# MSc Advanced Control and Systems Engineering with Extended Research

Year of entry: 2024

## Course unit details:Optimal & Robust Control

Unit code EEEN60262 15 FHEQ level 7 – master's degree or fourth year of an integrated master's degree Semester 2 No

### Overview

BRIEF DESCRIPTION OF THE UNIT

Optimal Control

• Quadratic Lyapunov functions for linear systems
• LQR (optimal state feedback) control
• Robustness of LQR control
• Kalman filter (optimal observers)
• LQG control (combining LQR state feedback and optimal observer)
• Loop transfer recovery
• H2 norms and H2 optimal control

Robust Control

Underpinning concepts:

• Singular value decomposition, the H-infinity norm and the H-infinity function space
• Well-posedness and internal stability of feedback interconnections
• Small-gain theorem

Uncertainty representations and robust stability analysis:

• Additive, multiplicative and inverse multiplicative uncertainty representations
• Linear Fractional Transformations (LFT) and LFT uncertainty representation
• Robust stability tests

Robust controller synthesis and robust control design methodology:

• Riccati based H-infinity control synthesis
• H-infinity loopshaping control design methodology

### Pre/co-requisites

Unit title Unit code Requirement type Description
Control Fundamentals EEEN64401 Pre-Requisite Compulsory
State-Space and Multivariable Control EEEN60109 Pre-Requisite Compulsory

### Aims

This course unit detail provides the framework for delivery in 2020/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates.

The course unit aims to:

• Introduce students to the fundamentals of LQG control
• Introduce students to the fundamentals of robustness analysis, robust control law synthesis and robust control design

### Learning outcomes

Students will be able to:

Knowledge and understanding

• Demonstrate knowledge of optimal control theory
• Analyse robustness of systems
• Understand how robust controllers are synthesised
• Design robust controllers

Intellectual skills

• Design controllers using optimal control theory
• Develop skills useful in controlling systems when accurate mathematical models are unavailable

Practical skills

• Apply optimal control methods to systems from a variety of technological areas
• Learn design methods that can be used in developing controllers for practical systems

Transferable skills and personal qualities

• Use the Kalman filter in fields outside control engineering
• Understand how to use the methods in application

Method Weight
Other 20%
Written exam 80%

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### Study hours

Scheduled activity hours
Lectures 30
Practical classes & workshops 8
Tutorials 3
Independent study hours
Independent study 109

### Teaching staff

Staff member Role
Guido Herrmann Unit coordinator
Joaquin Carrasco Gomez Unit coordinator