Neural network optimal feedback control with enhanced closed loop stability

TL;DR

This paper investigates neural network controllers for nonlinear systems, revealing that high test accuracy does not guarantee stability, and proposes architectures that reliably stabilize systems while maintaining optimality.

Contribution

It introduces two neural network architectures that locally approximate LQR for improved stability and provides preliminary theoretical insights into their stability properties.

Findings

Proposed NN architectures reliably stabilize systems.

High test accuracy does not ensure system stability.

Numerical simulations confirm effectiveness of the architectures.

Abstract

Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In this paper we use numerical simulations to demonstrate that typical test accuracy metrics do not effectively capture the ability of an NN controller to stabilize a system. In particular, some NNs with high test accuracy can fail to stabilize the dynamics. To address this we propose two NN architectures which locally approximate a linear quadratic regulator (LQR). Numerical simulations confirm our intuition that the proposed architectures reliably produce stabilizing feedback controllers without sacrificing optimality. In addition, we introduce a preliminary theoretical result describing some stability properties of such NN-controlled systems.