Optimal sampled-data control, and generalizations on time scales

Loïc Bourdin (1) , Emmanuel Trélat (2)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for which the state variable evolves on a given time scale (arbitrary non-empty closed subset of R), and the control variable evolves on a smaller time scale. Sampled-data systems are then a particular case. Our proof is based on the construction of appropriate needle-like variations and on the Ekeland variational principle.

Mots clés: time scale; Pontryagin maximum principle; sampled-data; optimal control

Domaines: Optimisation et contrôle [math.OC]

Loïc Bourdin, Emmanuel Trélat. Optimal sampled-data control, and generalizations on time scales. Mathematical Control and Related Fields, 2016, 6 (1), pp.53--94. ⟨hal-01110750v2⟩