Section: New Results

Observability and observer design for nonlinear systems

Participants : Jean-Pierre Barbot, Wilfrid Perruquetti, Gang Zheng, Denis Efimov.

Observability analysis and observer design are important issues in the field of control theory. Some recent results are listed below:

• The problem of observer design for fault detection in a class of nonlinear systems subject to parametric and signal uncertainties is studied in [22] . The design procedure includes formalized optimization of observer free parameters in terms of trade-offs for fault detection performance and robustness to external disturbances and model uncertainties. The technique makes use of some monotonicity conditions imposed on the estimation error dynamics. Efficiency of the proposed approach is demonstrated through the Oscillatory Failure Case in aircraft control surface servo-loops.

• An algorithm for the frequency and bias identification of a harmonic signal is presented in [14] , [15] . The solution is based on an adaptive observer technique and the hybrid systems method.

• An influence of a singular manifold of non observable states on reconstruction of chaotic attractors is analysed in [25] . The probability of visits of the observability singularity manifold and the relative time spent in the observability singularity manifold are introduced.

• In [36] , the cluster structured sparse signals are investigated. Under the framework of Bayesian compressive sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms, which are also taking into account the cluster prior, the proposed in [36] algorithm solves the inverse problem automatically–prior information on the number of clusters and the size of each cluster is unknown.

• The papers [54] , [86] , [87] present a new approach for observer design for a class of nonlinear singular systems which can be transformed into a special normal form. The interest of the proposed form is to facilitate the observer synthesis for the studied nonlinear singular systems. Necessary and sufficient geometrical conditions are deduced in order to guarantee the existence of a diffeomorphism, which transforms the studied nonlinear singular systems into the proposed normal form.

• The paper [85] investigates the observer design problem of for linear switched system with disturbance jumps. Detection of active sub-system and finite time estimation of states are respectively discussed. A switched finite time observer is proposed to guarantee the finite time convergence independent of the disturbance jumps.

• The paper [71] , [72] proposes a new observer scheme for chaotic and hyperchaotic systems. Firstly, a classical impulsive observer is investigated for Lorenz chaotic system. This approach is based on sufficient conditions for stability of impulsive dynamical systems. After, an hybrid observer is proposed for hypoerchaotic systems. In the paper [70] , a new method of strange attractor identification, under sparse measurement, is proposed this method is based on the concept of compressive sensing. For this, some particular impulsive observers have been presented with a decision scheme linked to diagnosis method, the identification of the strange attractor and state observation are done.

• The problem of state reconstruction for nonlinear differential-algebraic systems with unknown inputs is studied in [51] .

• In the paper [26] the design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both state and input for a class of nonlinear systems is proposed. Furthermore, the feasibility of the proposed strategy is illustrated by a numerical example.