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Section: New Results

System identification

On Local LTI Model Coherence for LPV Interpolation

Participant : Qinghua Zhang.

In the local approach to linear parameter varying (LPV) system identification, it is widely acknowledged that locally estimated linear state-space models should be made coherent before being interpolated, but the accurate meaning of the term " coherent " or " coherence " is rarely defined. The purpose of this study is to analyze the relevance of two existing definitions and to point out the consequence of this analysis on the practice of LPV system identification. This work has been carried out in collaboration with Lennart Ljung of Linköping University and Rik Pintelon of Vriije Universiteit Brussel, and the results have been published in [22].

Stability Analysis of the Kalman Predictor

Participant : Qinghua Zhang.

The stability of the Kalman filter, though less often mentioned than the optimality in the recent literature, is a crucial property for real time applications. The purpose of this paper is to complete the classical stability analysis of the Kalman filter for general time varying systems. A proof of the stability of the one step ahead predictor, which is embedded in the Kalman filter, is presented in this paper, whereas the classical results were focused on the stability of the filter. The predictor stability is particularly important for linear parameter varying (LPV) system identification by means of prediction error minimization. This work has been carried out in collaboration with Liangquan Zhang of Beijing University of Posts and Telecommunications, and the results have been published in [23].

Regularized Adaptive Observer to Address Deficient Excitation

Participant : Qinghua Zhang.

Adaptive observers are recursive algorithms for joint estimation of both state variables and unknown parameters. Usually some persistent excitation (PE) condition is required for the convergence of adaptive observers. However, in practice, it may happen that the PE condition is not satisfied, because the available sensor signals do not contain sufficient information for the considered recursive estimation problem, which is ill-posed. To remedy the lack of PE condition, inspired by typical methods for solving ill-posed inverse problems, this paper proposes a regularized adaptive observer for general linear time varying (LTV) systems. Regularization terms are introduced in both state and parameter estimation recursions, in order to preserve the state-parameter decoupling transformation involved in the design of the adaptive observer. Like in typical ill-posed inverse problems, regularization implies an estimation bias, which can be reduced by using prior knowledge about the unknown parameters. This work has been carried out in collaboration with Fouad Giri and Tarek Ahmed-Ali of Université de Normandie, and the results have been presented at [40].