Stochastic Filtering Scheme of Implicit Forms of Uncertain Max-Plus Linear Systems

Abstract

This article aims to improve the stochastic filtering algorithm with bounded disturbances, proposed in 1. This filter is efficient for max-plus linear systems in explicit form, i.e., the timed event graph (TEG) described by this system is initially with one token on each place. Nevertheless, it needs strong assumptions in order to be accurate for systems in implicit form, i.e., the corresponding TEG is initially with some token-free places which implies that some entries of the system state vector are dependent on each other. In this article, we consider a more general method without these assumptions. It is based on an iterative procedure that widely increases the accuracy of the estimation.