Mean Escape Time of Switched Riccati Differential Equations

TL;DR

This paper studies the mean escape time of a stochastic switched Riccati differential equation driven by a Poisson-like signal, providing a power series expression and an approximation formula, supported by numerical simulations.

Contribution

It introduces a power series expression for the mean escape time of switched Riccati equations and an approximation method for deterministic cases, expanding analytical tools in control theory.

Findings

Power series expression for mean escape time

Approximate formula for deterministic Riccati equations

Numerical simulations validating the results

Abstract

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.