Nonlinear System Analysis Using Convex Optimization

The foundations of dynamical systems theory can be traced back to Isaac Newton. Newton was the first to model the motion of physical systems as differential equations. Since then, dynamical systems theory has become one of the most important fields in modern science and engineering, having applications in astronomy, economics, population genetics, aerospace engineering and many more. Most physical systems are inherently nonlinear, exhibiting very rich dynamical behaviour, such as chaotic ‘’strange” attractors, local (rather than global) stability, complex limit cycles, etc.

Engineering systems are becoming increasingly more complicated, autonomous and remote, consider NASA’s Mars rover for instance. Therefore, to prevent potential system failures, it has become crucial to analyse and develop a deep understanding of the properties and behaviour of such nonlinear systems. Without this analysis, it is likely that the technological foundation of our society will become increasingly unreliable, making the deployment of remote autonomous systems economically infeasible.

The goal of this project is to develop several new methods that can be used to analyse and improve the autonomy of nonlinear systems. These methods will identify unstable states, design stabilizing or optimal controllers and compute invariant sets. There is scope here to combine traditional model-based methods with new data-driven machine learning methods to develop scalable and accurate novel computational tools.

Further project details can be found at:

https://www.sheffield.ac.uk/acse/phd/phd-position-control-theory

We require applicants to have either an undergraduate honours degree (1st) or MSc (Merit or Distinction) in a relevant science or engineering subject from a reputable institution.