Neural Network Optimal Feedback Control with Guaranteed Local Stability
This addresses a critical safety issue in deploying neural network controllers for high-dimensional nonlinear systems, such as unmanned aerial vehicles, by ensuring local stability, though it is incremental in improving existing neural network methods.
The paper tackled the problem of neural network controllers failing to locally stabilize dynamic systems despite high test accuracy, by proposing novel architectures that guarantee local asymptotic stability while learning near-optimal feedback policies. The results showed that standard neural networks could fail to stabilize in simulations, whereas the proposed architectures achieved local stability and near-optimal performance in high-dimensional nonlinear control problems.
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed architectures are compared against standard neural network feedback controllers through numerical simulations of two high-dimensional nonlinear optimal control problems: stabilization of an unstable Burgers-type partial differential equation, and altitude and course tracking for an unmanned aerial vehicle. The simulations demonstrate that standard neural networks can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stabilizing and can achieve near-optimal performance.