The Centre for Systems, Dynamics and Control
is one of the main research groups in the Scool of Mathematical Sciences. We place a lot of emphasis on understanding systems that are nonlinear. All models, for example in engineering, physics and biology, become nonlinear if one pushes them beyond a small region where a linear approximation is valid. Our research interests are as follows:
Imagine a dynamical system that has a number of inputs and outputs. Control theory gives ways of feeding the outputs back into the system in a way that allows one to control the system to a desired output. For example, there are sophisticated control systems in aircraft that ensure stable and level flights, even in the presence of moderate amounts of turbulence.
Dynamical Systems Theory
In its most general form, this is the mathematical theory of how systems evolve with time according to mathematically well-defined rules. Much of the theory has been developed to overcome the fact that one cannot find exact solutions and so there is a need for techniques that give qualitative information about the system in the absence of qualitative solutions.
Both Control and Dynamical Systems Theory rely heavily on the use of numerical techniques for simulation and prediction of the behaviour of dynamical and control systems. In many cases, numerical analysis is an integral part of both subjects.
We are involved in many applications that involve any combination of the above. This has lead to national and international interdisciplinary collaborations and research projects.