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- Title
GALERKIN APPROXIMATIONS OF NONLINEAR OPTIMAL CONTROL PROBLEMS IN HILBERT SPACES.
- Authors
CHEKROUN, MICKAËL D.; KRÖNER, AXEL; 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 S².
- Subjects
GALERKIN methods; APPROXIMATION theory; OPTIMAL control theory; NONLINEAR control theory; HILBERT space
- Publication
Electronic Journal of Differential Equations, 2017, Vol 2017, Issue 146-199, p1
- ISSN
1550-6150
- Publication type
Article