Resumen de On the fault diagnosis of dynamic systems using set-based approaches
PourasgharlafmejaniModel-based Fault Detection and Isolation (FDI) is a major theoretical topic that is becoming increasingly to one of the most significant key features to increase safety and reliability of complex automatic control systems. Basically, model-based FDI relies on the use of a mathematical model to describe the system behavior. However, uncertainty remains always present when modelling a system since its effect is non-negligible even if there are no process faults. One way to deal with uncertainty is to assume its unknown-but-bounded description. Generally speaking, the uncertainty in so-called \emph{set-based approaches} is represented by a set that is unknown-but-bounded at each time instant. Set-based approaches can be classified into three main paradigms: interval observer approach, set-membership approach and set-invariance approach. In this thesis, the influence of the uncertainty is addressed using the set-based approaches considering a zonotopic representation. Moreover, this thesis presents both analysis and comparison of the set-based approaches for the state estimation and FDI frameworks with the goal of establishing the advantages and disadvantages of each approach, and also, to find out their relationship in a formal mathematical framework. However, the mentioned set-based approaches implicitly assume time-varying uncertainty. In the set-based approach, the propagation of the state set is affected by several problems such as the wrapping effect, temporal variance on uncertain parameters (or uncertain parameter time dependency) and range evaluation of an interval function, especially in the case of using the interval hull of the set at each iteration. Therefore, conservative and unstable results may be obtained (for even a stable system) when using the set-based approach in the simulation of the system with parametric time-invariant uncertainties. On the other hand, the approximated state set can be computed based on a set of point-wise trajectories. This type of approach is called \emph{trajectory-based approach}. Therefore, the uncertain parameter time dependency is preserved if the set of point-wise trajectories is generated using the mentioned trajectory-based approach.
