Spatio-temporal constrained zonotopes for validation of optimal control problems | IEEE Conference Publication | IEEE Xplore
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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 ind...Show More

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.
Date of Conference: 14-17 December 2021
Date Added to IEEE Xplore: 01 February 2022
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Conference Location: Austin, TX, USA

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