Paper: A Control Theoretic Approach to Decentralized AI Economy Stabilization via Dynamic Buyback-and-Burn Mechanisms
Authors: Zehua Cheng, Wei Dai, Zhipeng Wang, Rui Sun, Nick Wen, Jiahao Sun
Date: 2026-01-15
Estimated Reading Time: 24 minutes
This paper proposes the Dynamic-Control Buyback Mechanism (DCBM), a control-theoretic framework for stabilizing token economies in decentralized AI networks. The authors model the token economy as a discrete-time dynamical system with treasury constraints and automated market maker price impact. Instead of static or threshold-based buyback rules, DCBM uses a Proportional-Integral-Derivative controller with a solvency-aware actuator to adjust buyback intensity based on deviations between market price and a time-weighted moving target. The mechanism incorporates strict treasury conservation, saturation limits, and a bounded sigmoid mapping to ensure asymptotic solvency. Agent-based simulations using jump-diffusion processes compare DCBM against no-buyback, fixed-rate, threshold, reinforcement learning, and model predictive control baselines across multiple market regimes. Results indicate that DCBM reduces volatility and operator churn while preserving treasury capital in downturns. Additional adversarial experiments show that structurally constrained PID configurations outperform static rules under manipulation attempts.
Core insights
- Closed-loop token stabilization: The token price is modeled as a discrete integrator driven by buyback expenditure through a constant product market maker. DCBM embeds this plant in a feedback loop where error is defined as the logarithmic deviation between TWAP and an EMA reference. This transforms buyback policy from a static rule into a state-dependent control system.
- Solvency-constrained actuation: Buyback expenditure is mapped as Jk = Tk · γ · tanh(max(0, uk)), ensuring that spending is bounded by treasury size. The authors formally prove that with γ ∈ (0,1), the treasury asymptotically approaches zero but never depletes fully. This eliminates discrete bankruptcy scenarios present in fixed-rate models.
- Integral drift correction: The integral term corrects steady-state deviations that proportional or threshold systems cannot remove. Clamped integration prevents windup when the treasury is exhausted. This enables counter-cyclical accumulation in bull markets and measured deployment in downturns.
- Liquidity-sensitive stability bounds: Linearization of the AMM shows plant gain αk = 2/yk, implying sensitivity increases as liquidity falls. Jury stability conditions impose bounds on Kp, Ki, and Kd that shrink as liquidity declines. Static gain settings therefore risk oscillation in low-liquidity regimes.
- Adversarial robustness via structural constraints: Derivative-on-measurement and TWAP filtering suppress high-frequency manipulation signals. Certified robustness configurations that constrain integral accumulation and derivative Lipschitz continuity materially reduce treasury drain compared to threshold heuristics under gradient-based attacks.
The proposed framework directly alters the supply dynamics of the token by coupling burn intensity to price deviation rather than revenue alone. Under the treasury evolution equation Tk+1 = Tk + Racc(k) − Jk − Cops, circulating supply decreases through AMM buy-and-burn actions, while treasury capital serves as the control energy reservoir. Unlike fixed-rate burn policies that mechanically tie Jk to revenue, DCBM decouples accumulation from stabilization. This separation allows revenue surpluses to build reserves during expansion phases instead of immediately contracting supply, altering the intertemporal profile of supply reduction.
Demand stabilization emerges indirectly through price targeting around an EMA trajectory. Because the plant behaves as pk+1 = pk + αkJk + ξk in the log-linearized form, buybacks accumulate into price corrections. This structure implies that without integral action, steady deviations persist. The inclusion of the integral term addresses this, but raises a tradeoff: how large can Ki be before oscillatory behavior dominates when liquidity shrinks? The Jury-derived gain constraints explicitly link controller aggressiveness to AMM depth, highlighting that token liquidity conditions directly determine safe policy space.
The sigmoid actuator introduces nonlinear saturation that modulates rewards to token holders. Since Jk is proportional to Tk, reward intensity scales with treasury capacity. During bull markets, treasury growth increases potential stabilization amplitude in future downturns. In bear regimes, bounded spending preserves runway. This creates a counter-cyclical reward distribution where burn intensity depends on cumulative deviation, not instantaneous volatility. Does this implicitly privilege long-term holders over short-term speculators by smoothing extreme drawdowns? The paper does not explicitly model holder heterogeneity beyond churn metrics, so this remains an inference.
Simulation results show volatility reductions relative to no-buyback and threshold systems across bull, bear, high-volatility, demand shock, and liquidity crisis scenarios. Operator churn declines materially in high-volatility regimes, linking price stabilization to compute provider retention. The treasury growth metric further indicates that fixed-rate models contract reserves during downturns, whereas DCBM preserves capital. However, the simulations rely on calibrated PID gains. How sensitive are outcomes to mis-specification of Kp, Ki, and Kd under structural breaks not captured by jump-diffusion processes? The limitations section acknowledges absence of adaptive gain scheduling, implying parameter rigidity remains an open risk.
Adversarial experiments treat the controller as a differentiable policy and apply gradient-based attacks. Threshold baselines exhibit near-total failure under small perturbation budgets, while certified PID variants substantially reduce success rates and treasury drain. The key mechanism is spectral filtering through TWAP and derivative damping, which increases the capital requirement for sustained manipulation. Yet robustness depends on structural constraints and clipping bounds. If on-chain governance modified γ or integral caps without careful analysis, could the stability guarantees degrade? The formal solvency proof ensures non-depletion, but stability under adversarial gain shifts would require renewed verification.
Overall, the paper reframes tokenomics as a constrained control problem where supply contraction, treasury preservation, and volatility suppression are jointly optimized through feedback. The integration of solvency-aware actuation, liquidity-sensitive stability bounds, and adversarial hardening produces a token economy that adapts expenditure to state variables rather than fixed heuristics. The primary economic implication is that stabilization capacity becomes endogenous to accumulated reserves and liquidity depth, linking long-term treasury management to short-term market dynamics.
