PhD defence Tábitha Esteves Rosa: "Data-driven dissipativity analysis with quadratic difference form supply-rate functions and its applications"

Promotors: Prof. Bayu Jayawardhana and Prof. Claudio de Persis

Abstract: Dissipativity property is a concept introduced in the early 70s by Jan C. Willems, to describe the input-output behaviour of a dissipative system. The main idea of this concept follows the energy conservation laws, where the rate change of a system's energy function, called storage function, is upper bounded by the power or work done to the system, commonly referred to as the supply-rate function. We call the inequality that describe this behavior as dissipativity inequality. As most real-world applications belong to the class of dissipative systems, investigating theoretical methods to analyse and deal with such systems can be the base of many practical solutions, for instance fault detection. In this thesis, we specifically investigate the verification of dissipativity properties of unknown LTI (linear time invariant) systems using input-output data and the application of the approach to a fault detection method. For validating our theoretical results, we apply the proposed methods in numerical simulations and practical real-world applications.

The first topic we address in this thesis concerns to the development of new dissipativity verification methods. For this, we consider dissipativity definitions based on a finite or an infinite time-horizon window of data. In both approaches, we make use of a quadratic difference form of supply-rate function. This representation is a generalization of the common QSR-dissipativity, where the supply-rate is given as a quadratic function of the inputs and outputs. In the quadratic difference form, we include also time-differences of the input and outputs. By using this form of supply-rate, we encompass the dissipativity analysis of all LTI systems and can apply the method to a vast range of applications and analyses, from passivity, $L_2$-stability to negative imaginary systems and mass-spring-damper systems. Part of our studies verifies the dissipativity using a single shot of data that is persistent exciting. The other part is built on the use of multiple shots of data for the identification of the dissipativity inequality. The use of multiple shots of data can be used, for instance, in cases where there are missing data or the lack of a single trajectory that is persistently exciting.

The second main subject we investigate is fault detection. Given that the dissipativity inequality describes the nominal behaviour of a dissipative system, we look into an approach that detects the presence of a fault based on this description. We apply and validate all of our proposed methods using theoretical examples and practical applications. The first practical application concerns to an educational two-degree-of-freedom planar manipulator from Quanser. Using data obtained from experiments using this manipulator, we are able to verify the dissipativity and subsequently apply the proposed fault detection algorithm and observe its advantages when comparing it to a standard principal component analysis algorithm. The second main practical study case is an ultra-high vacuum chemical vapor deposition (UHVCVD) process.

The UHVCVD process is a process used in the production of thin films. In this environment, the real-time process monitoring and control systems have to deal with uncertainties and batch-to-batch variation.

We perform a study on the variations seen in the process of deposition of multiple precursors, Sodium and Potassium, simultaneously or individually. More specifically, we present, analyse and show the variability issues in the calibration experiments that establish one-to-one mapping between the atomic absorption spectroscopy (AAS) measurements and the partial pressures of the evaporated elements, which limits the application of models. Further, we apply the fault detection method based on the dissipativity properties to identify a fault during the mentioned calibration experiments.

From the results shown in this thesis, we verify and validate the applicability of the use of our data-driven dissipativity verification approaches, including their applications in the fault detection context. We also indicate the potential applications and extensions of the methods introduced in this work.

Dissertation