SEKHEM-TSDD: Stability-Guaranteed Real-Time Decision Dynamics for Multi-Agent Systems

This work introduces SEKHEM-TSDD (Triangulated Stability Decision Dynamics), a novel stability-guaranteed real-time decision framework for multi-agent systems operating in uncertain and high-density environments. The proposed system integrates a structured multi-layer architecture with a unified decision law combining scoring, thresholding, and probabilistic softmax-based selection. The dynamics are formulated as a continuous-time system using ordinary differential equations, and global asymptotic stability is established through Lyapunov-based analysis. A triangulation principle is introduced to enable multi-source validation, significantly enhancing robustness against noise and conflicting inputs. Extensive simulations involving large-scale agent populations demonstrate fast convergence, stable behavior, and strong resilience under stochastic disturbances. The framework provides a scalable and mathematically grounded solution for next-generation autonomous systems and real-time decision-making applications.