Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

Citation:

Chekroun, Mickaël D., Axel Kröner, and Honghu Liu. 2017. “Galerkin approximations of nonlinear optimal control problems in Hilbert spaces.” Electronic Journal of Differential Equations 2017 (189): 1-40.

Date Published:

2017

Abstract:

Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach
relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary.   The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere S2.  

Publisher's version

Last updated on 04/25/2020