Distribution-free mode-estimators for a class of discrete-time jump-linear systems

Daniel Choukroun, Jason L. Speyer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

This paper is concerned with the development of recursive distribution-free mode-estimators for a class of discrete-time jump-linear systems. The cornerstone of the proposed filters consists of an algebraic manipulation of the dynamics equation of the continuous state. This equation turns out to be linear with respect to the mode vector, and, under the assumption of perfect state information, provides a linear observation equation for the mode. Appending this equation to the known linear dynamics equation of the mode yields a linear non-Gaussian state-space model. A first mode-estimator is then derived using standard Linear Filtering results. A second filter is developed as an application of a general discrete-time filter, which approximates the continuous-time optimal non-linear filter (the conditional mean estimator for continuous time) for small sample times. The second filter is preferred from a performance point of view. Model order reduction is applied in order to avoid singularity issues in the filters implementations. The second filter is envisioned as a useful tool in the analysis and design of dual controllers for this type of hybrid systems.

Original languageEnglish
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages6928-6933
Number of pages6
DOIs
StatePublished - 1 Dec 2005
Externally publishedYes
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: 12 Dec 200515 Dec 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Conference

Conference44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/TerritorySpain
CitySeville
Period12/12/0515/12/05

Keywords

  • Finite-alphabet homogenous Markov chain
  • Jump-linear system
  • Optimal non-linear filtering

ASJC Scopus subject areas

  • General Engineering

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