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Dr Tim Hughes

Lecturer in Mathematics

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My research concerns the fundamental mathematical principles that underlie the analysis, synthesis and control of interconnected systems (mechanical, electrical, financial, etc), and the application of mathematics to better understand and design such systems.

One strand of this research concerns the design of mechanical and electrical networks. This has exposed a number of important questions concerning minimality of such networks, which my research aims to address.

A second strand concerns passivity and passive control, where I have addressed fundamental questions on the relationship between passivity and controllability, and on optimal energy extraction from passive systems. The extraction of energy from a passive system with a renewable energy source is a feature of many renewable energy technologies, and I am interested in control and optimisation in this and other similar settings.

Recent research is concerned with the development and application of techniques and computationally efficient methods in real algebraic geometry for optimisation and control, which I am exploring together with my EPSRC funded PhD student Gareth Willetts.

I am also interested in monetary system dynamics and its effects on inequality and resource depletion, and am supervisor of Edward Branford's PhD on optimal control and its economic applications.

I lead the module 'Advanced interdisciplinary mathematics', which explores contemporary issues from ecology, epidemiology, society, renewable energy, and the environmental sciences from a mathematical sciences perspective. I also lead the module 'Dynamical Systems and Control', in which I demonstrate the underlying mathematical concepts using a Lego Mindstorms segway robot.

Keywords

Applied mathematics; Dynamical systems; Control; Mechanical systems; Networks; Electric circuits; Energy systems; Passivity; Optimal control; Polynomial Matrix Algebra; Interdisciplinary mathematics; Sustainable finance; Environmental sciences; Ecology; Epidemiology; Social systems.

Prospective PhD students

I am eager to hear from prospective PhD students. Please contact me for further details of potential projects.

Publications

Details of published work can be found under the Publications tab.

I have also deposited several preprints and postprints on ArXiV: https://arxiv.org/a/hughes_t_3

Biography

Having completed an MEng at the University of Cambridge Department of Engineering, I worked for 3 years for the product development consultancy 'The Technology Partnership plc'. I returned to the University of Cambridge in 2010 to undertake a PhD in Control Engineering, graduating in 2014. From 2013 to 2017, I was a Henslow Research Fellow at Fitzwilliam College, University of Cambridge, funded by the Cambridge Philosophical Society. In the final year of this research fellowship, I was additionally an affiliated lecturer at the University of Cambridge.

I joined Exeter in November 2017 as a lecturer in the Department of Mathematics on the Penryn Campus.