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Renato VIZUETE, Towards networks of infinite dimensions.



Lauréat du 2ème Prix de Thèse Impact Science de la Fondation CentraleSupélec 2022

Merci beaucoup d'avoir accepté l'interview

 

Can you describe your education leading up to your PhD?

I was always passionate about Mathematics. During my high school studies, I was interested in more advanced topics of Mathematics, specially in Calculus and differential equations.  My initial formation at the university was oriented towards electronics but in the last semesters I focused on more theoretical courses related to Control Systems. During my final project, I discovered the field of networks and multi-agent systems thanks to my supervisor, and I took my first steps in the research through networks of mobile robots.  

After obtaining my engineering diploma, I enrolled in a Master Program in Control Systems at the Université Grenoble Alpes. During this time, I focused on more advanced courses in control, and I started working on the recent theory of graphons, which can be considered as networks of infinite dimensions. My internship was about the use of graphons for the analysis and estimation of sampled networks and I was able to publish the results.

Since I wanted to continue my research in the field of control systems and networks with unusual dimensions, I decided to pursue my PhD at the Université Paris-Saclay on the topic of open multi-agent systems, where the dimension of the network changes with time.

 

How would you describe the time during your PhD?

It was a long trip where I learned how to do research. At the beginning, I thought that all the researchers were locked in an office until they got a big result that would change the world. However, I realized that research is more dynamic, where discussions with colleagues are really important, and it is common to visit other countries and laboratories to discover other academic environments.

The experience was really great, but also with many challenges and usually nothing goes according to the initial program. At the beginning, I thought that by following the desired plan, I was going to reach the goals at the end of the three years. Nevertheless, during the exchanges with my supervisors, in many cases we found unexpected difficulties that required a small deviation from the current field. In addition, I discovered other important topics and directions for the research and at the end, I obtained results that are different from what was initially expected.

 

How would you describe the significance and relevance of your results?

My research was one of the pioneer theses in open multi-agent systems that addresses a more realistic scenario where the set of agents is not fixed, allowing arrivals, departures and replacements of agents such as in real interactions (epidemics, platoon of vehicles, smart grids, social networks, swarm robotics).

I showed that the behavior of open multi-agent systems can be really different from classical multi-agent systems, since in many scenarios, the system can become unstable because of the openness. This will have a great impact on the design of new control and optimization algorithms in modern networks, since arrivals, departures and replacements must be taken into account to obtain a satisfactory level of performance.

Thanks to my results I got an award for a paper in optimization and another award for the results of my thesis.

 

What do you do on your current job, and how does it relate to your previous experience?

I am currently a postdoctoral researcher at the Mathematical Engineering Department at UCLouvain in Belgium. At the beginning, I was working on the identification of nonlinear networks. This new field was a bit challenging since no one had worked on the nonlinear case before and for this reason it was necessary to establish all the definitions, notation, and problems from scratch. Then, thanks to FNRS, I got the funding for my first research project “GAFOM” focused on the use of graphons for the analysis of open multi-agent systems. With this project, I plan to complement the results obtained during my PhD thesis, where graphons will provide additional tools in infinite dimensional systems and richer network topologies for open multi-agent systems. In addition, I collaborate in academic activities like teaching, supervision of students, etc.

 

What would be your main advice to a prospective Ph.D. student?

First, be patient. At the beginning, everyone wants to get results as soon as possible, but in many cases, it is more important to get a good understanding of the research topic and find a problem that could provide results in a timely manner.

Second, be innovative. Perhaps this is the most difficult part since it is more comfortable to do research in a well-established field. However, it is important to try to do something different since the new ideas are the key for the progress of science and the improvement of the world.

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