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We discuss a mathematical framework for analysis of optimal control problemson infinite-dimensional manifolds. Such problems arise in study of optimizationfor partial differential equations with some symmetry. It is shown that somenonsmooth analysis methods and Lagrangian charts techniques can be used forstudy of global variations of optimal trajectories of such control systems andderivation of maximum principle for them.

Pontryagin Maximum Principle for Control Systems on Infinite Dimensional Manifolds