PhD Positions, KU Leuven
In the research group of Wim Michiels, Faculty of Engineering Science of KU Leuven, Belgium, there are vacant positions for two fully funded PhD researchers for a four year, in the area of "Analytical and computational approaches for analysis and control of complex dynamical systems".
The mathematical modeling of complex engineering and biological systems naturally leads to a decomposition into simpler subsystems. Modelling the dynamics of subsystems typically leads to differential equations, while their interconnections give rise to algebraic equations. Furthermore, the fact that the transfer of material, energy and information (i.e., signal transmission) between subsystems is mostly not instantaneous, may be modeled by delay elements. All these model components can be integrated into one so-called Delay-Differential Algebraic Equation (DDAE) model. DDAE models are very flexible and promising for a systematic and automated modeling procedure, at the basis of simulation, prediction and control, yet there are still many open theoretical questions, mathematical and computational challenges.
The research program is built around two pillars, each one forming the core of an individual PhD project. The first pillar concerns investigating theoretical properties of DDAE models, developing mathematical analysis methods (to assess, for example, the stability and performance of the modeled system), perform uncertainty quantification (i.e., assessing the impact of modeling errors and exogenous perturbations on the results of the analysis), and to make the leap from analysis to the design of feedback controllers, in order to alter the performance, robustness or resilience of the system in a desirable or optimal way.
The second pillar specifically focuses on developing methodologies for analysis and control of time-periodic models. The time-periodicity may stem from the linearization of a nonlinear autonomous systems around a periodic orbit, from a periodic excitation, as in applications in electrical power systems, or from the application of recently proposed periodic control strategies for time-invariant systems. Particular attention will be paid to innovative schemes compensating part of the dynamics, to the use of delays for the purpose of control, and
to the development of optimal strategies for achieving phase synchronization in networks. Key in the methodology is the integration of analytical methods from control theory and computational methods from nonlinear dynamical systems.
The design of the control laws will be mainly model based, but complementary data-driven design methods and implementations will also be explored.
The focus of the PhD projects will be on control theory, control design methods and algorithmic innovations, but a close link with engineering applications will be ensured throughout the whole program, which enables a direct validation of the obtained results and algorithms and may inspire novel research questions. In particular, the applications addressed in this project are in the area of vibration control (vibration absorption and input shaping), machining, and electrical power engineering (multi-modular converter (MMC) for HVDC transmission).
More information about the program, the hosting research group and university, the intended profile of the applicants, as well as application instructions can be found at
https://www.kuleuven.be/personeel/jobsite/jobs/60111329
Applications will be considered as soon as they are received, and the opening will be closed as soon as a suitable candidate has been hired. The formal application deadline is June 7, 2022.
