# Course Title: Optimisation and Control

## Part A: Course Overview

Course Title: Optimisation and Control

Credit Points: 12.00

### Teaching Period(s)

MATH2198

City Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 2 2010,
Sem 2 2011,
Sem 2 2012,
Sem 2 2013,
Sem 2 2014,
Sem 2 2015

Course Coordinator: Prof Andrew Eberhard and Dr Robin Hill

Course Coordinator Phone: +61 3 9925 2616 / 9925 3161

Course Coordinator Email: andy.eb@rmit.edu.au / r.hill@rmit.edu.au

Course Coordinator Location: 8.9.12 / 8.9.77

Pre-requisite Courses and Assumed Knowledge and Capabilities

MATH2150 - Real and Complex Analysis
MATH2140 - Linear Algebra and Vector Calculus
MATH1155 - