CREATION OF DISCRETE ALGORITHM OF VEHICLE CONTROL WITH USING THE THEORY OF FINITE-SEQUENCE MACHINES AND THE METHODS OF MATHEMATICAL STATISTICS

Abstract

In the article a vehicle control model for the linear law of its speed change over the time is discussed. A distinctive feature of the formed mathematical model is that it was created with using analytical methods of discrete mathematics, set theory, theory of finite sequence machine and mathematical statistics. On the base of analysis of a simple law of motion a vehicle between two given points in a straight line with a constant decrease in speed, it is theoretically proved, that a mathematical model of such law of motion can be realized in the space of limited in time states, and, thus, it can be reduced to the corresponding model of a finite sequence machine. The undoubted advantage of the proposed mathematical model of the vehicle motion control system is its simplicity, as well as the absence of corrective action at those times when the vehicle movement corresponds to a given law with a slight error. This avoids unnecessary ejections of vehicle speed and oscillation processes that can occur in the case of a continuous control action in the time when the control system parameters are incorrectly selected. Mathematical models for the cases of quasi-stationary and random disturbing effects are considered separately. To simulate a random disturbing effect, the Student distribution law is used. It should be noted that the finite automaton scheme, had been obtained in this work, is universal and corresponds to both quasi-stationary and random disturbing effects. Only the analytical relations of discrete mathematics and mathematical statistics are changed, according to which the control law is formed through the analysis of the states of the finite sequence machine. The simulation results showed that with a quasi-stationary disturbing action, the control error is about 2-5%, and in the case of a random disturbing action, this error is about 5-8%. The proposed approach to the creation of control systems is quite universal and can be successfully used to synthesize control systems for other purposes, including technological ones.