多谢楼主！这里粘贴一段Wikipedia对 Hamilton–Jacobi–Bellman (HJB) equation 的介绍：

The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory. Classical variational problems, for example, the brachistochrone problem can be solved using this method. The HJB method can be generalized to stochastic systems as well.

The solution of the HJB equation is the 'value function', which gives the optimal cost-to-go for a given dynamical system with an associated cost function. The solution is open loop, but it also permits the solution of the closed loop problem.

The equation is a result of the theory of dynamic programming which was pioneered in the 1950s by Richard Bellman and coworkers.[1] The corresponding discrete-time equation is usually referred to as the Bellman equation. In continuous time, the result can be seen as an extension of earlier work in classical physics on the Hamilton-Jacobi equation by William Rowan Hamilton and Carl Gustav Jacob Jacobi.

链接是http://en.wikipedia.org/wiki/Ham ... %93Bellman_equation

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