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| ハミルトン-ヤコビ-ベルマン方程式× | Pontryagin Maximum Principle（ポン ujungin の最大値原理）× | |
|---|---|---|
| 分野 | 制御理論 | 制御理論 |
| 系統 | Machine learning | Machine learning |
| 提唱年≠ | 1957 | 1962 |
| 提唱者≠ | Richard Bellman | Lev Pontryagin |
| 種類 | algorithm | algorithm |
| 原典≠ | Bellman, R. (1957). Dynamic Programming. Princeton University Press. link ↗ | Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mischenko, E. F. (1962). The Mathematical Theory of Optimal Processes. John Wiley & Sons. link ↗ |
| 別名 | HJB Equation, Bellman Equation, Dynamic Programming | PMP, Optimal Control, Costate Method |
| 関連 | 3 | 3 |
| 概要≠ | The Hamilton-Jacobi-Bellman (HJB) equation is a partial differential equation characterizing the optimal cost-to-go function in dynamic programming. Developed by Bellman in 1957, HJB provides both necessary and sufficient conditions for optimality, enabling elegant theoretical analysis and numerical solutions for optimal control problems. HJB is fundamental to reinforcement learning, approximate dynamic programming, and real-time control. | 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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