CBF Control for Safety-Critical Multi-Agent Autonomous Systems

About the Project

Modern applications—from power grids to vehicle platoons—depend on large networks of autonomous subsystems. Without a solid theoretical underpinning, ensuring both collective objectives (coordination) and safety constraints can be intractable. Your work will bridge this gap by providing generalizable, provable design approach that apply across a wide range of networked systems.

This 3.5-year PhD project will develop a rigorous theoretical framework to ensure both coordinated behaviour and safety in interconnected dynamical systems. You will design and analyse a two-layer control architecture:

• Coordination Layer:
  Formulate passivity-based conditions that guarantee agents—modelled as general nonlinear systems—synchronize their outputs or follow desired collective patterns purely through local interactions.
• Safety Layer:
  Introduce a supervisory “filter” based on control-barrier functions that provably enforces state constraints (e.g. collision avoidance, bounded inputs) without destroying the coordination guarantees.

Eligibility

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

Candidate Profile:

We seek someone with strong mathematical maturity in control theory, dynamical systems, or applied mathematics. Familiarity with nonlinear systems analysis, graph theory, and formal methods (e.g., barrier certificates) is advantageous. You will collaborate with experts in control theory and have opportunities to test theoretical insights in simulation and hardware environments.

Funding

This 3.5 year project is fully funded for home students; the successful candidate will receive an annual tax free stipend set at the UKRI rate (£20,780 for 2025/26) and tuition fees will be paid. We expect the stipend to increase each year.

Overseas applicants may apply, but the award will only fund the UK/Home fee rate and stipend. Any difference in overseas tuition must be met by the student or through external funding.

Before you apply

We strongly recommend that you contact the supervisor(s) for this project before you apply. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.

How to apply

Apply online through our website: https://uom.link/pgr-apply-2425

When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees.

Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.

After you have applied you will be asked to upload the following supporting documents:

• Final Transcript and certificates of all awarded university level qualifications
• Interim Transcript of any university level qualifications in progress
• CV
• Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed. (This is mandatory for all applicants and the application will be put on hold without it).
• Contact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference)
• English Language certificate (if applicable)

Applications will remain open until the post has been filled.

If you have any questions about making an application, please contact our admissions team by emailing FSE.doctoralacademy.admissions@manchester.ac.uk.