Robust control of infinite-dimensional systems

The Department of Automatic Control and Systems Engineering at the University of Sheffield invites
applications for an exciting new project. The programme will start in February 2020.

Project Description

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.

Candidate Requirements and Eligibility

Prospective candidates should have a strong background in control theory and should be
familiar with partial differential equations. Programming skills are essential (MATLAB/Python).
More information about entry requirements can be found here:

Applicants with other qualifications or experience should contact the Department’s Research
Support Officer via so that we can check on your eligibility.

Funding Notes

Applicants can apply for a Scholarship from the University of Sheffield but should note that competition
for these Scholarships is highly competitive. It will be possible to make Scholarship applications from
the Autumn with a strict deadline in late January 2020. Specific information is available at:


To apply, please submit a PhD application using the University’s online application system via the
Postgraduate online application form. Within the application, please state Dr Anton Selivanov as your
preferred supervisor and state the project title as ‘Robust control of infinite-dimensional systems’

For informal queries, please contact Dr Anton Selivanov via
Please note that shortlisted candidates will be required to attend an interview (which may take place via Skype, in person or by phone).