Adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs

On adaptive observers design for a class of uniformly observable systems

“…Adaptive versions of high gain observers have been proposed in [7,9,6]. Though most contributions on adaptive observer design deal with linear parametrization, there are nevertheless results dealing with nonlinear parameterizations [1,9,11,13,15,21,22]. The problem of simultaneous state and parameter estimation is rather difficult compared to the one dealing with the state estimation only.…”

“…In this paper, we shall address such an equivalence problem for the class of multivariable nonlinear systems that are observable for any inputs with triangular Lipschitz nonlinearities involving some unknown parameters. An adaptive observer has been recently proposed in [9] using the adaptive approach for the single output case. More specifically, we will explore the strike similarity of the involved observation gain with the observation gain usually encountered in high gain observers.…”

“…More specifically, we will explore the strike similarity of the involved observation gain with the observation gain usually encountered in high gain observers. Such a feature allows to show that the adaptive observer proposed in [9] can be derived by adopting the augmented model approach while assuming the same persistent excitation condition. This paper is organized as follows.…”

Enhancement of adaptive observer robustness applying sliding mode techniques

“…Typically, the observer needs to generate estimates of the vector of unknown parameters and unmeasured state components under noisy environments (see for example [4,14]). Highgain observers with gain adaptation for time-varying or nonlinear systems have been studied in a number of recently published papers, see for instance [5,15,1,10].…”

Resistance to Noise of Non-linear Observers in Canonical Form Application to a Sludge Activation Model

“…For PI and ELO observer classes, (Söffker, et al, 2002) demonstrated a compensation effect on measurement errors ; (Khalifa & Mabrouk, 2015) addressed the problem of uncertainty of non-linear models. One way of overcoming the problem of parametric uncertainty is to use adaptive observers (Tyukina, et al, 2013;Farza, et al, 2014) in the particular case where the measurements are only available at discrete instants and have disturbances. Another approach (Mazenc & Dinh, 2014;Thabet, et al, 2014) consists of defining interval observers.…”