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| 庞特里亚金最大值原理× | 汉密尔顿-雅可比-贝尔曼方程× | |
|---|---|---|
| 领域 | 控制理论 | 控制理论 |
| 方法族 | Machine learning | Machine learning |
| 起源年份≠ | 1962 | 1957 |
| 提出者≠ | Lev Pontryagin | Richard Bellman |
| 类型 | algorithm | algorithm |
| 开创性文献≠ | Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mischenko, E. F. (1962). The Mathematical Theory of Optimal Processes. John Wiley & Sons. link ↗ | Bellman, R. (1957). Dynamic Programming. Princeton University Press. link ↗ |
| 别名 | PMP, Optimal Control, Costate Method | HJB Equation, Bellman Equation, Dynamic Programming |
| 相关 | 3 | 3 |
| 摘要≠ | 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. | 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. |
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