A Theory of Neural Networks for Control

Introduction

As neural networks are delivering groundbreaking performance in various machine learning frameworks—ranging from the basic framework of supervised learning to the powerful and challenging framework of control—immense efforts focus on developing underlying mathematical theories. Recent years witnessed breakthrough contributions to the theory of neural networks for supervised learning, by myself and others.

Challenges in Control Framework

Yet, from a theoretical perspective, much is left to be elucidated about neural networks in the powerful framework of control. This leads to a predominantly heuristic implementation, which hinders their use in control application domains where safety, robustness, and reliability are critical, such as:

• Healthcare
• Aerospace
• Manufacturing

Research Goals

The overarching goal of the proposed research is to develop a comprehensive mathematical theory of neural networks for control. This theory aims to provide:

1. An explanative formalism for intriguing empirical phenomena.
2. Breakthrough practical techniques that promote safety, robustness, and reliability.

The research aims to overcome major current challenges by harnessing powerful mathematical tools in the realms of tensor analysis and dynamical systems theory, which I have developed over the past decade.

Unique Positioning

Building on my academic record in the theory of neural networks for supervised learning, which is accompanied by vast practical industry experience with neural networks for control, I am confident in being uniquely positioned to pursue this pressing ambitious goal of developing a practical theory for neural networks in control.

Expected Outcomes

A successful outcome of the research will significantly broaden the theoretical knowledge on neural networks and unleash their power in critical control application domains, thereby having a transformative impact.