What is Dynamic programming, feedback control?

Dynamic programming computes the value function backward in time with the one-step principle, $V_t(x) = \max_u\{f(t, x, u) + \E[V_{t+1}(X_{t+1}) \mid X_t = x, u]\}$, from $V_T = g$. A feedback control is a control of the form $u_t = u^*(t, X_t)$, a function of the current state; dynamic programming produces one.