Monitoring, diagnostics and control of industrial systems are topics of yesterday, today and certainly tomorrow. Indeed, the development of technologies at a sustained pace, the fierce competition between manufacturers to gain market share, which has become globalized, encourage researchers to develop new approaches and / or techniques that would allow better control of these industrial processes, which have become very complex. The identification and control of these systems is part of this research. Starting from the fact that the perfect model does not exist, another level in the automation chain has been introduced. It concerns supervision and surveillance. It is within this framework that the first part of this project fits. In fact in this part one proposes to make modelization and the diagnosis of nonlinear and dynamic systems. These two characteristics are those of real processes, and they further complicate the task of researchers. Several works on the subject have been produced around the world, with more or less relevant advances. It is, in fact, from remarkable signals or indicators, to detect malfunctions and react accordingly, in order to guarantee the integrity of the process. These indicators are developed using kernel methods characterized by their efficiency in terms of generalizability. The interest of this part of the project in relation to the aspect of monitoring, diagnosis and even operational reliability of the processes is obvious.

In recent years, the theory of statistical learning, initiated by Vapnik, has seen increasing interest. These techniques exploit the theory of reproducing nuclei. The main idea is the kernel trick, allowing to transform observation data using non-linear application, in high dimensional space, where linear methods can be applied. In the proliferation of these methods, of which the Support Vector Machines are the spearhead, little work has been carried out on the opposite problem, ie the return to the space of observations. Paradoxically, although the nonlinear transformation induced by the nucleus is fundamental, the inverse return to the space of observations is often crucial. Solving this problem, known as the pre-image problem, allows new fields of application for kernel methods, including pattern recognition, feature extraction, signal denoising, and series analysis. temporal. It is within this framework that the second part of this project is developed. Indeed, the objective is to show that the kernel methods provide relevant solutions to several problems raised in signal and image processing, Different non-linear methods have been developed: the resolution of the pre-image problem under the constraints of non-negativity for pattern recognition, feature extraction and denoising, the autoregressive kernel model for time series prediction, and finally support vector machines for discrimination to improve classification performance.

Another application of kernel methods concerns the control of so-called complex systems based on models delivered by said methods.It would then be interesting to adapt two widely used control strategies, namely predictive control and control by sliding modes and to control them. test on the two real processes acquired by the laboratory. Another application of predictive control based on core methods is to regulate the heating power in smart buildings.

In fact, it is about two teams which work in parallel and which use the same tools, a first team which deals with the aspects of diagnosis and image processing and a second which will be devoted to the synthesis and the application. predictive and sliding control strategies.