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

Abstract

Running a dense neuro-fuzzy sliding mode controller (SMC) on a resource-constrained UAV edge platform forces a three-way trade-off between compute, formal stability guarantees, and robustness to uncertainty. We recast the extended Kalman filter (EKF) from state estimation into weight-space prediction, which lets the controller drop inactive fuzzy rules on the fly while retaining stability proofs built on martingale theory. The framework couples four ideas. EKF weight-space compression treats the innovation sequence as an approximate martingale difference sequence. A graph attention network (GAT) learns time-varying inter-channel coupling and feeds it straight into the SMC equivalent-control term. Reinforcement learning with Lyapunov post-regularization, wrapped in a Wasserstein distributional-robustness constraint, is shown to form a supermartingale. Finally, INT8 quantization-aware training prepares the whole stack for edge deployment. These pieces rest on a common martingale foundation that yields finite-sample pruning-error bounds (Azuma–Hoeffding), worst-case tracking bounds (Doob), stochastic stability via supermartingale Lyapunov functions, and a minimum dwell-time theorem for switching rule sets. Across 10,000 high-fidelity PyBullet simulation runs, the framework cuts active fuzzy rules by 73% on average at the cost of 0.3–0.5 cm of simulated tracking error, and the INT8-compiled inference stack attains 4.2 ms mean latency and 0.93 W measured on a Jetson Orin Nano in a bench-top (non-flight) benchmark. The hardware experiments reported here are the edge-inference benchmarks; closed-loop control results are simulation-based, and flight validation on the physical platform is left to future work.