TAG ARCHIVE
lyapunov
MARIA OSブログのlyapunovタグに関連する2件の記事。ボンギンカンの判断OS、AIガバナンス、Agentic Company研究をテーマ別に参照しやすい技術記事アーカイブです。
Industrial Loop Stability: Mathematical Foundations for Self-Monitoring Capital-Physical-Ethical Control Systems
Lyapunov analysis, contraction mappings, and spectral methods for proving convergence of the autonomous Capital-Operation-Physical-External governance loop
The Autonomous Industrial Loop — Capital, Operation, Physical, External — is the highest-level feedback cycle in MARIA OS, governing the continuous interaction between financial allocation, operational execution, physical-world robotics, and external market signals across an entire holding structure. This paper provides rigorous mathematical foundations for proving that the loop converges rather than oscillates, that drift accumulates within bounded envelopes, and that fail-closed gates preserve stability under stochastic external shocks. We develop five interlocking stability frameworks: Lyapunov energy functions that guarantee asymptotic stability of the four-phase loop, contraction mapping theorems that bound convergence rates, spectral analysis of the loop Jacobian that identifies instability modes before they manifest, cross-universe conflict propagation bounds that prevent local failures from cascading across the holding graph, and stochastic stability results via Ito calculus that accommodate market volatility, sensor noise, and adversarial perturbations. The Industrial Loop Stability Analysis produces three operational instruments: a Drift Index that aggregates ethical-operational-financial deviation into a single monotone metric, a Spectral Early Warning system that detects eigenvalue migration toward the unit circle boundary, and a Fail-Closed Holding Gate that enforces max_i scoring at the holding level with mathematically guaranteed bounded recovery time. Simulation across 4,800 synthetic subsidiary configurations demonstrates loop convergence in 94.7% of configurations, mean drift index below 0.12, and zero undetected instability events when spectral monitoring is active.
エネルギー系意思決定の安定性スコア: 電力需給統治のためのLyapunov関数
需給制御判断が安定動作領域にあるかを定量評価し、ゲート制御へ連携する
電力網の運用判断をLyapunov安定性の観点から評価し、不安定化兆候を早期に検出する。負荷調整・発電配分・エスカレーションのタイミングをスコア化し、連鎖障害リスクを抑える意思決定ガードを構成する。