مقایسهٔ روش‌ها

	معادله همیلتون-ژاکوبی-بلمن	کنترل پیش‌بین مدل
حوزه	نظریه کنترل	نظریه کنترل
خانواده	Machine learning	Machine learning
سال پیدایش	1957	1978
پدیدآور	Richard Bellman	Jacques Richalet
نوع	algorithm	algorithm
منبع بنیادین	Bellman, R. (1957). Dynamic Programming. Princeton University Press.	Richalet, J., Rault, A., Testud, J., & Papon, J. (1978). Model predictive heuristic control. Automatica, 14(5), 413-428.
نام‌های دیگر	HJB Equation, Bellman Equation, Dynamic Programming	MPC, Receding Horizon Control
مرتبط	3	5
خلاصه	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.	Model Predictive Control (MPC) is an advanced control strategy that uses an explicit process model to predict future system behavior over a finite horizon and solves an optimization problem at each control step. First formalized by Richalet et al. in 1978, MPC has become the dominant approach in process control industries, from chemical plants to autonomous vehicles, because it naturally handles constraints and can optimize multiple objectives simultaneously.