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| Phương trình Hamilton-Jacobi-Bellman× | Nguyên lý cực đại Pontryagin× | |
|---|---|---|
| Lĩnh vực | Lý thuyết điều khiển | Lý thuyết điều khiển |
| Họ | Machine learning | Machine learning |
| Năm ra đời≠ | 1957 | 1962 |
| Người khởi xướng≠ | Richard Bellman | Lev Pontryagin |
| Loại | algorithm | algorithm |
| Công trình gốc≠ | 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 ↗ |
| Tên gọi khác | HJB Equation, Bellman Equation, Dynamic Programming | PMP, Optimal Control, Costate Method |
| Liên quan | 3 | 3 |
| Tóm tắt≠ | 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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