

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