PhD position in Control Theory

What is Control Theory? 

Control theory is the indispensable hidden foundation of the modern industrial world. Control theory is critical in the continued safe and functional operation of the Mars rover, commercial aviation and national power grids. Even common technology such as the primitive flush toilet relies on control theory. For this case, it is simple to describe the controller. In the upper water bowl, there is a floating ball that sinks with the decreasing water level after each flush. The ball pulls open the water valve it is attached to. After the water bowl fills up again the floating ball rises and eventually stops pulling open the water valve, preventing the water bowl from overflowing. This is none other than a state feedback controller, where the water valve is opened or closed depending on the state of the water level.

Due to the rapid pace of current technological advancement, systems are becoming increasingly complex (think of the internet of things, driverless cars, plasma flow in nuclear fusion reactors, etc). State-of-the-art technologies describe systems using abstract mathematical models such as recursion equations, ODEs and PDEs. Before implementation in the physical world, controllers are typically synthesized on a digital computer. Because of this, control engineering provides a golden avenue for talented researchers with strong mathematical skills to make their mark.

Why study Control Theory? 

There is a major skills shortage in the UK. Engineering is a vital component of the economy delivering over 27% of GDP in the UK in 2014. Traditionally the UK has played a leading role in control theory since the dawn of the industrial revolution. There have also been major successes in recent times such as London-based Googles Deep Mind, starring in the Netflix documentary Alpha Go and solving the protein folding problem using machine learning.

In modern societies, there is an increasing need for tools that can accurately learn and identify system models while designing optimal controllers. The abundance of data has led to new machine learning techniques for controller synthesis. Unlike, classical model-based techniques there are no/little theoretical guarantees that these new data-driven techniques will conduct operations safely. This provides fertile research grounds in the area of combining classical model-based and modern data-driven methods. Arguably this is the most exciting and interesting time in history to enter the field of control theory.

Why Sheffield? 

• The Department of Automatic Control Systems Engineering (ACSE) is the only control theory department in the UK and the largest control theory department in Europe.
• ACSE has state-of-the-art facilities including dedicated robotics, computer and power system laboratories. 
• Sheffield has more trees per person than any other city in Europe and is considered to be one of the greenest cities in the UK. 
• Sheffield has a central location in the UK with excellent train links to both London and Scotland.

Project 1: Analysis of nonlinear ODEs

This plot depicts a simulation of the Lorenz system that is modelled by the following nonlinear ODE:

The Lorenz system holds special significance in the field as it was part of the inception of chaos theory.

The goal of this project is to develop new techniques based on convex optimization in order to efficiently compute the long-term properties of nonlinear ODEs, such as the Lorenz attractor. There is also scope here to design new methods for optimal controller synthesis that amounts to solving the HJB PDE:

Project 2: Battery scheduling using RL

The recent and increasing uptake of renewable energy resources (solar, wind, etc) has increased power demand variability. Cloudy windless days now have the potential to significantly reduce national power generation, increasing the likelihood of power cuts. In order to soften sudden power demand spikes, batteries can be controlled to charge and discharge optimally. This battery scheduling problem can be formulated as a Multi-Stage Optimization Problem (MSOP). The goal of this project is to develop new Reinforcement Learning (RL) techniques to solve such large-scale MSOPs.

High Level research goals 

• To understand the limits of using digital computers to synthesize controllers that yield intelligent cyber-physical systems (after all the human brain is not a digital computer).
• To discover new modular system design techniques and theories where decentralized control of individual subsystems can be shown to be globally optimal.