Observer Design for (max,plus) Linear System

TL;DR

This paper introduces an observer design method for max-plus linear systems using residuation theory, enabling state estimation based on known system matrices and observed inputs and outputs.

Contribution

It develops a novel observer design approach for max-plus linear systems leveraging residuation theory, extending classical observer concepts to idempotent semirings.

Findings

Observer design successfully estimates states in max-plus systems

Method leverages residuation theory for linear mapping inversion

Applicable to systems with known matrices and observed inputs/outputs

Abstract

This paper deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring.