Optimal Switching Synthesis for Jump Linear Systems with Gaussian initial state uncertainty

This paper provides a method to design an optimal switching sequence for jump linear systems with given Gaussian initial state uncertainty. In the practical perspective, the initial state contains some uncertainties that come from measurement errors or sensor inaccuracies and we assume that the type of this uncertainty has the form of Gaussian distribution. In order to cope with Gaussian initial state uncertainty and to measure the system performance, Wasserstein metric that defines the distance between probability density functions is used. Combining with the receding horizon framework, an optimal switching sequence for jump linear systems can be obtained by minimizing the objective function that is expressed in terms of Wasserstein distance. The proposed optimal switching synthesis also guarantees the mean square stability for jump linear systems. The validations of the proposed methods are verified by examples.Comment: ASME Dynamic Systems and Control Conference (DSCC), 201

Probabilistic Robustness Analysis of Stochastic Jump Linear Systems

In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a metric on the manifold of probability density functions is used as tool for the performance and the stability measures. Starting with Gaussian distribution to represent the initial state uncertainties, the probability density function of the system state evolves into mixture of Gaussian, where the number of Gaussian components grows exponentially. To cope with computational complexity caused by mixture of Gaussian, we prove that there exists an alternative probability density function that preserves exact information in the Wasserstein level. The usefulness and the efficiency of the proposed methods are demonstrated by example.Comment: 2014 ACC(American Control Conference) pape