Contribution au diagnostic des défauts des systèmes non-linéaires de type Takagi-Sugeno

Abstract

This thesis tackles the challenge of estimating sensor faults in a specific class of nonlinear systems. These systems operate continuously over time and can switch be-tween different modes. We model them using Takagi-Sugeno (T-S) models, which can handle nonlinearities in the system’s behavior. Additionally, the model accounts for external disturbances that are limited in size. This approach avoids the issue of having unmeasured premise variables, which can complicate estimation tasks. The core con-tribution of this research lies in proposing robust observers. These observers operate with the system’s switching mechanism and can simultaneously esti-mate state and sensor faults. The design of these observers is formulated using Linear Matrix Inequalities (LMIs), which are mathematical that simplify analysis. Our approach offers several advantages compared to previous studies. First, the LMI conditions are independent of a specific dwell time, making them more flexible. Second, by applying relaxation techniques and specific constraints, we achieve less conservative results compared to prior work, especially when dealing with the unmeasured nonlin-earities in the system. Furthermore, this thesis includes an optimization procedure to estimate the region within which the estimation error is guaranteed to remain. The effectiveness of the proposed design is demonstrated through several exam-ples. One example showcases the reduction in conservatism achieved by our approach. Another example illustrates the performance of the observers even when the system’s switching mechanism doesn’t perfectly match the observer’s assumptions.