قارن الطرق

	معادلة هاميلتون-جاكوبي-بيلمان	التحكم التنبؤي بالنموذج
المجال	نظرية التحكم	نظرية التحكم
العائلة	Machine learning	Machine learning
سنة النشأة	1957	1978
صاحب الطريقة	Richard Bellman	Jacques Richalet
النوع	algorithm	algorithm
المصدر التأسيسي	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.
الأسماء البديلة	HJB Equation, Bellman Equation, Dynamic Programming	MPC, Receding Horizon Control
ذات صلة	3	5
الملخص	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.