Hamilton–Jacobi–Bellman equation

Definition

Define the Hamiltonian

#incomplete

Then the HJB equation is

$\rho V(x) = \max_{u \in U} h(x,u) + V'(x) \cdot g(x,u)$

See also

• Pontryagin's maximum principle
• Hamiltonian (control theory)
• differential Riccati equation

References

1. https://benjaminmoll.com/wp-content/uploads/2019/07/Lecture4_ECO521_web.pdf
2. https://en.wikipedia.org/wiki/Hamilton–Jacobi–Bellman_equation
3. https://ocw.mit.edu/courses/16-323-principles-of-optimal-control-spring-2008/8db99aee192f44ac6c0542fc57748703_lec4.pdf
4. https://en.wikipedia.org/wiki/Hamiltonian_(control_theory)
5. https://archive.control.lth.se/media/Staff/Perninge/Lecture5.pdf
6. https://liberzon.csl.illinois.edu/teaching/cvoc/node95.html