# MA3H7 Control Theory

**Lecturer: **Professor Robert MacKay

**Term(s): **Term 2

**Status for Mathematics students: **List A

**Commitment: **30 one hour lectures

**Assessment: **Three hour examination

**Prerequisites: **MA106 Linear Algebra, MA133 Differential Equations [Recommended: ST112 Probability B]

**Leads to:**

**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:**

By the end of the module the student should be able to:

Explain and exploit role of controllability matrix in linear control systems.

Explain and exploit stabilization for linear control systems.

Derive and analyze the Kalman filter.

Understand linear ODEs and stability theory.

Understand and manipulate Gaussian probability distributions.

Understand basic variational calculus for constrained minimization in Hilbert space.

**Books:
**E. D. Sontag,

*Mathematical Control Theory: deterministic finite dimensional systems,*Texts in Applied Mathematics No 6, Springer Verlag, 1990.

J. Zabczyk,

*Mathematical Control Theory: An Introduction*, Birkhauser, 1992.