Section: New Results

Modeling, observation and control: systems modeled by ordinary differential equations

Nonlinear system identification

Participants : Pierre-Alexandre Bliman, Michel Sorine, Qinghua Zhang.

Our current researches on nonlinear system identification are mainly in the framework of the joint Franco-Chinese ANR-NSFC EBONSI project (See Section  7.5 ), started in March 2011 for three years, in collaboration with the Laboratory of Industrial Process Monitoring and Optimization of Peking University and with Centre de Recherche en Automatique de Nancy (CRAN). Three topics have been studied this year: system identification with a continuous time autoregressive model, system identification with quantized data, and Hammerstein-Wiener system identification.

Though discrete time models are widely used in system identification, some advantages of continuous time models are also of practical importance, in particular, the ability of fully benefiting from fast sampling devices. Our studies on this topic have resulted in a continuous time black-box model structure for nonlinear system identification, together with an efficient model estimation method. This model structure belongs to the class of continuous time nonlinear ARX (AutoRegressive with eXogenous input) models, with the particularity of being integrable. By applying techniques of adaptive observer, models of the proposed structure can be efficiently estimated from input-output data. This result has been presented at the last Journées Identification et Modélisation Expérimentale [49] .

System identification is usually based on sampled and quantized data, because of the important role of digital computers. When quantized data are coded with a sufficiently large number of bits, the effect of quantization is often ignored in the design of system identification methods. However, when data are quantized with few bits, sometimes to a single bit leading to binary data, then the effect of quantization must be explicitly taken into account. Data quantization can be modeled as a non differentiable hard nonlinearity, hence the well known gradient-based optimization methods cannot be used for the identification of such nonlinear systems. We have developed a quadratic programming-based method for system identification from quantized data, which, in contrast to most existing methods, can be applied to systems with general input excitations. This result has been presented at the last IFAC World Congress [46] .

A Hammerstein-Wiener system is composed of a dynamic linear subsystem preceded and followed by two static nonlinearities. Typically, the nonlinearities of such a system is caused by actuator and sensor distortions. The identification of such systems with a continuous time model had been studied by colleagues of CRAN with the refined instrumental variable (RIV) method. Stable low-pass filters were used to overcome the difficulties related to the continuous time nature of the model. Our study of this year is about the application of the Kalman filter at the place of the previously used low-pass filters. The advantages of this new method include the stability of the numerical algorithm and the fact that the Kalman filter does not color white noises.

Model-based fault diagnosis

Participants : Abdouramane Moussa Ali, Qinghua Zhang.

The increasing requirements for higher performance, efficiency, reliability and safety of modern engineering systems call for continuous research investigations in the field of fault detection and isolation. In the framework of the MODIPRO project funded by Paris Region ASTech, we are currently studying model-based fault diagnosis for nonlinear systems. Motivated by an application in the MODIPRO project, the considered system is modeled by nonlinear algebro-differential equations, with the particularity that the differential part of the model is linear in state variables. Instead of using general numerical solvers of algebro-differential equations, we are developing a method based on ordinary differential equation solvers, by taking advantage of the particular algebro-differential structure of the considered system.