Analyzing Uncertain Dynamical Systems after State-Space Transformations into Cooperative Form: Verification of Control and Fault Diagnosis

Abstract

When modeling real-life applications, uncertainty appears in the form of, for example, modeling approximations, measurement errors, or simply physical restrictions. Those uncertainties can either be treated as stochastic or as bounded, with known limits in the form of intervals. The latter is considered in this paper for a real-life application in the form of an electrical circuit. This is reasonable because the electrical circuit is subject to uncertainties, mainly due to circuit element tolerances and variable load conditions. Since conservative worst-case limits for such parameters are commonly known, interval methods can be applied. The aim of this paper is to demonstrate a possible overall handling of the given uncertain system. Firstly, this includes a control and a reliable computation of the states’ interval enclosures. On the one hand, this can be used to predict the system’s behavior, and on the other hand to verify the control numerically. Here, the implemented feedback control is based on linear matrix inequalities (LMIs) and the states are predicted using an interval enclosure technique based on cooperativity. Since the original system is not cooperative, a transformation is performed. Finally, an observer is implemented as a diagnosis tool regarding faulty measurements or component failures. Since adding a state-of-the-art observer would destroy this structure, a cooperativity-preserving method is applied. Overall, this paper combines methods from robust control design and interval-based evaluations, and presents a suitable observer technique to show the applicability of the presented methods.