Machine learningOptimal Control

Pontryagin Maximum Principle

The Pontryagin Maximum Principle (PMP) is a fundamental theorem in optimal control theory providing necessary conditions for optimality of a control trajectory. Published by Lev Pontryagin in 1962, PMP generalizes the calculus of variations to control problems with constraints and is the theoretical foundation enabling solution of complex trajectory optimization problems from spacecraft missions to industrial process optimization.

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Sources

  1. Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mischenko, E. F. (1962). The Mathematical Theory of Optimal Processes. John Wiley & Sons. link

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ScholarGatePontryagin Maximum Principle (Pontryagin Maximum Principle). Retrieved 2026-06-04 from https://scholargate.app/en/control-theory/pontryagin-maximum-principle