Representation of chance-constraints with strong asymptotic guarantees

Abstract : Given e ∈ (0, 1), a probability measure µ on Ω ⊂ Rp and a semi-algebraic set K ⊂ X × Ω, we consider the feasible set X(e) = {x ∈ X : Prob[(x, ω) ∈ K] ≥ 1 − e } associated with a chance-constraint. We provide a sequence outer approximations X_d(e) = {x ∈ X : h_d (x) ≥ 0}, d ∈ N, where h_d is a polynomial of degree d whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree d. We also obtain the strong and highly desirable asymptotic guarantee that λ(X_d(e) \X (e)) → 0 as d increases, where λ is the Lebesgue measure on X. Finallu inner approximations with same asymptotic guaranties are also obtained by considering the complement.
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Contributor : Jean Bernard Lasserre <>
Submitted on : Thursday, May 11, 2017 - 3:27:33 PM
Last modification on : Friday, January 10, 2020 - 9:10:08 PM
Long-term archiving on: Saturday, August 12, 2017 - 1:34:34 PM

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Jean-Bernard Lasserre. Representation of chance-constraints with strong asymptotic guarantees. IEEE Control Systems Letters, IEEE, 2017, 1 (1), pp.50--55. ⟨10.1109/LCSYS.2017.2704295 ⟩. ⟨hal-01487006v2⟩

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