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Communication Dans Un Congrès Année : 2021

Spatio-temporal constrained zonotopes for validation of optimal control problems

Résumé

A controlled system subject to dynamics with unknown but bounded parameters is considered. The control is defined as the solution of an optimal control problem, which induces hybrid dynamics. A method to enclose all optimal trajectories of this system is proposed. Using interval and zonotope based validated simulation and Pontryagin's Maximum Principle, a characterization of optimal trajectories, a conservative enclosure is constructed. The usual validated simulation framework is modified so that possible trajectories are enclosed with spatio-temporal zonotopes that simplify simulation through events. Then optimality conditions are propagated backward in time and added as constraints on the previously computed enclosure. The obtained constrained zonotopes form a thin enclosure of all optimal trajectories that is less susceptible to accumulation of error. This algorithm is applied on Goddard's problem, an aerospace problem with a bang-bang control.
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Dates et versions

hal-03197925 , version 1 (14-04-2021)
hal-03197925 , version 2 (31-03-2022)

Identifiants

  • HAL Id : hal-03197925 , version 2

Citer

Etienne Bertin, Bruno Hérissé, Julien Alexandre Dit Sandretto, Alexandre Chapoutot. Spatio-temporal constrained zonotopes for validation of optimal control problems. CDC 2021 : 60th Conference on Decision and Control, Dec 2021, Austin, United States. ⟨hal-03197925v2⟩
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