Calculus of Variations and Geometric Measure Theory

M. Bardi - G. Terrone

Periodic homogenization of deterministic control problems via limit occupational measures

created by bardi on 08 May 2014
modified on 02 Jan 2016


Published Paper

Inserted: 8 may 2014
Last Updated: 2 jan 2016

Journal: CIM Series in Mathematical Sciences
Volume: 1
Pages: 105-116
Year: 2015
Doi: 10.1007/978-3-319-16118-1$\_$7

in ``Dynamics, Games, and Science", J.-P. Bourguignon, R. Jeltsch, A. Pinto, M. Viana eds., Springer.


We consider optimal control problems where the dynamical system and the running cost are affected by fast periodic oscillations of the state variables. We show that, under suitable controllability and structure assumptions, it is possible to describe the limiting optimal control problem. The proofs make use of results in the theory of homogenization and singular perturbations of Hamilton-Jacobi equations.

Keywords: Homogenization, optimal control, limit occupational measures