Duc To NGUYEN soutient sa thèse de doctorat le mercredi 25 juin 2025 : « Interval Observers Based Fault Tolerant Control Of LPV Switched Systems »

Switched systems have drawn considerable attention from researchers due to their ability to model a variety of practical systems. The synthesis of observers for this class of systems has gained increasing interest over the past few decades since the estimation plays a fundamental role in determining the current system states, including measured and unmeasured variables, which is crucial for fault diagnosis and control. However, the conventional observer synthesis technique may struggle to cope with the uncertainties, resulting in reduced estimation accuracy and reliability. Moreover, in practical engineering applications, it is inevitable to encounter unknown inputs and faults due to unpredictable external disturbances, measurement noise, and potential actuator faults. Such factors may cause system performance degradation, instability, or even catastrophic failures. It is, therefore essential to enhance the system safety and reliability by developing well-designed algorithms that can effectively estimate and compensate for faults affecting the performance. The objective of this thesis is to provide some contributions to the state-of-the-art in the field of robust state estimation and fault-tolerant control (FTC) for a class of switched systems by addressing the aforementioned problems. The present research mainly focuses on addressing the challenge of robust state bounding estimation using interval observer techniques for uncertain switched systems subject to unknown but bounded exogenous disturbances and/or measurement noise. Based on the cooperativity system theory, the methodology presents novel interval observer structures that provide notable improvement, particularly in enhancing the robustness and accuracy of state estimation under uncertain conditions. In contrast to conventional observers may struggle to deal with uncertainties, the proposed observer can effectively cope with the problems by offering guaranteed lower and upper bounds of state estimations. In addition to robust state estimation, the thesis also focuses on the synthesis of active fault-tolerant control (AFTC) strategies designed to preserve system stability and ensure desired performance levels, even in the presence of faults. The approach employs a co-design methodology, which integrates the design of observers and controllers into a cohesive framework. This integrated design approach considers the bi-directional interaction between the estimation process and control actions, leading to the optimized overall system performance and enhanced resilience to faults. Sufficient conditions for proving the existence of the interval observers and controllers are formulated in terms of Linear Matrix Inequalities (LMIs) constraints. These conditions are derived through a combination of Lyapunov theory and Input-to-State-Stability (ISS) under the Average-Dwell Time (ADT) concept. Finally, to validate the efficacy of the proposed interval observer structures and the synthesized control laws, an application to the vehicle lateral dynamics model is presented, using MATLAB Simulink. The simulations validate the robustness of the interval observer structures and fault-tolerant control strategies, showing that the proposed approach can effectively maintain vehicle stability and control even in challenging and unpredictable environments. The results highlight the ability of the interval observers to accurately bound state estimates despite uncertainties, while the synthesized control laws successfully ensure system stability and performance even in the occurrence of faults.