Bio-Inspired Sparse Edge Inference with Martingale-Guaranteed Stability for UAV Neuro-Fuzzy Sliding Mode Control: An EKF–GNN–RL Framework

<title>Abstract</title> <p>Deploying advanced neuro-fuzzy sliding mode controllers (SMC) on resource-constrained UAV edge platforms faces a fundamental trilemma: computational cost, stability guarantees, and robustness to environmental uncertainty. This paper presents a bio-inspired sparse edge inference framework that reformulates the Extended Kalman Filter (EKF) from state estimation to weight-space prediction, enabling dynamic pruning of inactive fuzzy rules while providing rigorous stability proofs grounded in martingale theory and stochastic Lyapunov methods. The framework integrates four complementary mechanisms: (1) EKF-based weight-space compression that predicts weight update directions and identifies inactive rules at each control step, with innovation sequences proven to form martingale difference sequences; (2) a graph attention network (GAT) that learns dynamic inter-channel coupling from flight data; (3) reinforcement learning (RL) with Lyapunov post-regularization under Wasserstein distributional robustness constraints, where the policy iteration is proven to form a supermartingale; and (4) INT8 quantization-aware deployment optimized for edge hardware. The core theoretical contribution is a unified martingale framework that provides finite-sample error bounds via Azuma–Hoeffding concentration, worst-case tracking bounds via Doob’s maximal inequality, and stochastic stability via supermartingale Lyapunov functions. A novel minimum dwell-time theorem for switching rule sets extends classical switched systems theory with martingale perturbation analysis. Extensive simulations (10,000 Monte Carlo runs) and real-world flight experiments on a Jetson Orin Nano platform demonstrate: (i) 73% reduction in active fuzzy rules with less than 2% tracking accuracy degradation, (ii) 4.2 ms average inference latency at 0.93 W power consumption, (iii) statistically significant contributions from each component (p &lt; 0.01, Bonferroni-corrected), (iv) robust performance under wind gusts (0–10 m/s), payload changes (±30%), GPS dropout, and thermal throttling, and (v) 28.6% improved flight endurance over full-precision inference on a physical quadrotor with over 200 successful flights.</p>