In November 2021, Clarivate, i.e. the owner of the Web of Science, unveiled its 2021 Annual Highly Cited Researchers List. The list includes about 0.1 % of the world 's most cited scientists in their chosen fields. This annual list identifies 6,602 researchers across the globe, with six out of them mentioning Russia as the country where they are based. Among the highly cited researchers is Professor Nikolay Kuznetsov, Head of the Department of Applied Cybernetics at St Petersburg University and Head of the Russia’s leading research school.

2021 kuznetsov dynamics siberia

In our interview, Professor Kuznetsov spoke about how applied cybernetics started at the University and what tasks the University mathematicians are solving today.

For three consecutive years, you have been recognised as one of 0.1 % of the Highly Cited Researchers in your field across the globe. Could you tell us what this award means to you personally? How difficult is it to retain your position at the forefront of mathematics globally?     

I was first included in the Russian list of highly cited scientists in 2016 in the field of mathematics, and then in 2017 too. For the last three years since 2019, I have been included in the global list of Highly Cited Researchers for cross-field impact. This is a significant contribution to strengthening the position of St Petersburg University in the Shanghai Ranking of Universities (ARWU), where the status of a highly cited researcher has the same weight as receiving the Nobel Prize or the Fields Medal. In the Shanghai Ranking's Global Ranking of Academic Subjects in Automation & Control (this area is among the key areas of our research school), St Petersburg University ranks first among Russian universities and is among the top 100 universities across the globe. In 2017, the University was among 51-75; in 2018 we climbed up to 32nd place, which was the best result among Russian universities since the rankings had been introduced across all areas of knowledge; in 2019 we took 36th place; and in 2020-2021 we were among 51-75.                        

 

For me, the award is evidence that what we are doing is much in demand and up to date. Cross-field research that has been headed by me at the research school has generated a positive response in the global scientific community and made a positive contribution to the research and technological development of the Russian Federation. In 2018, our research school was recognised as the Russia’s Leading Scientific School (the Centre of Excellence) in the priority area of the research and technological development ‘The transition to advanced digital, intelligent manufacturing technologies, robotic systems, new materials and methods of design, the creation systems for processing large amounts of data, machine learning, and artificial intelligence’ in the field of mathematics and mechanics.

The status of the Leading Scientific School (the Centre of Excellence) of the Russian Federation is awarded to the research teams based on the results of a competitive selection. The research teams must: demonstrate significant influence in the renowned wide-ranging field through conducting world-level research; be built on the long-standing traditions; and preserve continuality of traditions in preparing highest calibre researchers. The head of the team must prepare candidates of sciences and doctors of sciences on a regular basis and build research teams in ways to benefit Russian science.

This year, Gennady Leonov is also included in the list of the most highly cited researchers according to the Web of Science. In 2005, he launched an initiative to introduce applied cybernetics at St Petersburg University. Today, you continue to enhance research in the school. What were these 15 years?

The key to our success is foundations laid by Vladimir Yakubovich (1926–2012) and Gennady Leonov (1947–2018), who were Corresponding Members of the Russian Academy of Sciences and opened the research school. Additionally, early-career researchers have made a positive contribution to what we have gained so far. Early-career researchers are the foundation of our research school today and will shape our research in future. The history of applied cybernetics at the Mathematics and Mechanics Faculty at St Petersburg University began in 2005 when Vladimir Yakubovich and Gennady Leonov launched an initiative to open a new field ‘Non-linear dynamics, informatics, and control’ at the Department of Theoretical Cybernetics.

In 2006, Gennady Leonov was selected as a Corresponding Member of the Russian Academy of Sciences. The Academic Council of the Mathematics and Mechanics Faculty asked the Rector of the University to open the Department of Applied Cybernetics to advance the new field that would be headed by Gennady Leonov. In 2007, the Rector of the University signed an order to open a new Department of Applied Cybernetics from the Department of Theoretical Cybernetics. The first members of the department were Gennady Leonov as the Head of the Department of Applied Cybernetics and me as an academic secretary. In 2008, a consortium of two departments, i.e. the Department of Applied Cybernetics and Department of Theoretical Cybernetics, with Gennady Leonov and Vladimir Yakubovich as their heads, was awarded the status of the Leading Scientific School (the Centre of Excellence) of the Russian Federation. In subsequent years, the Department of Applied Cybernetics confirmed this status. In 2018, Gennady Leonov, shortly before his death, appointed me as the head of the research school. Since 2018, the Department of Applied Cybernetics has retained the status of the Leading Scientific School (the Centre of Excellence) of the Russian Federation. 

 

Could you please tell us about some of the research problems or tasks you have been working on? What makes them so important to the global scientific community? What are the achievements you are especially proud of?

The creation and development of the theory of hidden oscillations have advanced us in solving some of the most fundamental problems and is much in demand in applied research today. The theory of hidden oscillations has opened up new horizons in determining the boundaries of stability and identifying unwanted fluctuations to prevent technological and man-made disasters. This is what we used to solve some of the urgent engineering problems. Among them were: an analysis of breakdowns of drilling rigs due to flexural-torsional vibrations of the drill; determination of stability boundaries and excitation of vibrations for a centrifugal regulator with a steam turbine servo drive; determination of the stability of a closed nonlinear dynamic model of the control system of the hydroelectric unit of the Sayano-Shushenskaya Hydro Power Plant; in solving the Gardner and Egan problem of stability and oscillations in phase synchronisation control systems; and problems of Mstislav Keldysh in nonlinear analysis of flutter suppression systems for aircraft controls to name but a few.

