论文标题
最佳控制问题中的霍姆顿 - 雅各比的敏感性和切换点的敏感性方法
A Hamilton-Jacobi approach of sensitivity of ODE flows and switching points in optimal control problems
论文作者
论文摘要
在控制膜系统的最佳控制问题中，其解决方案是Bang-bang或单数类型，使用汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程来验证最优性，涉及计算切换时间的部分衍生物，并相对于初始条件（时间和状态）切换状态。在本文中，我们建立了一个针对初始条件的普通微分方程（ODE）流的部分衍生物的公式，这比经典ODE所提供的更适合在HJB方程中使用。我们将获得的结果应用于触发时间和可达集的敏感性分析，在最佳控制问题中可以代表开关基因座。
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching times and switching states with respect to initial conditions (time and state). In this paper, we establish a formula for the partial derivatives of ordinary differential equations (ODE) flows with respect to initial conditions, which is more suitable for using in HJB equation than such provided by the classical theory of ODE. We apply the obtained results to the sensitivity analysis of hitting time and state of a reachable set, that in an optimal control problem can represent a switching locus.
