Pontryagin maximum principle for control systems on infinite dimensional manifolds. (English) Zbl 1312.49023
Summary: We discuss a mathematical framework for the analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in the study of dynamic optimization for partial differential equations with some symmetry. We develop nonsmooth analysis methods and Lagrangian charts techniques which can be used for the study of global variations of optimal trajectories of such control systems and the derivation of a maximum principle for them.
MSC:
| 49K27 | Optimality conditions for problems in abstract spaces |
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 49Q99 | Manifolds and measure-geometric topics |
| 58E25 | Applications of variational problems to control theory |
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