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<p>This work builds on the seminal paper (Winck et al. IFAC-PapersOnLine 58(1):36–41 <CitationRef CitationID="CR29">2024</CitationRef>) and evaluates an existing method against a new approach for state estimation in Max-Plus Linear systems with bounded uncertainties. Traditional stochastic filtering is inapplicable to this system class, even though the posterior probability density function (PDF) can be computed. Previous research has shown a limited scalability of the <i>disjunctive</i> approach using difference-bound matrices. To address this, we investigate an alternative method recently explored in Mufid et al. (IFAC-PapersOnLine 53(4):459–465 <CitationRef CitationID="CR21">2020</CitationRef>, IEEE Trans Autom Control 67(6):2700–2714 <CitationRef CitationID="CR22">2022</CitationRef>), employing Satisfiability Modulo Theory (SMT) techniques, despite their NP-hard nature. The main novelty of this work is the proposal of a <i>concise</i> method based on fixed-point iteration in max-plus algebra, which is known to be a pseudo-polynomial time algorithm. To compare both approaches, a representative autonomous system is used in the paper to illustrate the basic computations. The efficiency of both approaches is compared through numerical experiments.</p>

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SMT-based and fixed-point approaches for state estimation in max-plus linear systems

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Guilherme Espindola-Winck,
  • Laurent Hardouin,
  • Mehdi Lhommeau

摘要

This work builds on the seminal paper (Winck et al. IFAC-PapersOnLine 58(1):36–41 2024) and evaluates an existing method against a new approach for state estimation in Max-Plus Linear systems with bounded uncertainties. Traditional stochastic filtering is inapplicable to this system class, even though the posterior probability density function (PDF) can be computed. Previous research has shown a limited scalability of the disjunctive approach using difference-bound matrices. To address this, we investigate an alternative method recently explored in Mufid et al. (IFAC-PapersOnLine 53(4):459–465 2020, IEEE Trans Autom Control 67(6):2700–2714 2022), employing Satisfiability Modulo Theory (SMT) techniques, despite their NP-hard nature. The main novelty of this work is the proposal of a concise method based on fixed-point iteration in max-plus algebra, which is known to be a pseudo-polynomial time algorithm. To compare both approaches, a representative autonomous system is used in the paper to illustrate the basic computations. The efficiency of both approaches is compared through numerical experiments.