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Set-Membership Method for Discrete Optimal Control

Abstract : The objective of this paper is twofold. First we propose a new approach for computing C t 0 ,t f the subset of initial states of a system from which there exists at least one trajectory reaching a target T in a finite time t f from a time t 0. This is done considering a discrete time t k and a control vector continuous over a time [t k−1 ,t k ]. Then, using the previously mentioned work and given a cost function, the objective is to estimate an enclosure of the discrete optimal control vector from an initial state of C t 0 ,t f to the target. Whereas classical methods do not provide any guaranty on the set of state vectors that belong to the C t 0 ,t f , interval analysis and guaranteed numerical integration allow us to avoid any indetermination. We present an algorithm able to provide guaranteed characterizations of the inner C − t 0 ,t f and an the outer C + t 0 ,t f of C t 0 ,t f , such that C − t 0 ,t f ⊆ C t 0 ,t f ⊆ C + t 0 ,t f. In addition to that, the presented algorithm is extended in order enclose the discrete optimal control vector of the system, form an initial state to the target, by a set of discrete trajectories.
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https://hal.archives-ouvertes.fr/hal-00874162
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Submitted on : Tuesday, January 19, 2021 - 4:50:13 PM
Last modification on : Wednesday, October 20, 2021 - 3:19:29 AM
Long-term archiving on: : Tuesday, April 20, 2021 - 7:52:48 PM

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  • HAL Id : hal-00874162, version 1

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Rémy Guyonneau, Sébastien Lagrange, Laurent Hardouin, Mehdi Lhommeau. Set-Membership Method for Discrete Optimal Control. 10th International Conference on Informatics in Control, Automation and Robotics, Jul 2013, Reykjavík, Iceland. ⟨hal-00874162⟩

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