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Robust control of infinite-dimensional systems


   Department of Automatic Control and Systems Engineering

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  Dr A Selivanov  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

An infinite-dimensional system (also called a distributed-parameter system) is any system whose state space is infinite-dimensional. Typical examples are chemical and fusion reactors, oil drill strings, vibrating beams, quantum-mechanical systems, and traffic flows. Such systems are often modelled by partial differential equations (PDEs). Just like any mathematical model, PDEs are idealised approximations of the real-world processes that are always subject to external disturbances, measurement and control noise, unknown delays, and other deteriorating phenomena. Thus, for a theoretically developed controller to work in practice, it must be robust to such phenomena.

This research project aims to develop analytical methods to design stabilising 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 finite-dimensional observation and control of infinite-dimensional systems, analysis of PDEs with time-delays, input-to-state stability of distributed parameter systems, in-domain point control of multi-dimensional PDEs, and adaptive control of infinite-dimensional systems. The main research tools are Lyapunov functionals, linear matrix inequalities, and Fourier series.


Funding Notes

This is a self-funded research project. We require applicants to have either an undergraduate honours degree (1st) or MSc (Merit or Distinction) in a relevant science or engineering subject from a reputable institution. Full details of how to apply can be found at the following link:
https://www.sheffield.ac.uk/acse/research-degrees/applyphd
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
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