Efficient total least squares state and parameter estimation for differentially flat systems

Ji Liu, Sergio Mendoza, Guang Li, Hosam Fathy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


This paper proposes an efficient framework for the total least squares (TLS) estimation of differentially flat system states and parameters. Classical ordinary least squares (OLS) estimation assumes: (i) that only the dependent (i.e., output) signals are noisy, and that (ii) the independent (i.e., input) variables are known. In contrast, TLS estimation assumes both the input and output signals to be noisy. Solving TLS problems can be computationally expensive, particularly for nonlinear problems. This challenge arises because the input trajectory must be estimated in a TLS problem, rather than treated as given. This paper addresses this challenge for differentially flat systems by utilizing a pseudospectral expansion to express the input, state, and output trajectories in terms of a flat output trajectory. This transforms the TLS problem into an unconstrained nonlinear programming (NLP) problem with a small number of optimization variables. We demonstrate this framework for an example involving estimating the states and parameters of a second-order nonlinear flat system. Our approach reduces the number of optimization variables from 1503 to 33, while achieving state and parameter estimation errors below 5% and 7%, respectively.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781467386821
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2016 American Control Conference, ACC 2016
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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