Controller Design for Bilinear Neural Feedback Loops

TL;DR

This paper introduces a control design framework for bilinear systems with neural network feedback, ensuring local exponential stability through linear matrix inequalities, suitable for online implementation and robustness analysis.

Contribution

It develops a novel controller synthesis method combining linear fractional representations and LPV control for neural feedback loops.

Findings

Guarantees local exponential stability of neural feedback systems.

Controller synthesis via linear matrix inequalities solvable offline.

Provides tools for stability and robustness analysis of neural network interconnected systems.

Abstract

This paper considers a class of bilinear systems with a neural network in the loop. These arise naturally when employing machine learning techniques to approximate general, non-affine in the input, control systems. We propose a controller design framework that combines linear fractional representations and tools from linear parameter varying control to guarantee local exponential stability of a desired equilibrium. The controller is obtained from the solution of linear matrix inequalities, which can be solved offline, making the approach suitable for online applications. The proposed methodology offers tools for stability and robustness analysis of deep neural networks interconnected with dynamical systems.