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| Pontryagin Maximum Principle（ポン ujungin の最大値原理）× | 線形二次制御器× | |
|---|---|---|
| 分野 | 制御理論 | 制御理論 |
| 系統 | Machine learning | Machine learning |
| 提唱年≠ | 1962 | 1960 |
| 提唱者≠ | Lev Pontryagin | Rudolf Kalman |
| 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. link ↗ | Kalman, R. E. (1960). Contributions to the theory of optimal control. Boletin de la Sociedad Matematica Mexicana, 5(2), 102-119. link ↗ |
| 別名≠ | PMP, Optimal Control, Costate Method | LQR, Linear Quadratic Optimal Control |
| 関連≠ | 3 | 4 |
| 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. | 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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