View source for Bellman equation

A partial differential equation of a special type to solve a problem of [[Optimal control|optimal control]]. If the solution of Cauchy's problem for the Bellman equation can be found, the optimal solution of the original problem is readily obtained.

A recurrence relation for the solution of a discrete problem of optimal control. The method for obtaining the optimal solution with the aid of Bellman's equation is known as [[Dynamic programming|dynamic programming]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  R. Bellman,   "Dynamic programming" , Princeton Univ. Press  (1957)</TD></TR></table>



====Comments====
The Bellman equation for continuous-time optimal control problems is also often called the dynamic programming equation. Cf. the article [[Optimality, sufficient conditions for|Optimality, sufficient conditions for]] for examples and more details. There is also a variant for stochastic optimal control problems.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  W.H. Fleming,   R.W. Rishel,   "Deterministic and stochastic optimal control" , Springer  (1975)</TD></TR></table>