Dynamic programming in continuous time

Summary

Dynamic programming in continuous time solves an optimal control problem by studying its value function for all initial times and states at once. Its basis is Bellman's principle of optimality: the tail of an optimal trajectory is optimal for the problem that starts where the tail starts. In infinitesimal form this principle becomes the Hamilton–Jacobi–Bellman equation. It gives optimal controls in feedback form, which complements the open-loop necessary conditions of Pontryagin's maximum principle.