A mathematical model for evaluating the controllability of information management systems in complex adaptive environments

Abstract

Modern information management systems operate in complex adaptive environments characterised by high dynamics, uncertainty and continuous hybrid disturbances, which significantly complicates the maintenance of coordinated control. Under such conditions, traditional approaches focused on reliability and performance of individual components are insufficient, as they do not account for systemic interactions between subsystems and the risk of loss of overall controllability. This creates a need for the development of mathematical approaches for quantitative assessment of system controllability as a key property of the resilience of critical information infrastructure. The aim of this study is to develop a mathematical model for assessing the controllability of information management systems operating in complex adaptive environments, taking into account the interaction of functional subsystems, external and internal disturbances, and control actions that influence system dynamics. Methodology: The study employs a vector–matrix approach to dynamic modelling, in which the information management system is represented as a set of interacting functional subsystems described in the state space by a system of differential equations. The model incorporates inter-subsystem interactions, degradation processes, external disturbances and control actions, as well as the influence of cognitive factors on system behaviour. Numerical verification of the proposed model is performed using the fourth-order Runge–Kutta method within a scenario-based analysis framework. The information management system is formalised as a set of five interacting functional subsystems, including infrastructural, network-communication, application, analytical-cognitive and user levels. An integral system controllability coefficient is introduced as a scalar functional of subsystem states, interaction parameters and control inputs. It is shown that this coefficient enables quantitative identification of transitions between stable, adaptive, crisis and pre-collapse operating regimes. An interpretation scale is developed that relates the values of the coefficient to subsystem coordination and the probability of management desynchronisation. The results of numerical modelling confirm the sensitivity of the proposed indicator to destabilising influences and its ability to reflect the effectiveness of compensatory control actions. The proposed approach extends existing methods of assessing system stability and reliability by introducing a dynamic integral indicator that captures the combined influence of structural interactions, control actions and cognitive factors on system behaviour. The scientific novelty lies in the formalisation of system controllability as a quantitative functional characteristic that reflects the ability of a complex system to maintain coordinated operation under destabilising conditions. Practical value: The developed model provides a practical tool for application in real-time monitoring systems and decision support platforms for critical information infrastructure, enabling early detection of loss of controllability and supporting the design of adaptive response strategies.