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Mathematics and Statistics

Photo of Dr Tim Hughes

Dr Tim Hughes

Senior Lecturer in Mathematics


I am part of the Centre for Environmental Mathematics with research interests in the development of systems and control theory and its interdisciplinary applications to benefit society and the environment.

Prospective PhD students

I am eager to hear from prospective PhD students. I am particularly interested in projects concerning the design of social and alternative financial systems to achieve environmentally and socially sustainable outcomes. Examples include

  1. reform of international governance and innovations in international finance for sustainability;
  2. design and data analysis of local/ community level governance systems based on participatory methods and innovative ways of organising and management (e.g., sociocracy and commoning);
  3. design and data analysis of local and project oriented complementary currencies to build trust and collaborations within communities or achieve certain sustainability outcomes (e.g., management/conservation of ecosystems or fossil fuel reserves).

Such projects can involve a combination of practical action research and theoretical work in collaboration with partners working on international and local financial innovations, local community organisations, and practitioners of participatory democracy.

Please contact me for further details of potential projects. 


My research concerns the fundamental principles that underlie the analysis, synthesis and control of interconnected systems, and the application of these principles to better understand and design such systems.

My PhD and postdoctoral research focussed on the analysis and design of passive mechanical and electrical networks (i.e., networks without an in-built energy source). My research in this area has:

  1. addressed fundamental questions and developed universally applicable design techniques for networks that contain the least possible numbers of components;
  2. established fundamental properties concerning passive systems, and optimal energy extraction from such systems;
  3. developed computationally efficient methods and novel techniques in real algebraic geometry for optimisation and control in this setting and more broadly (in collaboration with my PhD student Gareth Willetts).

The extraction of energy from a passive system with a renewable energy source is a feature of many renewable energy technologies, and an anticipated future application of this work.

A growing focus of my research is the development and application of fundamental systems and control principles to policymaking for sustainability, enabling the formal design of policies to maximise sustainable development values, navigate planetary constraints, and support transition towards a fairer and more environmentally sustainable society. This will build on the work of my PhD student Edward Branford on discrete time optimal control and its application to sustainable economic systems.

I am strongly engaged in the innovative MSc Applied Data Science programmes and cross-disciplinary teaching at the interdisciplinary Penryn campus. I teach modules that span specialisms in Environment and Sustainability, Renewable Energy, Ecology and Evolution, and Modelling. I have developed and I currently lead modules on Applied Artificial Intelligence and Control; Mathematics for Environment and Sustainability; and Fundamentals of Data Science.

I have a growing interest in Education for Sustainable Development (ESD): “empowerment through knowledge, skills and values to protect the planet [UNESCO]”. I am the University of Exeter staff lead for the Responsible Futures institutional change programme and associated accreditation scheme, building partnerships with students and student unions on sustainability learning, inclusive of environmental justice. This is closely related to the University's Transformative Education programme, and in particular the intersection between its foci on sustainability and racial and social justice. 


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

I have also deposited several preprints and postprints on ArXiV:

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Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.

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  • Alharthi M. (2023) Optimal and Adaptive Control for Volterra Difference Equations.









  • Hughes TH. (2014) On the Synthesis of Passive Networks without Transformers. [PDF]
  • Smith MC, Hughes TH, Jiang JZ. (2014) A Survey of Classical and Recent Results in RLC Circuit Synthesis, 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, The Netherlands, 7th - 11th Jul 2014,, pages 1119-1120.
  • Hughes TH, Smith MC. (2014) Questions of minimality in RLC circuit synthesis, 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, The Netherlands, 7th - 11th Jul 2014,, pages 1558-1561.
  • Hughes TH. (2014) On Connections between the Cauchy Index, the Sylvester Matrix, Continued Fraction Expansions, and Circuit Synthesis, 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, The Netherlands, 7th - 11th Jul 2014,, pages 1121-1128.
  • Hughes TH, Smith MC. (2014) On the minimality and uniqueness of the bott-duffin realization procedure, IEEE Transactions on Automatic Control, volume 59, no. 7, pages 1858-1873, DOI:10.1109/TAC.2014.2312471.


  • Hughes TH, Smith MC. (2013) Algebraic criteria for circuit realisations, Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday, CreateSpace, 211-228.

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