Thesis supervisor: Péter Kovács
Location of studies (in Hungarian): Eötvös Loránd University, Faculty of Informatics Abbreviation of location of studies: ELTE
Description of the research topic:
Linear dynamic system modeling and approximation have long been carried out using methods based on rational orthogonal series expansions. One significant advantage of these methods is that they approximate the system by a linear combination of a finite number of basis elements, where the coefficients associated with each element provide specific information about the system's behavior. As a result, reliable system models can be obtained which are represented by a small number of parameters. Numerous algorithms based on rational orthogonal series expansions are known for tasks related to system identification, approximation, and model reduction. However, the development of dynamic system models based on rational orthogonal functions remains an actively researched area, including applications to nonlinear systems, adaptive model reduction, utilization of time-domain data, and development of non-parametric identification methods for linear systems.
The main research objective is to develop novel methods that address the aforementioned problems, with the basis of rational orthogonal series expansions. The research focuses the application of such series expansions in the case of time-domain data and the analysis of the numerical algorithms involved. Another task involves generalizing non-parametric identification methods for linear time-invariant dynamic systems and analyzing their uncertainties. This also includes the modification and adaptation of the developed methods in order to facilitate practical applications (e.g., increasing tolerance to noise). Additionally, investigating nonlinear systems using rational orthogonal basis functions is an important aspect of the research (e.g., studying Wiener-Hammerstein methods, applying Koopman operators, complementing with data-driven methods, etc.). The developed theoretical approaches are applied by the researcher to solve real-world engineering problems (e.g., modeling and identification of systems describing the longitudinal and lateral dynamics of vehicles).
Further requirements: The PhD student must possess the mathematical knowledge required to analyze and construct dynamic system models.
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