Decentralized set-valued state estimation and prediction for hybrid systems: A symbolic approach

TL;DR

This paper introduces a symbolic, decentralized method for set-valued state estimation and prediction in hybrid systems, reducing computational complexity by decomposing the problem into distributed state machines.

Contribution

It presents a novel decentralized scheme that approximates and then recovers exact state estimates for hybrid systems using structural decomposition algorithms.

Findings

Decentralized scheme reduces computational complexity.

Outer approximation of state sets is achieved.

Exact state set recovery is possible with structural algorithms.

Abstract

A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conj unction of a finite number of distributed state machines, which are specified by an appropriate decomposition of the external signal space. It aims at a distribution of computational tasks into smaller ones, allocated to individual distributed state machines, leading to a potentially significant reduction in the overall space/time computational complexity. We show that, in general, such a scheme outerapproximates the state set estimates and predictions of the original monolithic state machine. By utilizing structural properties of the transition relation of the latter, in a next step, we propose constructive decomposition algorithms for a recovery of the exact state set outcomes.