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A Control Theoretic Approach to Decentralized AI Economy Stabilization via Dynamic Buyback-and-Burn Mechanisms

Zehua Cheng, Wei Dai, Zhipeng Wang, Rui Sun, Nick Wen, Jiahao Sun

TL;DR

This paper addresses the volatility of native tokens in decentralized AI networks by introducing the Dynamic-Control Buyback Mechanism (DCBM), a control-theoretic framework that uses a solvency-constrained Proportional-Integral-Derivative (PID) controller to regulate buybacks and burns. It formalizes the economy as a discrete-time dynamical system with a CPMM-based plant and a treasury that must remain solvent, then demonstrates stability, asymptotic solvency, and adversarial robustness through theoretical analysis and extensive agent-based Jump-Diffusion simulations. Key contributions include a formal problem formulation, a fixed-point, on-chain implementation of a PID controller with integral windup protection and a sigmoid actuator, and comprehensive evaluation showing reduced price volatility by ~66% and lower operator churn from 19.5% to 8.1% in high-volatility regimes, along with robustness insights under MEV-style attacks. The findings suggest that replacing static tokenomics with continuous, constraint-aware control loops enables secure, sustainable decentralized AI networks with improved treasury health and resilience against adversarial dynamics.

Abstract

The democratization of artificial intelligence through decentralized networks represents a paradigm shift in computational provisioning, yet the long-term viability of these ecosystems is critically endangered by the extreme volatility of their native economic layers. Current tokenomic models, which predominantly rely on static or threshold-based buyback heuristics, are ill-equipped to handle complex system dynamics and often function pro-cyclically, exacerbating instability during market downturns. To bridge this gap, we propose the Dynamic-Control Buyback Mechanism (DCBM), a formalized control-theoretic framework that utilizes a Proportional-Integral-Derivative (PID) controller with strict solvency constraints to regulate the token economy as a dynamical system. Extensive agent-based simulations utilizing Jump-Diffusion processes demonstrate that DCBM fundamentally outperforms static baselines, reducing token price volatility by approximately 66% and lowering operator churn from 19.5% to 8.1% in high-volatility regimes. These findings establish that converting tokenomics from static rules into continuous, structurally constrained control loops is a necessary condition for secure and sustainable decentralized intelligence networks.

A Control Theoretic Approach to Decentralized AI Economy Stabilization via Dynamic Buyback-and-Burn Mechanisms

TL;DR

This paper addresses the volatility of native tokens in decentralized AI networks by introducing the Dynamic-Control Buyback Mechanism (DCBM), a control-theoretic framework that uses a solvency-constrained Proportional-Integral-Derivative (PID) controller to regulate buybacks and burns. It formalizes the economy as a discrete-time dynamical system with a CPMM-based plant and a treasury that must remain solvent, then demonstrates stability, asymptotic solvency, and adversarial robustness through theoretical analysis and extensive agent-based Jump-Diffusion simulations. Key contributions include a formal problem formulation, a fixed-point, on-chain implementation of a PID controller with integral windup protection and a sigmoid actuator, and comprehensive evaluation showing reduced price volatility by ~66% and lower operator churn from 19.5% to 8.1% in high-volatility regimes, along with robustness insights under MEV-style attacks. The findings suggest that replacing static tokenomics with continuous, constraint-aware control loops enables secure, sustainable decentralized AI networks with improved treasury health and resilience against adversarial dynamics.

Abstract

The democratization of artificial intelligence through decentralized networks represents a paradigm shift in computational provisioning, yet the long-term viability of these ecosystems is critically endangered by the extreme volatility of their native economic layers. Current tokenomic models, which predominantly rely on static or threshold-based buyback heuristics, are ill-equipped to handle complex system dynamics and often function pro-cyclically, exacerbating instability during market downturns. To bridge this gap, we propose the Dynamic-Control Buyback Mechanism (DCBM), a formalized control-theoretic framework that utilizes a Proportional-Integral-Derivative (PID) controller with strict solvency constraints to regulate the token economy as a dynamical system. Extensive agent-based simulations utilizing Jump-Diffusion processes demonstrate that DCBM fundamentally outperforms static baselines, reducing token price volatility by approximately 66% and lowering operator churn from 19.5% to 8.1% in high-volatility regimes. These findings establish that converting tokenomics from static rules into continuous, structurally constrained control loops is a necessary condition for secure and sustainable decentralized intelligence networks.
Paper Structure (28 sections, 3 theorems, 16 equations, 2 figures, 3 tables)

This paper contains 28 sections, 3 theorems, 16 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Formal Problem Formulation
  5. Dynamical System Modeling and State Space
  6. Dynamic-Control Buyback Mechanism
  7. Game-Theoretic Robustness
  8. Theoretical Analysis
  9. Plant Model Derivation (AMM Dynamics)
  10. Closed-Loop Stability Analysis
  11. Proof of Asymptotic Solvency
  12. Robustness to Impulse Attacks
  13. Experiments
  14. Dataset Preparation
  15. Baseline Implementation
  16. ...and 13 more sections

Key Result

Proposition 3.1

Given an initial treasury $T_0 > 0$ and parameter $\gamma \in (0,1)$, the treasury balance $T_k$ remains strictly positive for all finite $k$, regardless of the magnitude or duration of revenue collapse ($R_k = 0$).

Figures (2)

  • Figure 1: Closed-loop control architecture of the Dynamic-Control Buyback Mechanism (DCBM). The schematic illustrates the feedback loop designed to stabilize the decentralized AI economy. a, The Error Interface computes the logarithmic deviation ($e_k$) between the target Time-Weighted Average Price (TWAP) and the real-time Spot Price. b, The PID Controller processes this error, applying proportional, integral (clamped), and derivative gains to calculate a raw intervention intensity ($u_k$). c, The Solvency Actuator functions as a critical safety valve, strictly bounding the physical buyback expenditure ($J_k$) by the current Treasury Balance ($T_k$) and the circuit breaker parameter ($\gamma$), ensuring asymptotic solvency regardless of market conditions. d, The AMM Plant represents the market environment where the buy-and-burn action is executed, altering the token price state for the subsequent control epoch ($k+1$).
  • Figure 2: Schematic representation of baseline stabilization mechanisms. The diagram illustrates the five control strategies evaluated against the proposed DCBM: (1) No Buyback, where fees are fully distributed to operators without burning; (2) Fixed-Rate Buyback, which applies a static percentage burn (e.g., 50%) regardless of market state; (3) Threshold Buyback, a heuristic approach triggering buybacks only when spot price $P_t$ falls below the moving average $P_{MA,t}$; (4) Model Predictive Control (MPC), which minimizes predicted error over a finite horizon; and (5) Reinforcement Learning (PPO), utilizing a neural policy to maximize a reward function based on stability and control effort.

Theorems & Definitions (3)

  • Proposition 3.1: Asymptotic Solvency
  • Theorem 4.1: Gain Sensitivity
  • Theorem 4.2: Non-Depletion