Data-driven dissipativity analysis with quadratic difference form supply-rate functions and its applications

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 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.

Dissertation: https://hdl.handle.net/11370/4bbf086e-3942-48b0-896a-da8da40ef236