FESSNC: Fast Exponentially Stable and Safe Neural Controller

TL;DR

This paper introduces FESSNC, a neural controller framework that guarantees exponential stability and safety in stochastic systems, utilizing novel projection methods and scalable Hessian estimation to enhance learning efficiency and robustness.

Contribution

We propose a new neural control framework with rigorous stability and safety guarantees, including novel projection operators and scalable Hessian estimation techniques.

Findings

FESSNC outperforms existing methods in stability and safety.

The projection operators effectively enforce stability and safety constraints.

Scalable Hessian estimation accelerates training and testing processes.

Abstract

In order to stabilize nonlinear systems modeled by stochastic differential equations, we design a Fast Exponentially Stable and Safe Neural Controller (FESSNC) for fast learning controllers. Our framework is parameterized by neural networks, and realizing both rigorous exponential stability and safety guarantees. Concretely, we design heuristic methods to learn the exponentially stable and the safe controllers, respectively, in light of the classic stochastic exponential stability theory and our established theorem on guaranteeing the almost-sure safety for stochastic dynamics. More significantly, to rigorously ensure the stability and the safety guarantees for the learned controllers, we develop a projection operator, projecting to the space of exponentially-stable and safe controllers. To reduce the high computation cost of solving the projection operation, approximate projection operators are delicately proposed with closed forms that map the learned controllers to the target controller space. Furthermore, we employ Hutchinson's trace estimator for a scalable unbiased estimate of the Hessian matrix that is used in the projection operator, which thus allows for computation cost reduction and therefore can accelerate the training and testing processes. More importantly, our approximate projection operations can be applied to the nonparametric control methods to improve their stability and safety performance. We empirically demonstrate the superiority of the FESSNC over the existing methods.