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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.

International scientific cooperation View all
03 Nov 2017
The main goal of the RUDN University and UNISDR Office for Northeast Asia and Global Education and Training Institute for Disaster Risk Reduction at Incheon (UNISDR ONEA-GETI) cooperation is to obtain knowledge about disaster risk reduction and international experience in this area for creating training courses for basic and additional professional education in RUDN
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Student's Scientific Initiatives View all
03 Nov 2017
June 22 - 26, 2017 in Barnaul, Altai State University, took place the Summer Academy of the BRICS Youth Assembly, an international event that brought together representatives of different countries
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RUDN chemist creates catalyst to produce anti-mosquito substances

A chemist from RUDN University has developed a catalyst for the production of eugenol acetate, a substance that destroys the larvae of mosquitoes transmitting dangerous diseases, being a safe chemical for human health.

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RUDN soil scientists developed a new method for assessing soil fertility

RUDN soil scientists have revealed a direct correlation between the rate of soil formation of carbon dioxide, called CO2 emissions, and the content of microbial biomass in it. It is known that CO2 emission from soil is mainly conditioned by respiration of soil microorganisms and plant roots. The more CO2 soil emits, the more microbial biomass it usually contains. It was shown that CO2 emission by chernozem of different ecosystems (or different types of land use) correlates with the content of microbial biomass, and most closely with the rate of its microbial respiration. And the soil with good microbial properties has the “best quality”, is more fertile, provides the highest yield of crops and other plant biomass.

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RUDN University chemists proposed a way to reduce three times the temperature for the oxidation of alkanes

RUDN University chemists and their colleagues from the Russian Academy of Sciences have proposed new catalysts that allow to reduce the temperature of the oxidation reaction of alkanes three times — from 150 to 50 degrees. This significantly reduces the cost of synthesizing alcohols, aldehydes and other compounds needed, in particular, for the production of nylon and capron.

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