Content: Will include the study of controllability, stabilization, observability, filtering and optimal control. Furthermore connections between these concepts will also be studied. Both linear and nonlinear systems will be considered. The module will comprise six chapters. The necessary background material in linear algebra, differential equations and probability will be developed as part of the course.

1. Introduction to Key Concepts.
2. Background Material.
3. Controllability.
4. Stabilization.
5. Observability and Filtering.
6. Optimal Control.

Aims: The aim of the module is to show how, as a result of extensive interests of mathematicians, control theory has developed from being a theoretical basis for control engineering into a versatile and active branch of applied mathematics.

Objectives: The objective is to ensure the aims are carried out by teaching the state space theory approach as outlined in the syllabus.

Books:

E. D. Sontag, Mathematical Control Theory, Texts in Applied Mathematics No 6, Springer Verlag, 1990.

J. Zabczyk, Mathematical Control Theory: An Introduction, Systems and Control, Birkhauser, 1992.