Controlled polyhedral sweeping processes: Existence, stability, and optimality conditions
- Henrion, René
- Jourani, Abderrahim
- Mordukhovich, Boris S.
2020 Mathematics Subject Classification
- 49J52 49J53 49K24 49M25
- Sweeping process, moving polyhedra, existence of feasible solutions, qualitative stability, optimal control, discrete approximations, necessary optimality and suboptimality conditions
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 polyhedra, 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 suboptimality conditions for sweeping control systems with endpoint constrains by using constructive discrete approximations.
- J. Differential Equations, 366 (2023), pp. 408--443, DOI https://doi.org/10.1016/j.jde.2023.04.010 .