Spectral Normalized Neural Networks Funnel Control for Servo System with Unknown Dynamics

This paper proposes a novel spectral normalized neural networks funnel control approach for servo system with unknown dynamics. The approach introduces spectral normalization technology into the funnel controller design to address the unknown dynamics. Spectral normalization techniques can restrict the spectral norm of the weight matrices of the neural networks, leading to more stable and robust networks. The spectral normalized neural network exhibits strong generalization ability and can adapt to offline learning strategies, which significantly reduce the system's computation cost. Moreover, based on the funnel control architecture, the system output is constrained to remain within an acceptable boundary, optimizing transient performance and guaranteeing satisfactory control performance. All signals of the closed-loop system are bounded based on Lyapunov stability analysis. Finally, simulation results demonstrate that this approach provides commendable tracking performance and superior generalization capabilities.