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A RUDN mathematician has developed a solution for a perturbed differential containment—a generalized case of a differential equation. The development will calculate optimal paths 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 equal 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 - Theory - Mathematics
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 light turns green and remains for 30 seconds. The control problem is calculating how the car should move to reduce its energy consumption to...
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