Admissibility Control: Stabilising Systems via Margin Restoration

This paper introduces admissibility control as a domain-neutral framework for stabilising systems through restoration of admissibility margin. Building on prior work establishing admissibility as a pre-condition for system membership and continuation, and admissibility margin as a quantitative indicator of proximity to constraint violation, this work defines the operational mechanisms required to actively maintain system stability. Admissibility control is formalised as the process of increasing admissibility margin by reducing constraint pressure, reconfiguring system structure, or redirecting system trajectories within admissible space. Stability is redefined as a dynamic condition maintained through sufficient distance from governing constraint boundaries rather than static equilibrium. The framework establishes clear stability, instability, and collapse conditions based on margin behaviour and introduces a universal control objective: restoring positive margin growth (dM/dt > 0). This enables proactive intervention prior to boundary contact, shifting system management from reactive correction to preventative stabilisation. The approach is demonstrated across artificial intelligence systems, fluid dynamics, and healthcare systems, illustrating domain-independent applicability. Results show that early margin restoration prevents drift from progressing into structural closure. This work completes the operational cycle of the Paton System: admissibility (possibility), validation (invariance), margin (measurement), and control (stabilisation), forming a full lifecycle framework for analysing and managing system behaviour.