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\begin{document}

\title{LMI-Based Neural Observer for State and Nonlinear Function Estimation}



\author[1]{Rajesh Rajamani}%
\author[2]{Woongsun Jeon}%
\author[3]{Ali Zemouche}%
\author[4]{Ankush Chakrabarty}%
\affil[1]{University of Minnesota Twin Cities}%
\affil[2]{Chung-Ang University College of Engineering}%
\affil[3]{Universite de Lorraine IUT Henri Poincare-Longwy}%
\affil[4]{Mitsubishi Electric Research Laboratories}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
This paper develops a neuro-adaptive observer for state and nonlinear
function estimation in systems with partially modeled process dynamics.
The developed adaptive observer is shown to provide exponentially stable
estimation errors in which both states and neural parameters converge to
their true values. When the neural approximator has an approximation
error with respect to the true nonlinear function, the observer can be
used to provide an H [?] bound on the estimation error. The paper does not
require assumptions on the process dynamics or output equation being
linear functions of neural network weights and instead assumes a
reasonable affine parameter dependence in the process dynamics. A convex
problem is formulated and an equivalent polytopic observer design method
is developed. Finally, a hybrid estimation system that switches between
a neuro-adaptive observer for system identification and a regular
nonlinear observer for state estimation is proposed. The switched
operation enables parameter estimation updates whenever adequate
measurements are available. The performance of the developed adaptive
observer is shown through simulations for a Van der Pol oscillator and a
single link robot. In the application, no manual tuning of adaptation
gains is needed and estimates of both the states and the nonlinear
functions converge successfully.%
\end{abstract}%



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\textbf{Hosted file}

\verb`NAOdraft_20230908.docx`  available at \url{https://authorea.com/users/661429/articles/664512-lmi-based-neural-observer-for-state-and-nonlinear-function-estimation}

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