Pontryagin Maximum Principle
In this chapter we prove the fundamental necessary condition of optimality for optimal control problems — Pontryagin Maximum Principle (PMP). In order to obtain a coordinate-free formulation of PMP on manifolds, we apply the technique of Symplectic Geometry developed in the previous chapter. The first classical version of PMP was obtained for optimal control problems in ℝ n by L. S. Pontryagin and his collaborators .
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