<p>The article proposes a formalized approach to analyzing the evolution controllability of complex multi-agent systems based on an integral entropy-based indicator of the controllability loss risk. A multilevel model of multi-agent system dynamics is constructed that integrates the agent microdynamics, the mesostructural organization of the interaction network, and macrolevel invariants governing system evolution. At the macrolevel, an integral indicator is introduced and formulated as a composition of barrier components that reflect macrodynamics variability, the risk of violating the invariance of the feasible state domain, and the loss of spectral stability of the system regime. This construction enables quantitative assessment of the proximiy of the system trajectory to the controllability loss boundary. The predictive properties of the indicator are examined through a series of numerical experiments employing scenarios of both stable and critical evolution of the multi-agent system. Monte Carlo validation results demonstrate the capability of the proposed approach to detect pre-critical system dynamics regimes and to distinguish between stable and unstable revolutionary regimes in complex multi-agent systems.</p>