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  • Print publication year: 2019
  • Online publication date: October 2019

8 - Endpoint Map and Exponential Map

Summary

In this chapter we introduce the endpoint map that associates a control function $u$ with the final point of the admissible trajectory associated with $u$ and starting from a given point. This viewpoint permits us to interpret candidate abnormal length-minimizers as critical points of the endpoint map. It is then natural to introduce Lagrange multipliers. First-order conditions recover Pontryagin extremals, while second-order conditions give new information.

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