Set-Membership Method for Discrete Optimal Control

• Main Authors: Guyonneau, Rémy, Lagrange, Sébastien, Hardouin, Laurent, Lhommeau, Mehdi
• Other Authors: Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Université d'Angers (UA)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2013
• Subjects: Non-Linear Systems; Interval Analysis; Guaranteed Numerical Integration; Optimal control; [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering; Reykjavík; Iceland
• Online Access: https://hal.archives-ouvertes.fr/hal-00874162; https://hal.archives-ouvertes.fr/hal-00874162/document; https://hal.archives-ouvertes.fr/hal-00874162/file/ICINCO2013.pdf

International audience 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.