ERROR ESTIMATES FOR SECOND ORDER HAMILTON-JACOBI-BELLMAN EQUATIONS. APPROXIMATION OF PROBABILISTIC REACHABLE SETS

作者：Assellaou Mohamed^*; Bokanowski Olivier; Zidani Hasnaa

来源：Discrete and Continuous Dynamical Systems, 2015, 35(9): 3933-3964.

DOI：10.3934/dcds.2015.35.3933

• Error estimates for HJB equations
• numerical approximation
• un-bounded and discontinuous value function
• chance constraints
• level-set approach
• stochastic reachability analysis

This work deals with numerical approximations of unbounded and discontinuous value functions associated to some stochastic control problems. We derive error estimates for monotone schemes based on a Semi-Lagrangian method (or more generally in the form of a Markov chain approximation). A motivation of this study consists in approximating chance-constrained reachability sets. The latters will be characterized as level sets of a discontinuous value function associated to an adequate stochastic control problem. A precise analysis of the level-set approach is carried out and some numerical simulations are given to illustrate the approach.

• 出版日期2015-9