论文标题
无界控件的非平滑问题问题的最小值条件
Goh conditions for minima of nonsmooth problems with unbounded controls
论文作者
论文摘要
对于最佳控制问题的最小化器的高阶必要条件通常是在状态变量中连续可区分的系统获得的。在这里，通过利用设定值的谎言括号的概念，我们获得了具有Lipschitz连续动力学和无限控制的控制仿射系统的GOH型条件。为了管理同时缺乏伴随方程的平滑度和类似谎言括号的变化，我们使用了准差异商的概念。我们以一个奏效的示例结束了本文，其中已建立的高阶条件能够排除控制标准最大原理的控制的最佳性。
Higher order necessary conditions for a minimizer of an optimal control problem are generally obtained for systems whose dynamics is continuously differentiable in the state variable. Here, by making use of the notion of set-valued Lie bracket we obtain a Goh-type condition for a control affine system with Lipschitz continuous dynamics and unbounded controls. In order to manage the simultaneous lack of smoothness of the adjoint equation and of the Lie bracket-like variations we make use of the notion of Quasi Differential Quotient. We conclude the paper with a worked out example where the established higher order condition is capable to rule out the optimality of a control verifying the standard maximum principle.
