New results on the relationship between dynamic programming and the maximum principle
New results on the relationship between dynamic programming and the maximum principle
复制标题
动态规划与极大值原理关系的新结果
DOI：
10.1007/bf02551239
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
R. Vinter
中科院分区：
文献类型：
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作者：
R. Vinter
最优控制理论的动态规划方法试图将价值函数 V 描述为 Hamilton-Jacobian-Bellman 方程的解。长期以来，根据方程 (H(t, x*(t), u*(t), p(t)),−p(t))=√V(t,x*(t)) 关联庞特里亚金极大值原理和动态规划的启发式论证，其中 (x*, u*) 是所考虑的最优控制过程，p(t) 是共极值，H 是哈密顿量。这种关系之前仅在非常有限的假设下得到验证。我们证明了新的结果，建立了针对一大类非光滑问题的关系，现在用 V 的广义梯度表示。
The dynamic programming approach to optimal control theory attempts to characterize the value functionV as a solution to the Hamilton-Jacobian-Bellman equation. Heuristic arguments have long been advanced relating the Pontryagin maximum principle and dynamic programming according to the equation (H(t, x*(t), u*(t), p(t)),−p(t))=√V(t,x*(t)), where (x*, u*) is the optimal control process under consideration,p(t), is the coextremal, andH is the Hamiltonian. The relationship has previously been verified under only very restrictive hypotheses. We prove new results, establishing the relationship, now expressed in terms of the generalized gradient ofV, for a large class of nonsmooth problems.