Decentralized set-valued state estimation based on non-deterministic chains

TL;DR

This paper introduces a decentralized framework for set-valued state estimation of hybrid systems, improving computational efficiency and accuracy through signal space decomposition and structural analysis.

Contribution

It proposes a novel decentralized approach that recovers exact state sets and reduces computational complexity compared to centralized methods.

Findings

Exact state set recovery under specific decomposition rules

Significant reduction in computational complexity

Applicability to hybrid state machine systems

Abstract

A general decentralized computational framework for set-valued state estimation and prediction for the class of systems that accept a hybrid state machine representation is considered in this article. The decentralized scheme consists of a conjunction of distributed state machines that are specified by a decomposition of the external signal space. While this is shown to produce, in general, outer approximations of the outcomes of the original monolithic state machine, here, specific rules for the signal space decomposition are devised by utilizing structural properties of the underyling transition relation, leading to a recovery of the exact state set results. By applying a suitable approximation algorithm, we show that computational complexity in the decentralized setting may thereby essentially reduce as compared to the centralized estimation scheme.