Self-Steering AI: A Mathematical Framework for Dynamic Goal Adaptation in Autonomous Systems — Expanded Working Notes

Self-Steering AI: Expanded Working Notes This working paper develops self-steering AI: a mathematical framework in which goals are not fixed specifications but dynamic state variables that evolve under stability and safety constraints. The framework formalizes goal evolution via a steering operator Φ\PhiΦ and a safety projection ΠC\Pi_{\mathcal C}ΠC. We provide Lyapunov stability analysis, information-theoretic bounds on adaptation, and reference neural architectures (including transformer-based steering operators). Validation is conducted through simulation studies in navigation, resource allocation, and multi-agent coordination, showing 15–30% gains compared to fixed-goal baselines. This expanded version adds:– Extended mathematical analysis (bounds, proofs)– Refined neural architectures (transformers, GNNs, attention)– Detailed implementation notes– Broadened applications (robotics, healthcare, finance)– Expanded simulation-based validation Important: All results are computational simulations; no physical-world experiments are included. Collaboration: The author is available for consulting, joint pilots, or exclusive sponsorship agreements to advance this research privately with industry partners. Previous version: 10.5281/zenodo.17220380self-steering AI, dynamic goals, AI safety, alignment, reinforcement learning, Lyapunov stability, control theory, information-theoretic bounds, multi-agent systems, robotics, adaptive AI, autonomous AI