About the Project
Infinite-dimensional systems are those with a state space of infinite dimension. Typical examples include fusion reactors, oil drill strings, chemical reactors, traffic flows, etc. Such systems often require feedback control to remain stable. A popular way of modelling infinite-dimensional systems is using partial differential equations (PDEs), which can describe heat transfer, wave propagation, fluid flows, and other processes. Just like any mathematical model, PDEs are idealized approximations of the real-world processes, which inevitably have parameter uncertainties, external disturbances, measurement and control noise, unknown delays, etc. Thus, the implementation of a theoretically developed controller requires it to be robust to such phenomena.
This research project aims to develop analytical methods to design stabilizing controllers for infinite-dimensional systems and quantify their robustness. This research area is an inexhaustible source of theoretically challenging and practically relevant problems. Possible research directions are control of multi-dimensional PDEs, analysis of PDEs with time-delays in sensors and actuators, PI control of PDEs, adaptive control of infinite-dimensional systems. The main research tools are the Lyapunov functionals, linear matrix inequalities, and Fourier series. Potential applications include control of traffic and multi-agent systems, tokamak stabilization, and air pollution suppression.
This is a self-funded research project.
We require applicants to have either an undergraduate honours degree (2:1) or MSc (Merit or Distinction) in a relevant science or engineering subject from a reputable institution. Prospective candidates for this project should have a strong background in control theory and should be familiar with partial differential equations. Programming skills are essential (MATLAB/Python).
Full details of how to apply can be found at the following link:
Applicants can apply for a Scholarship from the University of Sheffield but should note that competition for these Scholarships is highly competitive: https://www.sheffield.ac.uk/postgraduate/phd/scholarships