Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation^*

¹ University of Graz, Institute of Mathematics and Scientific Computing, Heinrichstr. 36, 8010 Graz, Austria.
² Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Straße 69, 4040 Linz, Austria.

^** Corresponding author: daniel.walter@oeaw.ac.at

Received: 14 January 2020
Accepted: 15 January 2021

Abstract

A learning approach for optimal feedback gains for nonlinear continuous time control systems is proposed and analysed. The goal is to establish a rigorous framework for computing approximating optimal feedback gains using neural networks. The approach rests on two main ingredients. First, an optimal control formulation involving an ensemble of trajectories with ‘control’ variables given by the feedback gain functions. Second, an approximation to the feedback functions via realizations of neural networks. Based on universal approximation properties we prove the existence and convergence of optimal stabilizing neural network feedback controllers.