论文标题
切换riccati微分方程的平均逃生时间
Mean Escape Time of Switched Riccati Differential Equations
论文作者
论文摘要
Riccati微分方程是一级和二次的普通微分方程，在系统和控制理论中具有各种应用。在本文中，我们分析了由泊松样随机信号驱动的开关的Riccati微分方程。我们特别关注开关riccati微分方程的平均逃逸时间的计算。本文的贡献是双重的。我们首先表明，在假设所述的子系统被描述为确定性的riccati微分方程在有限时间内逃脱，无论其初始状态如何，切换的riccati微分方程的平均逃逸时间都可以予以表达。为了进一步扩展此结果的适用性，我们提出了一个近似公式，用于计算确定性riccati微分方程的逃生时间。我们提供数值模拟，以说明获得的结果。
Riccati differential equations is the class of first-order and quadratic ordinary differential equations and has various applications in the systems and control theory. In this paper, we analyze a switched Riccati differential equation that is driven by a Poisson-like stochastic signal. We specifically focus on the computation of the mean escape time of the switched Riccati differential equation. The contribution of this paper is twofold. We first show that, under the assumption that the subsystems described as a deterministic Riccati differential equation escape in finite time regardless of its initial state, the mean escape time of the switched Riccati differential equation admits a power series expression. In order to further expand the applicability of this result, we then present an approximative formula for computing the escape time of deterministic Riccati differential equations. We present numerical simulations to illustrate the obtained results.
