论文标题
部分可观测时空混沌系统的无模型预测
Viscosity solutions of Hamilton-Jacobi equations for neutral-type systems
论文作者
论文摘要
该论文涉及与路径依赖的汉密尔顿 - 雅各布方程式有关的共同导数，该衍生物在研究中立形式的中性型系统的最佳控制问题和差异游戏中出现。考虑了此类方程的cauchy问题的粘度（广义）解决方案。证明了粘度解决方案的存在，独特性和一致性。获得了粘度解的等效定义，包括最小值和DINI解决方案的定义。给出了将结果应用于Hale形式的中性型系统的最佳控制问题。
The paper deals with path-dependent Hamilton-Jacobi equations with a coinvariant derivative which arise in investigations of optimal control problems and differential games for neutral-type systems in Hale's form. A viscosity (generalized) solution of a Cauchy problem for such equations is considered. The existence, uniqueness, and consistency of the viscosity solution are proved. Equivalent definitions of the viscosity solution, including the definitions of minimax and Dini solutions, are obtained. Application of the results to an optimal control problem for neutral-type systems in Hale's form are given.
