Proportional-Integral observer design for nonlinear uncertain systems modelled by a multiple model approach

Abstract

In this paper, a decoupled multiple model approach is used in order to cope with the state estimation of uncertain nonlinear systems. The proposed decoupled multiple model provides flexibility in the modelling stage because the dimension of the submodels can be different and this constitutes the main difference with respect to the classically used multiple model scheme. The state estimation is performed using a Proportional Integral Observer (PIO) which is well known for its robustness properties with respect to uncertainties and perturbations. The Lyapunov second method is employed in order to provide sufficient existence conditions of the observer, in LMI terms, and to compute the optimal gains of the PIO. The effectiveness of the proposed methodology is illustrated by a simulation example.

Robust multiobserver design for discrete uncertain nonlinear systems with time-varying delay

“…Recently, research on a robust observer design for Takagi -Sugeno multimodel, which is subject to uncertainties or time-delay, has been active (Asemania and Majd, 2015; Derakhshana and Fatehia, 2013; Wang, 2004; Zhu and Xu, 2015). However, few works are interested in the design of multiobservers for nonlinear systems described by discrete decoupled multimodel in the presence of parametric uncertainties (Orjuela et al, 2008) or time-varying delay (Atia et al, 2014, 2015; Orjuela et al, 2007). To the best of our knowledge, the design of a robust multiobserver for a decoupled multimodel in the simultaneous presence of parametric uncertainties, time-varying delay and measurement noise has not yet been investigated and is still open, which motivates our present work.…”

Robust mode recognition in Hybrid Dynamical Systems with nonlinear modes

“…In the following, it is supposed that these premise variables are known. For one mode j represented by h j local models, TS representation ( [18]) is thus given by:…”

Nonlinear Burn Control in Tokamak Fusion Reactors via Output Feedback

“…PIO designs differ from classical observers by the presence of an integral component in the output injection term, which provides an additional degree of freedom that can be used to decrease sensitivity to model uncertainties and disturbances. Output feedback controllers with PIOs have been proposed for general linear systems (Beale and Shafai, 1989) and have been applied to certain nonlinear systems (Jung et al, 2007;Orjuela et al, 2008). For the nominal system, the observer design proposed in this work is stable for suitably small state estimation errors or observer gains.…”