Stability and Control of Hybrid Nonlinear Dynamical Systems

Hybrid dynamic models are used to investigate the behaviour of systems in many applications, such as radar and sonar tracking of sources, communications, speech recognition, manufacturing systems and drug control. Continuous and discrete-valued states are used to characterise these systems where discrete-valued ones usually used either to capture different modes of the system such as the failure of a machine in a manufacturing system or the manoeuvre of a ship. Hybrid systems are also natural representations of joint systems when computer controllers are used with physical systems.

Hybrid systems also arises when a number of simple controllers, rather than a complex controller, are used to control a system by switching between them. Then the problem is to design the simple controllers and the optimal switching policies. This approach is an extension of the technique known as the ``bang-bang control’' in the literature where the system is controlled by switching between the minimum and maximum values of the system input. This kind of approach has received significant attention in the literature. However, most of the current work in the literature focus on linear systems.

The objective of this research is to consider the stability and control of hybrid nonlinear dynamical systems where a number of controllers are used to generate the control input by switching between them. The tools that will be developed in this project can also be applied to drug control models.

For more information please contact Peng Shi.