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Lyapunov meets Machine Learning: Stability Analysis and Controller Design using Machine Learning

   School of Electronics, Electrical Engineering and Computer Science

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  Dr Pantelis Sopasakis, Prof S McLoone  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project

About a century ago, Aleksandr Lyapunov proposed that system stability can be studied using “energy functions,” known as Lyapunov functions: roughly speaking, if the energy stored in the system dissipates, the system is stable. The challenge is that, more often than not, it is difficult to determine such functions. A recent paper entitled “Advancing mathematics by guiding human intuition with AI,” (by A. Davies et al.) that appeared in Nature in July 2021, has received lots of attention: the authors suggest that machine learning can assist mathematicians in their quest for new conjectures and theorems. Without doubt, control theory has a lot to gain from machine learning. The main goal of this project will be the construction of Lyapunov functions and control Lyapunov functions via machine learning methodologies such as neural networks, symbolic regression, and reinforcement learning.

Project Description:

In this project we will propose a new learning framework to discover (control) Lyapunov functions, (control) invariant sets and reachable sets for constrained dynamical systems by leveraging recent advancements in deep neural networks, reinforcement learning and symbolic regression. At the same time, special emphasis will be placed on the simplicity of the derived Lyapunov functions. In particular,

  1. The successful candidate will propose a novel learning framework for the design of (control) Lyapunov functions, (control) invariant sets and reachable sets for constrained dynamical systems,
  2. Propose new conjectures related to stability, reachability and invariance,
  3. Test and verify the proposed framework in realistic scenarios such as control problems in aerospace and autonomous vehicles.

Project Key Words: Control theory; Machine Learning; Symbolic Regression; Neural Networks; Reinforcement Learning; Deep Neural Networks; Artificial Intelligence; Lyapunov Stability.

Start Date: 01/10/22

Application Closing date: 28/02/22

For further information about eligibility criteria please refer to the DfE Postgraduate Studentship Terms and Conditions 2021-22 at

Applicants should apply electronically through the Queen’s online application portal at:

Academic Requirements:

A minimum 2.1 honours degree or equivalent in Computer Science or Electrical and Electronic Engineering or relevant degree is required.

Funding Notes:

This three year studentship, for full-time PhD study, is potentially funded by the Department for the Economy (DfE) and commences on 1 October 2022. For UK domiciled students the value of an award includes the cost of approved tuition fees as well as maintenance support (Fees £4,500 pa and Stipend rate £15,609 pa - 2022-23 rates to be confirmed). To be considered eligible for a full DfE studentship award you must have been ordinarily resident in the United Kingdom for the full three year period before the first day of the first academic year of the course, normally 1st October.

For candidates who do not meet the above residency requirements, a small number of international studentships may be available from the School. These are expected to be highly competitive, and a selection process will determine the strongest candidates across a range of School projects, who may then be offered funding for their chosen project.

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