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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.

Visiting Professors View all
03 Nov 2017
Michele Pagano is a graduate of the University of Pisa, a leading scientist, the author of more than 200 publications in international journals, and a participant in many international research projects
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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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30 Dec
Biologists from RUDN University discovered the secret of flaxseed oil with long shelf life

Biologists from RUDN University working together with their colleagues from the Institute of Molecular Biology of the Russian Academy of Sciences and the Institute of Flax studied the genes that determine the fatty acid composition in flaxseed oil and identified polymorphisms in six of them. The team also found out what gene variations could extend the shelf life of flaxseed oil. This data can be used to improve the genetic selection of new flax breeds. The results were published in the BMC Plant Biology journal.

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11 Oct
Mowing Is More Harmful to Soil Than Grazing

A team of biologists analyzed soil samples from a pasture and a regularly mowed meadow and found out that grazing lets more carbon get into the soil than mowing. This, in turn, improves the carbon cycle and makes microorganisms more efficient.

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11 Oct
Soil scientists suggest method for remediating urban garden soils contaminated with lead and arsenic

The soils of urban gardens and vegetable patches contain a lot of toxicants (including lead and arsenic) in high concentrations which can be harmful to the health of children and people with chronic diseases. A team of soil scientists from RUDN University suggested a remediation method developed based on data collected in a garden of Brooklyn (NY, U.S.).

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