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Article Dans Une Revue Journal of Differential Equations Année : 2023

Controlled polyhedral sweeping processes: Existence, stability, and optimality conditions

Résumé

This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhe-dra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and subop-timality conditions for sweeping control systems with endpoint constrains by using constructive discrete approximations.

Dates et versions

hal-04356673 , version 1 (20-12-2023)

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René Henrion, Abderrahim Jourani, Boris Mordukhovich. Controlled polyhedral sweeping processes: Existence, stability, and optimality conditions. Journal of Differential Equations, 2023, 366, pp.408-443. ⟨10.1016/j.jde.2023.04.010⟩. ⟨hal-04356673⟩
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