A Control-Theoretic Framework for AI Safety: Stability, Robustness, and Assurance

Abstract: AI systems increasingly operate as feedback-driven agents in open environments, where unsafe behavior can arise under model error, non-stationarity, or adversarial perturbations. Building on concept analysis from control theory, this study develops a control-theoretic framework for AI safety organized around three pillars—stability, robustness, and assurance. The framework analyzes AI decision processes as uncertain dynamical systems, formalizes safety as invariance and constraint satisfaction, and links algorithmic behavior to verifiable properties. The central problem addressed is the lack of scalable, end-to-end guarantees that persist under distribution shift and learning-in-the-loop. Methodology integrates Lyapunov and control-barrier functions, distributionally robust model predictive control, and reachability analysis with compositional verification and runtime shielding. Synthesis procedures are provided for policy wrapping and training-time regularization, together with tractable certificates that yield sufficient conditions for closed-loop stability and high-probability constraint satisfaction under bounded uncertainty. The framework is evaluated through theoretical results (existence and construction of certificates; performance–safety trade-off bounds) and empirical studies on representative control and decision-making tasks, using containerized protocols for reproducibility. Results indicate substantial reductions in safety-constraint violations and improved stability margins at modest utility cost, with robustness maintained under perturbations and environment drift. The impact is twofold: (i) a principled route to deployable assurance cases for AI components, and (ii) guidance for standards, auditing, and governance through transparent safety artifacts (certificates, monitors, and protocol cards). The framework aligns with high-impact journal expectations for rigor, reproducibility, and policy relevance. Keywords: AI safety, control theory, stability, robustness, assurance, Lyapunov functions, control barrier functions, reachability analysis, robust model predictive control, runtime verification, compositional verification, distribution shift, adversarial robustness, safe reinforcement learning, certification