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  "body": "\n## Summary\n\nDynamic programming in continuous time solves an optimal control problem by studying its [[value function|K6G0DRQ3CP]] for all initial times and states at once.\nIts basis is Bellman's principle of optimality: the tail of an optimal trajectory is optimal for the problem that starts where the tail starts.\nIn infinitesimal form this principle becomes the [[Hamilton–Jacobi–Bellman equation|SJP9HW82VX]].\nIt gives optimal controls in feedback form, which complements the open-loop necessary conditions of [[Pontryagin's maximum principle|7RPV2T29CF]].\n\n## Explanations\n\n### L1 human\n\nTo plan the cheapest trip, one can work backward from the destination.\nIf you know the cheapest remaining cost from every place at a later time, the best move now is easy to find.\nDynamic programming in continuous time applies this idea at every instant.\nThe result is a rule that tells you what to do in every situation, not just along one planned path.\n",
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