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| 汉密尔顿-雅可比-贝尔曼方程× | 线性二次调节器× | |
|---|---|---|
| 领域 | 控制理论 | 控制理论 |
| 方法族 | Machine learning | Machine learning |
| 起源年份≠ | 1957 | 1960 |
| 提出者≠ | Richard Bellman | Rudolf Kalman |
| 类型 | algorithm | algorithm |
| 开创性文献≠ | Bellman, R. (1957). Dynamic Programming. Princeton University Press. link ↗ | Kalman, R. E. (1960). Contributions to the theory of optimal control. Boletin de la Sociedad Matematica Mexicana, 5(2), 102-119. link ↗ |
| 别名≠ | HJB Equation, Bellman Equation, Dynamic Programming | LQR, Linear Quadratic Optimal Control |
| 相关≠ | 3 | 4 |
| 摘要≠ | 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 Linear Quadratic Regulator (LQR) is a classical optimal control algorithm that computes a linear feedback law to minimize a quadratic cost function for a linear dynamical system. Introduced by Kalman in 1960, LQR provides a provably optimal, closed-form solution for linear systems and remains fundamental in control theory, robotics, and aerospace applications because of its theoretical elegance and computational efficiency. |
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