Robust Adaptive Observer Design for Uncertain Systems With Bounded Disturbances

Abstract

This paper presents a robust adaptive observer design methodology for a class of uncertain nonlinear systems in the presence of time-varying unknown parameters with absolutely integrable derivatives, and nonvanishing disturbances. Using the universal approximation property of radial basis function (RBF) neural networks and the adaptive bounding technique, the developed observer achieves asymptotic convergence of state estimation error to zero, while ensuring boundedness of parameter errors. A comparative simulation study is presented by the end.

Adaptive variable structure state estimation for uncertain systems with persistently bounded disturbances

“…It is noted that in the existing adaptive observation schemes, the main challenge is how to define a feedback signal for adjusting the estimate of the unknown parameter. This problem was solved by assuming the unknown uncertainties to satisfy a matching condition in [19], or by imposing a SPR-like condition on the linear part of the system in [23][24][25]. It is observed that no matching condition or SPR-like condition is required in the derivation process of our results, thanks to using the orthogonal projections of the state estimation error in (10).…”

“…The resulting state estimation error is uniformly ultimately bounded (UUB) with an ultimate bound. Moreover, we note that the main challenge in the existing adaptive observer schemes [19,[23][24][25] was how to define a feedback signal for updating the adaptive law of bounding parameter estimate. In the proposed estimation scheme, using the orthogonal projection of the 2005 state estimation error, the update law is represented in terms of the available measurement error signal while no limit condition is required.…”

NNs Based Asymptotic Adaptive Observer Without Riccati Constraint And Chattering

“…Recently in [1] and [2] it was considered the asymptotic observation, based on linearly parameterize neural networks (LPNNs), of a class of uncertain nonlinear systems in the presence of time-varying unknown parameters and non-vanishing disturbances. However, the proposed methods present several drawbacks, which restrict the application: 1) observer in [1] is based on a decaying-width design, hence it can exhibit chattering phenomenon when the width has decayed practically to zero, 2) observer in [2] is discontinuous, then also exhibit chattering, and it assume that the unknown parameters have absolutely integrable derivatives. In addition, observers in [1] and [2] rely on a Riccati equation solution to be implemented.…”

LMI-based Adaptive Observers for Nonlinear Systems

“…The design of the observer depends on the ability to solve an LMI problem under a conservative matrix equality refering to "matchning conditions" of the dynamic representation. Even, it has been reported and applied in many other works in the literature (Dimassi et al, 2010;Liu, 2009;Dong & Mei, 2007;Stepanyan & Hovakimyan, 2007;Zhu, 2007), this concept is still hard to achieve within some (but very common) dynamics as discussed in .…”