手法を比較

	ハミルトン-ヤコビ-ベルマン方程式	モデル予測制御
分野	制御理論	制御理論
系統	Machine learning	Machine learning
提唱年	1957	1978
提唱者	Richard Bellman	Jacques Richalet
種類	algorithm	algorithm
原典	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.
別名	HJB Equation, Bellman Equation, Dynamic Programming	MPC, Receding Horizon Control
関連	3	5
概要	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.	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.