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معادله همیلتون-ژاکوبی-بلمن×تنظیم‌کننده خطی-درجه‌دوم (Linear Quadratic Regulator)×
حوزهنظریه کنترلنظریه کنترل
خانوادهMachine learningMachine learning
سال پیدایش19571960
پدیدآورRichard BellmanRudolf Kalman
نوعalgorithmalgorithm
منبع بنیادینBellman, 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 ↗
نام‌های دیگرHJB Equation, Bellman Equation, Dynamic ProgrammingLQR, Linear Quadratic Optimal Control
مرتبط34
خلاصهThe 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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ScholarGateمقایسهٔ روش‌ها: Hamilton-Jacobi-Bellman Equation · Linear Quadratic Regulator. بازیابی‌شده در 2026-06-19 از https://scholargate.app/fa/compare