Stability Margins of Neural Network Controllers

TL;DR

This paper introduces a training method for neural network controllers that guarantees stability margins for uncertain linear systems by combining reward optimization with stability certification via semidefinite programming.

Contribution

It proposes a novel training approach that enforces stability margins in neural network controllers for linear plants with uncertainties, using integral quadratic constraints.

Findings

Successfully certifies stability margins during training.

Balances reward maximization with stability guarantees.

Applicable to systems with nonlinearities and uncertainties.

Abstract

We present a method to train neural network controllers with guaranteed stability margins. The method is applicable to linear time-invariant plants interconnected with uncertainties and nonlinearities that are described by integral quadratic constraints. The type of stability margin we consider is the disk margin. Our training method alternates between a training step to maximize reward and a stability margin-enforcing step. In the stability margin enforcing-step, we solve a semidefinite program to project the controller into the set of controllers for which we can certify the desired disk margin.