Set-Membership Method for Discrete Optimal Control

Rémy Guyonneau (1) , Sébastien Lagrange (1) , Laurent Hardouin (1) , Mehdi Lhommeau (1)

1 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés

The objective of this paper is twofold: to propose a new approach for computing Ct0,tf 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 t0, and, using that work and given a cost function, to estimate an enclosure of the optimal control vector from an initial state of Ct0 ,t f to the target. Whereas classical methods do not provide any guaranteed on the set of state vectors that belong to the Ct0 ,t f , interval analysis and guarantee numerical integration allow us to avoid any indetermination. We present an algorithm able to provide guaranteed characterizations of the inner C− t0,tf and an the outer C+ of C , such that C− ⊆ C ⊆ C+ . In addition to that, the presented algorithm is t0,tf t0,tf t0,tf t0,tf t0,tf extended in order enclose the optimal control vector of the system, form an initial state to the target, by a set of trajectories.

Domaines: Optimisation et contrôle [math.OC]

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, ICINCO, 2013, Reykjavik, Iceland. 2013, ⟨10.5220/0004458001930200⟩. ⟨hal-01113457⟩