In 2020, Academician Vladimir Fortov invited me to take part in the meeting of the Bureau of the Department of Power Engineering, Mechanical Engineering, Mechanics and Control Processes of the Russian Academy of Sciences to deliver a report ‘Hidden oscillations and stability of control systems: theory and applications’. In the same year, I was awarded the St Petersburg University Prize for Scientific Works in the category ‘Fundamental Achievements in Science’. In 2021, I received the International Afraimovich Award for the creation and development of the theory of hidden oscillations, delivered invited reports ‘The theory of hidden oscillations and global stability of dynamical systems’ at the Caucasus Mathematical Centre and ‘The theory of hidden oscillations and stability of dynamical systems’ at the European Workshop on Applied Mathematics at the Technical University of Ostrava (Czech Republic). On 13 December, I was invited to deliver a report ‘Hidden attractors in science and technologies’ at the meeting of the Finnish Academy of Sciences and Letters.

 

What are the research projects you are currently working on?

This year, we are completing a prestigious international Russian-Indian grant of the Russian Science Foundation 'Multistability and hidden oscillations in dynamical systems' (project No 19-41-02002, 2019-2021). We continue the St Petersburg University’s project 'Modern analytical and numerical methods and artificial intelligence for analysing regular and chaotic dynamics'. A unique location and historical ties of St Petersburg ensure that we are actively expanding cooperation between St Petersburg University and universities in Finland. This year, we have a new partner, i.e. the School of Engineering Sciences at Lappeenranta-Lahti University of Technology LUT, Finland, in our Russian-Finnish research and educational agenda of joint academic programmes between St Petersburg University and the Faculty of Information Technology at the University of Jyväskylä. We have been successfully implementing our agenda since 2007 with the financial support of the scholarship schemes of the President of the Russian Federation for study abroad, academic funds of Finland, and support of the Russian Embassy in the Republic of Finland and the Consulate General of the Republic of Finland in St Petersburg. This year, we received the prestigious grant of the Platform of Excellence for Complex System Design: Toward Double Doctor Degree between Leading Research Schools of Finland and Russia for 2021–2023 to develop our research and educational agenda within the framework of the Team Finland Knowledge initiative.

Nikolay Kuznetsov was born in 1979 in Leningrad in a family of researchers and teachers. He was named after his great-grandfather Nikolay Kuznetsov who was a military engineer of the 1st rank, organiser and Head of the Department of Mathematics and Mechanics, Head of the Mechanical Faculty at the Dzerzhinsky Higher Naval Engineering School. In 1996, he graduated from physical and mathematical lyceum No 239. In 2001, he graduated with honours from St Petersburg University. In 2004, he defended his candidate dissertation at St Petersburg University. In 2004-2006, he received a degree in Management at Baltic State Technical University. In 2006, he started to pursue the doctoral programme at St Petersburg University and in 2008 he defended PhD as part of the joint Russian-Finnish research and academic programme at the University of Jyväskylä (Finland). In 2016, he defended his doctoral dissertation on the topic ‘Analytical and numerical methods for the study of hidden oscillations’ at St Petersburg University. Since 2018, Nikolay Kuznetsov is Professor and Head of the Department of Applied Cybernetics at St Petersburg University. In 2020, he became a laureate of the national award 'Professor of the Year' and was elected a foreign member of the Finnish Academy of Sciences and Letters. In 2020, he became a laureate of the St Petersburg University Prize for scientific works and in 2021 he received the Afraimovich Prize for his work on the theory of hidden oscillations and stability of dynamical systems.

Applied cybernetics bridges fundamental and applied disciplines, including those that you could only meet in science fiction. Among them are neuro-management, machine learning and computer vision. How do you see the development of cybernetics in future?

Cybernetics has gone through various stages of its development. They were associated with rapid development of engineering technologies, mathematical theories, computing technology, and information technology. Today, we are observing and developing cybernetics primarily associated with artificial intelligence. Each new step forward is something that makes you look back and understand what can be replaced and what remains up-to-date and will be used in future, what tasks have appeared and what tasks remain unsolved. Computing systems and artificial intelligence have already successfully replaced chess players, go players, and successfully solve many complex problems for humans. The challenge we are going to face in future might be how to replace scientists with artificial intelligence? This is exactly what we have talked about with Aleksandr Malich in the programme ‘The Hour of Science at St Petersburg University’.

In this regard, developing academic programmes and preparing new talented specialists are essential. This year, I took part at the professorial forum 'Science and Technology in the 21st Century: Trends and Prospects for Development' and delivered a report ‘Preparing high-calibre experts in the field of cybernetics, IT technologies and artificial intelligence on the basis of fundamental mathematics: experience of the Department of Applied Cybernetics at St Petersburg University’. I talked about new bachelor's programmes 'Applied Mathematics, Programming and Artificial Intelligence' and master's programme 'Mathematical Modelling, Programming and Artificial Intelligence', which we developed together with leading Russian and foreign experts and IT companies to train students in the field of machine learning and artificial intelligence.

When it comes to the development of cybernetics and artificial intelligence, I am always pleased to tell that on 8 September 2021, the Governor of St Petersburg signed a decree to establish a new award of the Government of St Petersburg for outstanding research results in the field of science and technology in the category 'Cybernetics and Artificial Intelligence' which is named after the founder of the Department of Applied Cybernetics Gennady Leonov.