# Unit information: Control Theory in 2020/21

Unit name Control Theory EMATM2700 10 M/7 Teaching Block 2 (weeks 13 - 24) Professor. Di Bernardo Not open EMAT20200 or equivalent None Department of Engineering Mathematics Faculty of Engineering

## Description

This unit introduces students to the theory of Automatic Control. The aim is to illustrate the skills and analytical tools required to analyse appropriate control strategies for both linear and nonlinear dynamical systems. Emphasis is given to Optimal Control Strategies particularly relevant in applications and on the control of complex multi agent systems. The syllabus includes foundation topics such as linearisation, controllability and observability together with more advanced ones, e.g. optimal control theory, network control systems and adaptive control.

Control theory is a branch of Applied Mathematics whose recent developments have made possible, for example, the implementation of autopilots on aeroplanes and the landing of automatic interplanetary probes on Mars. Nowadays, novel challenges have arisen which require a proper mathematical understanding. Hybrid Control, Internet congestion control and the control of networks are just some examples of recent applications of control theory.

If you have taken previous courses in control or nonlinear dynamics and chaos, this course will give you the opportunity to look at some of the "hot" research topics in modern control theory and dynamical systems.

The course is based on a series of lectures and computer demonstrations. The syllabus includes linearisation techniques; controllability and observability of linear dynamical systems; stability theory and Lyapunov techniques; optimal control; controllability of multi agent systems; synchronisation and control of complex networks; applications to physics and engineering.

No previous course in control or nonlinear dynamics is required.

Aims: This unit is intended to introduce you to the mathematical foundations of Control Theory. The aim of the course is to allow you to develop new skills and analytical tools required to analyse and design methods for the control of both linear and nonlinear dynamical systems.

## Intended learning outcomes

By the end of this module, you will be able to use appropriate analytical tools to model and control a given physical system. Specifically, we will discuss how to:

1. Decide in advance if a given dynamical system is controllable and stabilizable
2. Design state feedback controllers to change the evolution of a dynamical system of interest
3. Optimize the control system design to minimize the control energy spent or achieve control in minimum time
4. Tame the complex dynamics of nonlinear systems and exploit chaos and bifurcations for control system design

Lectures

## Assessment Details

2-hour written examination: 100% (all learning outcomes)