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

TL;DR

This paper introduces a method to design optimal switching sequences for jump linear systems with Gaussian initial uncertainties, using Wasserstein metrics within a receding horizon framework to ensure stability and performance.

Contribution

It presents a novel approach combining Wasserstein distance and receding horizon control for optimal switching synthesis under Gaussian uncertainties.

Findings

The method guarantees mean square stability.

It effectively minimizes system performance metrics.

Validated through multiple example simulations.

Abstract

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.