Maths, business & society: portrait of Alesia Herasimenka

Sponsored by the learned societies Société Française de Statistique (SFDS), Société de Mathématiques Appliquées et Industrielles (SMAI ) and Société Mathématique de France (SMF) , the 2024 thesis prize was awarded at the 13th Forum Entreprises & Mathématiques on Monday October 7, 2024.

• Thesis title: Optimal control of solar sails
• Issuing university: Université Côte d'Azur
• Supervisors: Jean-Baptiste CAILLAU, Jean-Baptiste POMET and Lamberto DELL'ELCE
• Company: European Space Agency (ESA)
• Currently Surrey Fellow in Space, Surrey Space Centre, School of Mathematics and Physics, University of Surrey

What motivated you to do a thesis with links to the socio-economic world?

I wanted to work on real missions, not just theoretical ones. In discussions with my thesis supervisors, we came up with the idea of applying for co-funding fromESA to have the opportunity to collaborate with them. To do this, we had to write a project proposal and apply on their platform, and they selected my project. My work focused on convex optimization and optimal control algorithms for solar sails. The ESA is not very interested in solar sails, unlike the Japanese space agency (JAXA) or NASA, but they feel that the algorithms I developed during my thesis are promising for other applications such as proximity operations and rendezvous between satellites.

Can you tell us about your thesis topic?

The subject of my thesis is optimal control applied to solar sails. Optimal control is a mathematical framework. Solar sails are satellites that use light to propel themselves, in the same way as a sailing boat uses the wind! Except that it doesn't work with wind, but with light. It's the same thing in space: photons interact with the large surface of a satellite and push it in a given direction. There's a lot of interest in this type of propulsion today, as it can be used for interstellar missions. This means that satellites can be sent a very long way in just a few decades, compared with hundreds of years with conventional propulsion.

How did the subject of your thesis come about?

I'd say it was a gradual process. I began my studies with economics, before moving on to mechanical engineering. It was through various projects and courses that I gradually became interested in aerospace. During an exchange semester in Sweden, we had a course on the mechanics of supersonic flight, i.e. everything to do with supersonic aircraft as well as rockets. I found it fascinating! I went on to manage a student project involving the construction of a small rocket, and then I did a few internships on satellites... it came gradually.

What were the main challenges you encountered during your research?

It's not often easy to find an exciting thesis topic in the field you want. It was even harder for me to find a thesis as a foreigner, especially in the field of space, which is considered a defense field in France. Initially, I wanted to do a thesis in partnership with a company, but the only option for me was to do my thesis in a research institute. That's why I decided to apply to ESA for their collaboration and support.

How has your work benefited or will it benefit the socio-economic world in the future?

My subject has deepened our understanding of low propulsion space missions. The algorithms I developed can be used for many things, not just solar sails. It's becoming more and more interesting these days, because we want to be able to build a lunar space station, send satellites in formation, etc. From our point of view, it's a very interesting field. From our point of view, it's also a step forward for the development of solar sails for ambitious long-term missions, and less expensive, as these missions would require less fuel.

What advice would you give to young people wishing to direct their mathematical research towards concrete applications?

First of all, I'd say that a thesis doesn't necessarily restrict you to something specific for three years, but rather opens the door to quite different things. We're pretty free during the thesis, and it's great to be able to discuss things, explore the direction we want to take, explore different avenues. And if we don't like something, we can also change our approach. A thesis also gives you the chance to collaborate with lots of people, go to conferences and meet new people. You learn a lot about other fields, and that's very stimulating. In my opinion, the most important thing is to choose the right team. I don't like working alone, and my thesis supervisors were very attentive and always available to me, which is a rarity in the academic world.

How do you see the role of mathematics in solving current societal problems?

Mathematics is at the root of everything: it's a language that we use to translate physics or chemistry equations in a formal way, it enables us to have algorithms that work, it enables us to have an approach to solving different problems. In my field, for example, to find an optimal trajectory, we use the mathematical approach of optimal control. This enables a finer, more sophisticated resolution, perhaps more complicated but often better than the simpler engineering tools.

As a young researcher, how do you see the link between academic mathematical research and the socio-economic world evolving?

I think mathematics is used to solve everyday problems. Whether in space, medicine, finance or even politics. I believe that the development of humanity depends to a large extent on scientific progress, and mathematics is the foundation of all the sciences.

What are your plans for the future?

I'd like to work on ambitious space missions that will go beyond our current knowledge of the universe. Of course, you can't do a whole mission on your own, so I'd like to be part of a large international team.