Analysis and control of multi-agent systems using partial differential equations

The Department of Automatic Control and Systems Engineering at the University of Sheffield invites applications for an exciting new project. The programme will start in February 2020.

Project Description

Smart grids, social networks, traffic flows, communication networks – all these are typical examples of multi-agent systems. It is common for such systems to grow rapidly in size and complexity due to the continuous introduction of new agents. As a result, standard control methods fail, and we witness massive system breakdowns such as power blackouts. Thus, there is a demand for new scalable solutions for the analysis and control of multi-agent systems.
Partial differential equations (PDEs) are a natural framework for studying large-scale multi-agent systems that provides a solution to the scalability problem. When cooperating agents are identical, and their communication topology is uniform, one can take the continuum limit of the ordinary differential equations (ODEs) describing the multi-agent system and obtain a PDE. The form of the PDE depends on the agents’ dynamics and network structure but does not depend on the number of agents. Consequently, such PDEs provide analysis methods whose complexity does not change when the number of agents grows.

This research topic is full of challenging questions: What is the best way to associate the state of a multi- agent system with the state of a PDE? How many agents justify the usage of PDEs? How to interpret the results derived for the PDE in terms of the original multi-agent system? If the control has been synthesised for the PDE, how can one implement it in the multi-agent system? What are the conditions on the local dynamics and communication topology that make it possible to associate a well-posed PDE with a given multi-agent system?

Candidate Requirements and Eligibility

Prospective candidates should have a strong background in control theory and should be familiar with partial differential equations. Programming skills are essential (MATLAB/Python).

More information about entry requirements can be found here:

Applicants with other qualifications or experience should contact the Department’s Research Support Officer via so that we can check on your eligibility.

Funding Notes

Applicants can apply for a Scholarship from the University of Sheffield but should note that competition for these Scholarships is highly competitive. It will be possible to make Scholarship applications from the Autumn with a strict deadline in late January 2020. Specific information is available at: