Pontryagin Maximum Principle

  • Andrei A. Agrachev
  • Yuri L. Sachkov
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 87)


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 [15].


Hamiltonian System Optimal Control Problem Hamiltonian Function Cotangent Bundle Admissible Control 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Andrei A. Agrachev
    • 1
  • Yuri L. Sachkov
    • 2
  1. 1.SISSA-ISASTriesteItaly
  2. 2.Program Systems InstitutePereslavl-ZalesskyRussia

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