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Spatio-temporal constrained zonotopes for validation of optimal control problems

Abstract : 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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Preprints, Working Papers, ...
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Contributor : Etienne Bertin <>
Submitted on : Wednesday, April 14, 2021 - 12:31:25 PM
Last modification on : Monday, May 17, 2021 - 12:35:33 AM
Long-term archiving on: : Thursday, July 15, 2021 - 6:27:39 PM


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  • HAL Id : hal-03197925, version 1


Etienne Bertin, Bruno Hérissé, Julien Alexandre Dit Sandretto, Alexandre Chapoutot. Spatio-temporal constrained zonotopes for validation of optimal control problems. 2021. ⟨hal-03197925⟩



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