The entropy penalized minimum energy estimator

Sérgio Pequito*, A. Pedro Aguiar, Diogo A. Gomes

*Corresponding author for this work

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

1 Scopus citations

Abstract

This paper addresses the state estimation problem of nonlinear systems. We formulate the problem using a minimum energy estimator (MEE) approach and propose an entropy penalized scheme to approximate the viscosity solution of the Hamilton-Jacobi equation that follows from the MEE formulation. We derive an explicit observer algorithm that is iterative and filtering-like, which continuously improves the state estimation as more measurements arise. In addition, we propose a computationally efficient procedure to estimate the state by performing an approximation of the nonlinear system along the trajectory of the estimate. In this case, for the first and second order approximations of the state equation, we derive a closed-form (iterative) solution for the Hessian of the entropy-like version of the optimal cost function of the MEE. We illustrate and contrast the performance of our algorithms with the extended Kalman filter (EKF) using specific nonlinear examples with the feature that the EKF do not converge to the correct value.

Original languageEnglish (US)
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages1285-1290
Number of pages6
DOIs
StatePublished - 2009
Externally publishedYes
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: Dec 15 2009Dec 18 2009

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period12/15/0912/18/09

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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