A distributed-parameter system is a dynamical system with an infinite-dimensional state space. Such systems are usually described by partial differential equations (PDEs). Famous examples are chemical and fusion reactors, oil drill strings, vibrating beams, quantum-mechanical systems, and traffic flows. Without proper control, these systems lose their usefulness: fusion reactors fade, drill bits stick and slip, and traffic flows stall in jams. It is incredibly challenging to control these systems since the number of sensors and actuators is always finite while the state is infinite-dimensional. Moreover, like any mathematical model, PDEs are idealised approximations of real-world processes, which are affected by external disturbances, unknown delays, measurement and control noise, and other deteriorating phenomena. Therefore, for a theoretically developed controller to work in practice, it must be robust to such phenomena.
This PhD project aims to develop analytical methods for the design of robust controllers for distributed-parameter systems. This research area is an inexhaustible source of theoretically challenging and practically important problems. We will:
- consider various PDEs (e.g., reaction-diffusion equation, wave equation, beam equation, etc.),
- identify available sensors and actuators in the systems described by these PDEs,
- design feedback control laws guaranteeing the desired system behaviour,
- study the robustness of the designed controllers.
The main research tools are Lyapunov functionals, linear matrix inequalities, and Fourier series.
If you would like to learn about the PhD project more or have any questions, please, feel free to contact the project supervisor, Dr Anton Selivanov, at [Email Address Removed].
- R. Katz and E. Fridman, “Constructive method for finite-dimensional observer-based control of 1-D parabolic PDEs,” Automatica, vol. 122, p. 109285, 2020.
- A. Selivanov and E. Fridman, “Delayed H-infinity control of 2D diffusion systems under delayed pointlike measurements,” Automatica, vol. 109, p. 108541, 2019.
- E. Fridman and N. Bar Am, “Sampled-data distributed H-infinity control of transport reaction systems,” SIAM Journal on Control and Optimization, vol. 51, no. 2, pp. 1500–1527, 2013.
- E. Fridman and A. Blighovsky, “Robust sampled-data control of a class of semilinear parabolic systems,” Automatica, vol. 48, no. 5, pp. 826–836, 2012.
Strong mathematical background (in calculus, linear algebra, ODEs, and functional analysis) and familiarity with PDEs are essential. Experience in control theory is desirable but not mandatory – a mathematically literate candidate can quickly fulfil possible gaps. Most importantly, we are looking for candidates passionate about maths and fundamental research in general.
Applicants are required to hold a BSc/MSc degree in mathematics or engineering. If the degree is not from an English-speaking country, the applicant needs an overall IELTS grade of 6.5 with a minimum of 6.0 in each component (or equivalent). For further details, visit https://www.sheffield.ac.uk/postgraduate/phd/apply.
The University of Sheffield is a Russel Group university in the Top 100 World Universities according to the QS World University Rankings. It is located in the centre of the UK, right next to the Peak District National Park. The Department of Automatic Control and Systems Engineering (ACSE) is the only department in the UK dedicated to Control Engineering. The standard duration of a PhD in the UK is 3.5 years. To learn more about student life in Sheffield, visit https://www.sheffield.ac.uk/sheffield-guide.
Informal enquiries are encouraged and should be addressed to Dr Anton Selivanov at [Email Address Removed].
- You can apply for this project here: https://www.sheffield.ac.uk/postgradapplication/
- Suitable candidates will be invited for an online interview in December/January.
- Candidates who pass the interview will be invited to apply for the University of Sheffield PhD scholarship. The application deadline is 25 January 2023.
- Start date: Autumn Semester 2023.