Analysis of a Discrete Model of an Adaptive Control System for Conflicting Nonhomogeneous Flows

Abstract

Using the Lyapunov–Yablonsky approach based on cybernetics, we construct and study a mathematical model of an adaptive control system for conflicting flows of nonhomogeneous customers. The state of the facility and queue lengths for conflicting input flows are chosen as the state of the control system. The Markov property of the sequence of states of the system is proved and they are classified. A necessary condition is found for the existence of a stationary mode in the system.