Section: New Results

Automatic control

Observability conservation by output feedback and observability Gramian bounds

Participants : Qinghua Zhang, Liangquan Zhang.

Though it is a trivial fact that the observability of a linear state space system is conserved by output feedback, it requires a rigorous proof to generalize this result to uniform complete observability, which is defined with the observability Gramian. The purpose of this work is to complete such a proof. Some issues in existing results are also discussed. The uniform complete observability of closed loop systems is useful for the analysis of some adaptive systems and of the Kalman filter. This study has been accomplished in the framework of the ITEA MODRIO project and the results have been published in Automatica [20] .

Weighted principal component analysis for Wiener system Identification: regularization and non-Gaussian excitations

Participant : Qinghua Zhang.

This work has been carried out in collaboration with Vincent Laurain (CRAN/CNRS/Université de Lorraine) and with Jiandong Wang (Peking University).

Finite impulse response (FIR) Wiener systems driven by Gaussian inputs can be efficiently identified by a well-known correlation-based method, except those involving even static nonlinearities. To overcome this deficiency, another method based on weighted principal component analysis (wPCA) has been recently proposed. Like the correlation-based method, the wPCA is designed to estimate the linear dynamic subsystem of a Wiener system without assuming any parametric form of the nonlinearity. To enlarge the applicability of this method, it is shown in this work that high order FIR approximation of IIR Wiener systems can be efficiently estimated by controlling the variance of parameter estimates with regularization techniques. The case of non-Gaussian inputs is also studied by means of importance sampling. The results of this study have been presented in [22] .

LPV system common state basis estimation from independent local LTI models

Participant : Qinghua Zhang.

This work has been carried out in collaboration with Lennart Ljung (Linköping University).

For the identification of a linear parameter varying (LPV) system steered by a scheduling variable evolving within a finite set, the local approach consists in separately estimating local linear time invariant (LTI) models corresponding to fixed values of the scheduling variable. It is shown in this work that, without any global structural assumption of the considered LPV system, the local state-space LTI models do not contain the necessary information about the similarity transformations making them coherent. Nevertheless, it is possible to estimate these similarity transformations from input-output data under appropriate input excitation conditions. These estimations result in a common state basis of the transformed local LTI models, so that they form a coherent global LPV model, suitable for numerical simulations in the case of fast scheduling variable evolutions. This study has been accomplished in the framework of the ITEA MODRIO project and the results have been presented in [39] .