We are looking for a motivated candidate to pursue PhD / MSc by Research based on a project entitled 'Machine learning based approach for numerical analysis of nonlinear dynamics of unmanned systems'. Read more Read less

Stability analysis of autonomous systems and designing controllers or policies to guarantee a target behaviour are of great importance in many domains, such as aerospace, autonomous driving and robotics. As opposed to Linear Time Invariant systems, whose stability can be analysed globally, most of the nonlinear systems usually achieve stability only in a specific region around some equilibrium point so called Region of Attraction (ROA). Knowledge of the stability region is essential in many applications since it enhance the efficiency of a controller design. For example, an autonomous swarm of drones will remain safe under more diverse and potentially harsh conditions. ROA is an important metric of the system robustness, showing how much the initial state can be disturbed away from the expected steady state that is usually the designed operation point in practice. Besides, an actual dynamical system can have multiple stable equilibrium points; so that one has to decide the ROA for a specific one.

However, finding the exact ROA for a nonlinear and complex system, such as aircraft, autonomous car or swarm of drones, both numerically and analytically might be impossible. The problem is complicated by an active use of nonlinear filters, adaptive and/or reinforcement learning control policies. There are several promising novel numerical approaches including machine learning-based ones that provides a route for stability analysis and control algorithm design of nonlinear systems.

This project aims at development of a numerical approach (e.g. machine learning based) for estimation of ROA and designing control algorithm providing desired behaviour under maximization of stability region of unmanned aerial systems. Recently developed methods of relaxations based on Sum of Squares and synthesis of formal Lyapunov Neural Networks for nonlinear systems and systems with reinforcement learning control policies could be one of the choices to leverage in the development of the approach.

The project envisages that the effectiveness will be validated for different applications and platforms, including nonlinear/adaptive/reinforcement learning control, multi-agent systems.

About Cranfield University

Cranfield is an exclusively postgraduate university that is a global leader for education and transformational research in technology and management.

Cranfield University has been ranked amongst the world’s top universities in the latest QS World University Rankings by Subject.

In the subject area ‘Engineering – Mechanical, Aeronautical and Manufacturing’ Cranfield has been ranked 27th in the world, climbing 18 places from last year’s ranking and attaining top scores in Employer and Academic Reputation.

This PhD will be hosted by the Centre for Autonomous and Cyber-Physical Systems. The Centre for Autonomous and Cyber-Physical Systems is one of the world’s largest centres of postgraduate education and research, with over 200 MSc and PhD students.

The Centre for Autonomous and Cyber-Physical Systems at Cranfield has a leading reputation in autonomous and space systems, established with over 15 years of research in this field. We cover all types of autonomous systems including airborne, ground and marine as well as autonomous space exploration.

We are renowned for being a leading European centre for postgraduate teaching and research in autonomous and cyber-physical systems with approximately 500 alumni members around the world working in the aerospace industry. Over the last two decades we have developed a significant body of research and its applications in autonomous systems.

At a glance

  • Application deadline20 Apr 2023
  • Award type(s)PhD, MSc by Research
  • Duration of awardPhD: 3 years; MSc by Research: 1 year
  • EligibilityUK, EU, Rest of World
  • Reference numberSATM276 for PhD or SATM277 for MSc by Research

Entry requirements

Applicants must have a first- or second-class UK honours degree or equivalent in Maths, Physics, engineering or a related area.


This is a self-funded opportunity so the student would need to source their own funding. However, bursary can be considered for an exceptional candidate. The application is open to UK and international students.

Cranfield Doctoral Network

Research students at Cranfield benefit from being part of a dynamic, focused and professional study environment and all become valued members of the Cranfield Doctoral Network. This network brings together both research students and staff, providing a platform for our researchers to share ideas and collaborate in a multi-disciplinary environment. It aims to encourage an effective and vibrant research culture, founded upon the diversity of activities and knowledge. A tailored programme of seminars and events, alongside our Doctoral Researchers Core Development programme (transferable skills training), provide those studying a research degree with a wealth of social and networking opportunities.

How to apply

If you are eligible to apply for this research studentship please complete the relevant application form below:

Online application form for PhD 

Online application form for MSc by Research

For further information please contact - Dr Dmitry Ignatyev

E: d.ignatyev@cranfield.ac.uk