论文标题
汉密尔顿的minimax解决方案 - 具有分数共同导数的雅各比方程
Minimax Solutions of Hamilton--Jacobi Equations with Fractional Coinvariant Derivatives
论文作者
论文摘要
我们考虑了汉密尔顿 - 雅各比方程的库奇问题，该方程式具有（0，1）$ in（0，1）$的订单$α\的共同衍生物。这种问题自然出现在动态系统的最佳控制问题中，这些问题由普通微分方程与$α$的CAPUTO分数衍生物描述。我们提出了一个在被考虑的问题的最小值解决方案中的广义概念。我们证明存在Minimax解决方案，是唯一的，并且与此问题的经典解决方案一致。特别是，我们特别注意比较原理的证明，该原理需要构建合适的lyapunov-krasovskii功能。
We consider a Cauchy problem for a Hamilton--Jacobi equation with coinvariant derivatives of an order $α\in (0, 1)$. Such problems arise naturally in optimal control problems for dynamical systems which evolution is described by ordinary differential equations with the Caputo fractional derivatives of the order $α$. We propose a notion of a generalized in the minimax sense solution of the considered problem. We prove that a minimax solution exists, is unique, and is consistent with a classical solution of this problem. In particular, we give a special attention to the proof of a comparison principle, which requires construction of a suitable Lyapunov--Krasovskii functional.
