Mickael D. Chekroun, Axel Kroner, Honghu Liu
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
.
Submitted April 2, 2017. Published July 28, 2017.
Math Subject Classifications: 35Q86, 35Q93, 35K58, 49J15, 49J20, 86-08.
Key Words: Nonlinear optimal control problems; Galerkin approximations;
Greenhouse gas emissions; Energy balance models;
Trotter-Kato approximations.
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Mickaël D. Chekroun Department of Atmospheric & Oceanic Sciences University of California Los Angeles, CA 90095-1565, USA email: mchekroun@atmos.ucla.edu | |
Axel Kröner Institut für Mathematik Humbolt-Universität Berlin 10099 Berlin, Germany email: axel.kroener@inria.fr | |
Honghu Liu Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061, USA email: hhliu@vt.edu |
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