Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

Keywords: optimal control, Pontryagin principle, interval arithmetics, bounded uncertainties, penalization

Abstract

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

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Author Biographies

Elliot Brendel, ONERA, France

DTIS/NPGA

Bruno Hérissé, ONERA, France

DTIS/NPGA

Julien Alexandre dit Sandretto, ENSTA, France

U2IS

Alexandre Chapoutot, ENSTA, France

U2IS

Published
2021-02-03
How to Cite
Bertin, E., Brendel, E., Hérissé, B., Alexandre dit Sandretto, J., & Chapoutot, A. (2021). Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics. Acta Cybernetica, 25(1), 101-125. https://doi.org/10.14232/actacyb.285798