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	Pontryagin Maximum Principle（ポン ujungin の最大値原理）	モデル予測制御
分野	制御理論	制御理論
系統	Machine learning	Machine learning
提唱年	1962	1978
提唱者	Lev Pontryagin	Jacques Richalet
種類	algorithm	algorithm
原典	Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mischenko, E. F. (1962). The Mathematical Theory of Optimal Processes. John Wiley & Sons.	Richalet, J., Rault, A., Testud, J., & Papon, J. (1978). Model predictive heuristic control. Automatica, 14(5), 413-428.
別名	PMP, Optimal Control, Costate Method	MPC, Receding Horizon Control
関連	3	5
概要	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.	Model Predictive Control (MPC) is an advanced control strategy that uses an explicit process model to predict future system behavior over a finite horizon and solves an optimization problem at each control step. First formalized by Richalet et al. in 1978, MPC has become the dominant approach in process control industries, from chemical plants to autonomous vehicles, because it naturally handles constraints and can optimize multiple objectives simultaneously.