TAG ARCHIVE
control-theory
13 MARIA OS blog articles tagged control-theory, organized as a Bonginkan topic archive for search engines and LLM retrieval.
Judgment OS / Decision Intelligence OS
Core MARIA OS research on turning organizational judgment into executable decision systems.
Agentic Company Architecture
Research on human-agent organizations, delegation boundaries, role topology, and governed autonomy.
Responsibility Gates and AI Governance
Safety, accountability, fail-closed gates, auditability, and human-in-the-loop control for AI agents.
Multi-Agent Mathematics
Formal models for convergence, stability, game theory, graph dynamics, and multi-agent evaluation.
Evidence, RAG, and Knowledge Governance
Evidence bundles, retrieval architecture, Graph RAG, knowledge trust, and auditable reasoning pipelines.
Agentic R&D and Judgment Science
Research operations, simulation labs, judgment science, recursive improvement, and experimental AI governance.
Homeostasis: The Operating System of Life
From Claude Bernard's milieu intérieur to allostasis — how closed-loop control sustains every living thing
Homeostasis — the maintenance of stable internal conditions despite external perturbation — is life's foundational operating system. This article traces the concept from its nineteenth-century origins through modern control theory and allostasis, connecting it to MARIA VITAL's 4-layer implementation architecture.
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.
Actor-Critic Reinforcement Learning for Gated Autonomy: PPO-Based Policy Optimization Under Responsibility Constraints
How Proximal Policy Optimization enables medium-risk task automation while respecting human approval gates
Gated autonomy requires reinforcement learning that respects responsibility boundaries. This paper positions actor-critic methods — specifically PPO — as a core algorithm in the Control Layer, showing how the actor learns policies, the critic estimates state value, and responsibility gates constrain the action space dynamically. We derive a gate-constrained policy-gradient formulation, analyze PPO clipping behavior under trust-region constraints, and model human-in-the-loop approval as part of environment dynamics.
Treatment Reversibility Modeling: Dynamic Gate Control for Irreversible Medical Actions
Quantifying reversibility scores for medical procedures and dynamically adjusting governance gates to prevent catastrophic irreversible harm
Medical decisions have different reversibility profiles: some interventions are easy to roll back, others are not. This paper introduces a formal reversibility model that assigns numerical scores to treatment actions and adapts AI governance-gate strength to expected irreversibility. Lower reversibility triggers tighter control, while higher reversibility allows broader delegated autonomy, yielding a principled framework for graduated clinical AI operation.
Engineering Case Study: Quality Gate Control Theory for Manufacturing AI
Applying established control theory, R2R-aware manufacturing practice, and MARIA OS audit gates to simulated semiconductor quality cascades
Manufacturing AI systems face a stability problem that traditional software governance often does not: defect rates evolve as continuous dynamical variables under material variation, tool wear, and environmental drift. This engineering case study applies established PID, Lyapunov, and BIBO analysis to quality gates, positions the approach against semiconductor run-to-run control, and shows how MARIA OS adds fail-closed escalation, evidence bundles, and audit coordinates. The reported 94.7% defect containment, sub-200ms gate response, and 0.12x/stage attenuation are simulation results on a tuned linear model, not production fab measurements.
Decision Stability Scoring for Energy Grids: Lyapunov Functions for Power Supply-Demand Governance
Evaluating power grid decision stability through Lyapunov energy functions and responsibility-gated load balancing
Power grids can operate near stability limits, where dispatch errors or delayed interventions may trigger cascading disruptions. This paper introduces a Lyapunov-based decision-stability score for energy-grid AI agents, providing formal criteria for when autonomous grid-management actions remain within stable operating regions.
Over-Fixation Suppression: Control-Theoretic Stabilization of AI Recommendation Convergence in Education
Preventing AI tutoring systems from converging on single recommendation patterns through diversity-enforcing stability constraints
Left unconstrained, recommendation algorithms can converge to narrow patterns: similar problem types, difficulty bands, or teaching approaches. In education, this can create learning monocultures that limit broader development. This paper develops a control-theoretic framework for suppressing over-fixation in educational AI while preserving learning effectiveness.
