Pontryagin Maximum Principle for Control Systems on Infinite Dimensional Manifolds

TL;DR

This paper develops a mathematical framework for deriving the Pontryagin Maximum Principle in infinite-dimensional manifold control systems, especially those involving PDEs with symmetry, using nonsmooth analysis and Lagrangian charts.

Contribution

It introduces a novel approach combining nonsmooth analysis and Lagrangian charts to analyze optimal control problems on infinite-dimensional manifolds.

Findings

Established a maximum principle for control systems on infinite-dimensional manifolds.

Applied nonsmooth analysis methods to study global variations of trajectories.

Provided a framework for optimization in PDE control problems with symmetry.

Abstract

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