Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equations

TL;DR

This paper introduces a supervised learning method that uses gradient information from State-dependent Riccati Equation solutions to train neural networks for real-time stabilization of large-scale nonlinear systems.

Contribution

It presents a novel approach combining Riccati equation solutions with gradient-augmented training to enable efficient feedback law approximation.

Findings

Neural networks can replace real-time Riccati equation solves in stabilization tasks.

Gradient information improves training efficiency and accuracy.

Method scales to high-dimensional nonlinear systems.

Abstract

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solves. The training phase is enriched by the use gradient information in the loss function, which is weighted through the use of hyperparameters. High-dimensional nonlinear stabilization tests demonstrate that real-time sequential large-scale Algebraic Riccati Equation solves can be substituted by a suitably trained feedforward neural network.