2016
DOI: 10.1137/15m1023737
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State-Constrained Stochastic Optimal Control Problems via Reachability Approach

Abstract: Abstract. This paper deals with a class of stochastic optimal control problems (SOCP) in presence of state-constraints. It is well-known that for such problems the value function is, in general, discontinuous and its characterization by a Hamilton-Jacobi equation requires additional assumptions involving an interplay between the boundary of the set of constraints and the dynamics of the controlled system. Here, we give a characterization of the epigraph of the value function without assuming the usual controll… Show more

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Cited by 27 publications
(51 citation statements)
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“…They extend the state space by a conditional probability process in order to reduce the problem to a standard stochastic target problem. Bokanowski, Picarelli and Zidani [1] reformulate a stochastic control problem with a state constraint as a target problem by introducing a conditional expectation process as a new controlled variable.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…They extend the state space by a conditional probability process in order to reduce the problem to a standard stochastic target problem. Bokanowski, Picarelli and Zidani [1] reformulate a stochastic control problem with a state constraint as a target problem by introducing a conditional expectation process as a new controlled variable.…”
Section: Introductionmentioning
confidence: 99%
“…For λ < 1 there exist no optimal stopping times and for λ ≥ 1 stopping immediately τ = 0 is optimal. But for λ = 1 all stopping times τ a that embed the distributiona 2 δ −1 + (1 − a)δ 0 + a 2 δ 1 , a ∈ [0,1] into W are also optimal. It holds that E[τ a ] = a.…”
mentioning
confidence: 99%
“…The optimal control problem under state constraint has been studied by different papers (see e.g. [3] and the references therein), it can be formulated as follows:…”
Section: An Optimal Control Problem Under Constraints In Continuous Timementioning
confidence: 99%
“…), or one can use the so-called level-set approach to reformulate it into an optimization problem over a family of (unconstrained) singular control problems (see e.g. Bokanowski, Picarelli and Zidani [3] and the references therein). In the second main approach, one looks for necessary optimality conditions in the form of Pontryagin's maximum principle, involving a Lagrange multiplier, see e.g.…”
Section: Introductionmentioning
confidence: 99%
“…This objective is achieved at the price of augmenting the state and control space by additional components and considering unbounded controls. More precisely, following the ideas developed in [24] for the case of a constraint holding pointwise in time almost surely, our approach relies on two main steps. The first one consists in building on the equivalence results developed in [25,26] to convert, by means of the martingale representation theorem, the original problem into a stochastic target problem involving almost-sure constraints and unbounded controls.…”
Section: Introductionmentioning
confidence: 99%