101. Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics
- Author
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Bruno Hérissé, Julien Alexandre Dit Sandretto, Alexandre Chapoutot, Elliot Brendel, Etienne Bertin, ENSTA ParisTech UCP, Institut Polytechnique Paris, 828 bd des Maréchaux, 91762 Palaiseau cedex France, DTIS, ONERA, Université Paris Saclay [Palaiseau], and ONERA-Université Paris-Saclay
- Subjects
Interval Arithmetic ,0209 industrial biotechnology ,Information Systems and Management ,Optimal Control ,Computer science ,0211 other engineering and technologies ,Enclosure ,02 engineering and technology ,Interval (mathematics) ,Management Science and Operations Research ,Theoretical Computer Science ,[SPI]Engineering Sciences [physics] ,020901 industrial engineering & automation ,Simple (abstract algebra) ,Control theory ,Computer Science (miscellaneous) ,[INFO]Computer Science [cs] ,[MATH]Mathematics [math] ,Electrical and Electronic Engineering ,[PHYS]Physics [physics] ,021103 operations research ,Open-loop controller ,Optimal control ,Bounded Uncertainties ,Bounded function ,Trajectory ,Computer Vision and Pattern Recognition ,Realization (systems) ,Penalization ,Software - Abstract
International audience; An interval method based on Pontryagin's 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 validate an optimal guidance algorithm on a concrete system with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, and showcased on a simple system. These enclosures can guarantee that a given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties. Contrarily, the probability of failure may not be eliminated and the problem might need to be adjusted.
- Published
- 2021