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EnglishIn this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually hard to compute) optimal control and the MPC approach is investigated theoretically in the mean-field limit. We establish a computable and provable bound on the difference in the cost functional for MPC controlled and optimal controlled system dynamics in the mean-field limit. The result of the present work extends previous findings for systems of ordinary differential equations. Numerical results in the mean-field setting are given.
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| Data di pubblicazione: | 2017 | |
| Titolo: | Performance bounds for the mean-field limit of constrained dynamics | |
| Autori: | Herty, Michael; Zanella, Mattia | |
| Rivista: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | |
| Parole Chiave: | Consensus models; Mean-field limits; Model predictive control; Analysis; Discrete Mathematics and Combinatorics; Applied Mathematics | |
| Abstract in inglese: | In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually hard to compute) optimal control and the MPC approach is investigated theoretically in the mean-field limit. We establish a computable and provable bound on the difference in the cost functional for MPC controlled and optimal controlled system dynamics in the mean-field limit. The result of the present work extends previous findings for systems of ordinary differential equations. Numerical results in the mean-field setting are given. | |
| Digital Object Identifier (DOI): | 10.3934/dcds.2017086 | |
| Handle: | http://hdl.handle.net/11392/2359989 | |
| Appare nelle tipologie: | 03.1 Articolo su rivista |
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