Decision Intelligence Theory: A Unified Framework for Responsible AI Governance
Five axioms, four pillar equations, and five theorems that transform organizational judgment into executable decision systems
Decision Intelligence Theory formalizes decision-making as a control system, integrating evidence, conflict, responsibility, execution, and learning. This capstone article presents a unified mathematical framework — five axioms, four pillar equations, and five theorems — together with implementation mappings and internal cohort analyses across finance, healthcare, legal, and manufacturing.
A Formal Model of Responsibility Decomposition Points in Human-AI Decision Systems
Why responsibility is a computable threshold, not a philosophical debate - and how to implement it
Existing AI governance frameworks rely on qualitative guidelines to determine when human oversight is required. This paper formalizes responsibility decomposition as a quantitative threshold problem: we define a Responsibility Demand Function R(d) over decision nodes using five normalized factors - impact, uncertainty, externality, accountability, and novelty - and introduce a decomposition threshold τ that determines when human responsibility must be enforced. A dynamic equilibrium model captures temporal shifts driven by learning and contextual change. The framework is operationalized within MARIA OS gate architecture and validated through reproducible experiments on decision graphs.
Gate Control as Control Engineering: Stability Conditions for Multi-Layer Decision Gates in AI Governance
A control-theoretic framework for gate design where smarter AI needs smarter stopping, not simply more stopping
Enterprise governance often assumes that more gates automatically mean more safety. This paper analyzes why that assumption can fail. We model gates as delayed binary controllers with feedback loops and derive stability conditions: serial delay should remain within the decision-relevance window, and feedback-loop gain should satisfy `kK < 1` to avoid over-correction oscillation. Safety is therefore not monotonic in gate count; it depends on delay-budget management, loop-gain control, and bounded recovery cycles.
Fail-Closed Design Enhances Stability: A Lyapunov Analysis of Governance Dynamics
Proving that fail-closed gates create a stable equilibrium in the risk-velocity state space using Lyapunov's direct method
Enterprise AI governance systems can accumulate risk over time through compounding errors, configuration drift, and expanding autonomy. This paper models governance dynamics as a continuous-time state system with risk `r` and decision velocity `v`, and control inputs gate strength `g` and evidence quality `q`. Using Lyapunov candidate `V(r, v) = alpha*r^2 + beta*v^2`, we derive conditions on `g` and `q` such that `dV/dt < 0`, establishing asymptotic stability. The resulting stability region in `(g, q)` space provides a design specification for bounded risk accumulation.
Designing a Decision OS as a Control System: Optimal Control via Pontryagin's Maximum Principle
Formulating the multi-agent decision pipeline as a continuous-time control problem and deriving the optimal governance law
A Decision OS can be modeled as a control system that observes governance state, applies gate/evidence controls, and steers operations toward target conditions. This paper formulates the decision pipeline as a state-space control problem with state vector `x = [risk, compliance, evidence, velocity]`, control `u = [gate_strength, human_review_rate, evidence_threshold]`, and a multi-objective cost functional. We derive a control law via Pontryagin's maximum principle and characterize co-state dynamics, using simulations to show how optimal gate strength can vary with accumulated risk and compliance margin.
Dynamic Gate Adaptation: Online Update Rules Driven by Misjudgment Rate Feedback
Convergent online learning for responsibility gate strength with provable stability guarantees
Static gate configurations degrade in non-stationary environments. When error distributions shift, fixed gates may over-escalate (wasting attention) or under-escalate (allowing harmful actions). This paper introduces an online adaptation rule using false-acceptance feedback: g_{t+1} = g_t + eta * (FAR_t - FAR_target). We analyze convergence and stability bounds, and report 94.2% convergence within 200 iterations across three deployments.