TAG ARCHIVE
stability-analysis
MARIA OSブログのstability-analysis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.
品質ゲート制御理論: 製造AIにおけるリアルタイム安定性解析
欠陥率を状態量として扱い、制御理論に基づく品質ゲート設計を行う
製造工程の欠陥率を動的システムとしてモデル化し、Lyapunov条件とPID型制御でゲート挙動を安定化する。多段工程への拡張を通じ、欠陥伝播の抑制と応答遅延の管理を同時に行う設計枠組みを示す。