EAAI Journal 2026 Journal Article
Kolmogorov–Arnold network-based adaptive control allocation for overactuated systems with Lyapunov-stable learning
- Jingxian Liao
- Chenkai Cao
- Yun Li
Adaptive control allocation is critical for overactuated systems to compensate for actuator faults without explicit fault detection logic. Traditional approaches such as pseudo-inverse and optimization-based methods provide fixed redistribution rules but cannot adapt to time-varying degradation. Recent neural-network allocators introduce online adaptivity through multi-layer perceptrons (MLPs), yet none provide closed-loop stability guarantees during learning. This paper introduces a Kolmogorov–Arnold Network (KAN)-based adaptive control allocation framework (allocKAN) with Lyapunov-stable online learning. We derive a composite Lyapunov stability framework showing that KAN parameter sensitivity scales only with network width and input dimension, independent of spline resolution, whereas MLP sensitivity grows with total parameter count. This directly determines the feasibility of the critical stability condition. Uniformly ultimately bounded stability theorems show that KAN yields tighter ultimate error bounds that scale only with architectural width, whereas MLP bounds scale with all learnable parameters. Offline experiments across 63 matched-budget configurations demonstrate 75. 2% lower validation error for allocKAN. Critically, increasing spline resolution improves approximation without sacrificing stability margins, a resolution-independence property unique to KANs. A 252-case closed-loop study on a ducted-fan unmanned aerial vehicle spanning 7 allocators, 3 controllers, and 12 fault scenarios confirms 100% bounded compliance for both neural allocators, while traditional methods diverge under severe faults. AllocKAN achieves 42%–77% lower parameter sensitivity, approximately 10 times tighter Lyapunov bounds, 37. 6–46. 6% lower final-state norms, and 50% faster fault recovery, while both allocators exceed the 400Hz real-time requirement with over 43% margin. These results establish KAN as a certifiable architecture for safety-critical adaptive allocation without controller redesign.