A RUDN Mathematician Calculated Parameters for Optimal Crowd and Traffic Control
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.
The RUDN University Science and Innovation Prize winners were honoured at the extended meeting of the Academic Council. In 2024 the terms of the traditional RUDN University Prize were changed: for the first time the competition was announced in two categories: leading scientists and young scientists.
According to the International Energy Agency (IEA), electricity consumption in Africa has increased by more than 100% over the past two years (2020-2022). However, 74.9% of this energy is still produced by burning organic fuels — natural gas, coal and oil. At the same time, the level of electrification on the continent remains extremely low — only 24%, while in other developing countries it reaches 40%. Even in grid-connected areas, electricity supply is often unreliable: industrial enterprises lose energy on an average of 56 days a year.
Today, diagnosis and treatment planning with orthodontists takes several days. Also, complications can arise during treatment that slow down the patient's recovery process. For example, improper orthodontic treatment planning can lead to temporomandibular joint dysfunction.
The RUDN University Science and Innovation Prize winners were honoured at the extended meeting of the Academic Council. In 2024 the terms of the traditional RUDN University Prize were changed: for the first time the competition was announced in two categories: leading scientists and young scientists.
According to the International Energy Agency (IEA), electricity consumption in Africa has increased by more than 100% over the past two years (2020-2022). However, 74.9% of this energy is still produced by burning organic fuels — natural gas, coal and oil. At the same time, the level of electrification on the continent remains extremely low — only 24%, while in other developing countries it reaches 40%. Even in grid-connected areas, electricity supply is often unreliable: industrial enterprises lose energy on an average of 56 days a year.
Today, diagnosis and treatment planning with orthodontists takes several days. Also, complications can arise during treatment that slow down the patient's recovery process. For example, improper orthodontic treatment planning can lead to temporomandibular joint dysfunction.