UDC 004.75
MATHEMATICAL MODELING AND NUMERICAL STABILITY ANALYSIS OF A CONSENSUS PROTOCOL IN DECENTRALIZED MULTI-AGENT SYSTEMS
M. M. Blagirev, Postgraduate Student, Assistant at the Department of Instrumental and Applied Software
Engineering, Institute of Information Technologies, MIREA – Russian Technological University, Moscow,
Russia;
orcid.org/0009-0008-2853-3411, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
E. N. Miftakhov, Doctor of Physical and Mathematical Sciences, Professor at the Department
of Instrumental and Applied Software Engineering, Institute of Information Technologies, MIREA – Russian
Technological University, Moscow, Russia;
orcid.org/0000-0002-0471-5949, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
This paper presents a mathematical model of a decentralized multi-agent system designed to analyze
consensus-reaching algorithms under the conditions of local information exchange between agents. An approach is proposed for describing agent dynamics based on a continuous state model, communication network topology, and trust coefficients characterizing the reliability of transmitted information. For steadystate
operation, a linear consensus protocol is proposed and an analysis of its asymptotic stability is carried
out. To verify the results obtained, a simulation software package that implements numerical integration of
agents’ state equations has been developed. During computational experiments, various operating modes of
the system and the influence of key perturbation factors were investigated. The simulation results showed
that, under ideal conditions, the system converges to consensus monotonically; if permissible integration
step is exceeded, it loses stability; and in the presence of delays, it retains convergence but exhibits slowing
of transient process and the emergence of damped oscillations. The results obtained confirm the applicability
of the developed model for analyzing the stability of decentralized multi-agent systems and justify the need to
develop adaptive control protocols that take into account the quality of communication channels.
Key words: decentralized multi-agent systems; reaching consensus; mathematical modeling; trust coefficients; stability; adaptive control; simulation modeling.