Mathematics: Fully Funded Swansea University PhD Scholarship: Solving Polynomial Systems For Feedback Control
Funding provider: Swansea University's Faculty of Science and Engineering
Subject areas: Applied Algebra and Geometry
Project start date:
- 1 April 2022 (Enrolment open from mid–March)
- 1 July 2022 (Enrolment open from mid-June)
- Principal supervisor- Dr Nelly Villamizar (Senior Lecturer, Department of Mathematics)
- Second supervisor- Professor Chenggui Yuan (Department of Mathematics)
Aligned programme of study: PhD in Mathematics
Mode of study: Full-time
Different control design problems in power electronics, robotic locomotion, and agent-based models can be cast in terms of polynomial systems. That is, a set of algebraic equations representing the different design and system constraints for which we need to find suitable real solutions. In order to enable the implementation of optimal control policies, such polynomial systems need to be solved in real time, in a data-driven framework where the system itself is updated from real-time measurements.
This project focuses on algebraic and geometric aspects of polynomial systems and the study of effective solution methods with an outlook to applications in feedback control design.
The overarching goal of this project is to explore novel solution methods for polynomial systems by combining elements from applied algebraic geometry and symbolic computation, including tools from elimination theory, Groebner bases, resultants, and Sturm sequences, with efficient iterative methods in optimization.
By analysing the structure of polynomial systems arising in feedback control problems (such as pole placement, model predictive control, and switching control), we will develop an applied algebraic geometry methodology for the computation of control laws in real time.