Machine learningOptimal Control
Hamilton-Jacobi-Bellman Equation
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.
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Sources
- Bellman, R. (1957). Dynamic Programming. Princeton University Press. link ↗
- Kirk, D. E. (2004). Optimal Control Theory: An Introduction (2nd ed.). Dover Publications. DOI: 10.1007/978-0-387-39246-5 ↗