论文标题
汉密尔顿 - 雅各比 - 贝尔曼 - 伊萨克斯方程的粘度解决方案
Viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations for time-delay systems
论文作者
论文摘要
该论文处理动态系统的零和差分游戏，该游戏由非线性延迟微分方程在由分段连续函数定义的初始条件下描述。得出了汉密尔顿 - 雅各布（Hamilton-Jacobi-Bellman-ISAAC）方程的相应cauchy问题，并得出了共同变量的衍生物，并考虑了此问题的粘度解决方案的定义。事实证明，差异游戏具有独特的粘度解决方案的值。此外，基于与共同变化衍生物相对应的子和超差异的概念，获得了粘度解决方案的无限描述。给出了应用这些结果的示例。
The paper deals with a zero-sum differential game for a dynamical system which motion is described by a nonlinear delay differential equation under an initial condition defined by a piecewise continuous function. The corresponding Cauchy problem for Hamilton-Jacobi-Bellman-Isaacs equation with coinvariant derivatives is derived and the definition of a viscosity solution of this problem is considered. It is proved that the differential game has the value that is the unique viscosity solution. Moreover, based on notions of sub- and superdifferentials corresponding to coinvariant derivatives, the infinitesimal description of the viscosity solution is obtained. The example of applying these results is given.
