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A RUDN Mathematician Calculated Parameters for Optimal Crowd and Traffic Control
A RUDN Mathematician Calculated Parameters for Optimal Crowd and Traffic Control
A RUDN mathematician developed a solution for a perturbed differential containment - a generalized case of a differential equation. The development will help calculate optimal ways for the movement of a crowd or a flow of cars. It may also be used to manage robotic cars and multi-agent robotic systems. The results of the study were published in the Journal of Differential Equations.

The majority of physical processes can be described using differential equations. To do so, an unknown quantity (e.g. temperature or velocity) is presented as a function. A differential equation may be written for such a function, and its solution will describe the behavior of the unknown quantity. However, in some cases writing a differential equation is impossible, and mathematicians have to use so-called differential containments - equations in which the equality sign is replaced with the sign of containment or inclusion. A RUDN mathematician developed a comprehensive solution for a group of differential containments and showed its possible applications in city management cases.

Optimal control problems are covered by a special theory in mathematics. The idea of such problems lies in developing (quantitatively or theoretically) a control law that would bring a system to a certain given state in the most efficient way. Imagine a car that is approaching traffic lights. When the distance between them is 250 meters, the green light turns on and remains for 30 seconds. One has to calculate how the car should move to reduce its energy consumption to the minimum. At first this may appear as a problem for school children, but not that both acceleration and slowdown consume the fuel. Therefore, such a problem lies in the scope of the optimal control theory and can be solved using a differential containment.

Using the differential containment in question, one can describe the movement of a crowd. Imagine there are a lot of people in a room, and each of them needs to leave it as quickly as possible. However, there is only one exit. The results obtained by the mathematicians will help calculate the trajectory and speed of movement for each particular person.

The results of the study may be practically applied to the calculation of optimal routes for robotic cars. Another possible area of application is multi-agent robotic systems, i.e. systems of several AI robots working on the same task, such as sorting or transportation of goods. Several robots of this kind form a crowd, and for their work to be efficient, optimal speeds and trajectories should be calculated for each of them.

Main Publications View all
15 Nov 2017
RUDN University scientists publish results of their scientific researches in highly-recognized in whole world and indexed in international databases journals (Web of Science, Scopus ect.). That, of course, corresponds to the high status of the University and its international recognition. Publications of June-September 2017 ( In Journals of categories Q1-Q3)
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02 Apr
The Financial Support of RUDN Scientific Journals: Results Are Announced

The results of the contest launched to support the development of scientific journals of RUDN University are summed up. The purpose of the contest is to contribute to the improvement of the academic reputation of RUDN University both as a research center and a publisher of authoritative scientific journals.

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02 Apr
RUDN Tree Talkers Will Monitor the State of Trees in Moscow

In 2020, the Moscow City Government will begin to monitor urban trees using devices created by RUDN scientists. This was announced by the head of Moscow Department of Nature Management and Environmental Protection Anton Kulbachevsky during the 20th anniversary meeting of the Panel of the Department. The event was held on March 2, 2020. Elvira Dovletyarova, head of the Department of Landscape Design and Sustainable Ecosystems of the Agrarian and Technological Institute of RUDN University took the floor as a visiting expert.

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02 Apr
RUDN University Chemist Invented a "Line Production" Method of Synthesis of 28 Biologically Active Molecules

A chemist at RUDN University has invented a new method for the synthesis of a large group of complex poly-heterocyclic organic compounds, which draw interest as possible future medications. The researcher turned to a two-step reaction, in which he used affordable and cheap organic reagents and catalysts based on gold, which allowed him to synthesize as many as 28 new molecules. This approach will significantly expand the libraries of biologically active substances. The work was published in Organic & Biomolecular Chemistry.

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