Математична модель оптимального керування рухом електрорухомого складу на підставі вирішення рівнянь Гамільтона-Якобі-Беллмана

Abstract

Optimal control is a powerful tool, which allows you to solve complex management tasks, including motion control of electric rolling stock on railways. The optimization problem is a common concern of management theory. It consideres the current factor as an abstract object, which seeks to maximize the expected benefits (or minimize losses) at some future period of time. A mathematical model of electric rolling stock control systems, based on the solution of Hamilton-Jacobi-Bellman equation using the method of dynamic programming and solution of the problem relating to the time coordinate has been developed in this paper. To reduce the volume of calculations it has been proposed to determine the optimal expert system in the direction relating to the movement time of electric rolling stock - reverse Bellman approach. It is assumed that the end point of electric rolling stock movement is known - the ultimate coordinate of movement and given time of movement, and the final velocity at this point is zero - which corresponds to the arrival of the train to the destination.