具有微分包含的Mayer问题的灵敏度关系
Sensitivity relations for the Mayer problem with differential inclusions
摘要：
在最优控制中，灵敏度关系通常被理解为包含体，其识别由对偶弧和哈密尔顿算子形成的对，沿着相关的最小化轨迹评估，作为值函数的合适的广义梯度。本文得到了与微分包含$\dot x\in F(x)$相关的Mayer问题的灵敏度关系，并应用灵敏度关系导出了最优性条件.我们的第一个应用程序涉及的最大值原理，并包括在显示，一个双弧可以构造的每一个元素的superdifferential的最终成本。作为我们的第二个应用，对于值函数在某个点$(t,x)$处的每个非零极限梯度，我们将在$(t,x)$处的一族最优轨迹与对应于不同极限梯度的族具有空相交的性质相关联。
英文摘要：
In optimal control,sensitivity relations are usually understood as inclusions that identify the pair formed by the dual arc and the Hamiltonian, evaluated along the associated minimizing trajectory, as a suitable generalized gradient of the value function. In this paper, sensitivity relations are obtained for the Mayer problem associated with the differential inclusion $\dot x\in F(x)$ and applied to derive optimality conditions. Our first application concerns the maximum principle and consists in showing that a dual arc can be constructed for every element of the superdifferential of the final cost. As our second application, with every nonzero limiting gradient of the value function at some point $(t,x)$ we associate a family of optimal trajectories at $(t,x)$ with the property that families corresponding to distinct limiting gradients have empty intersection.
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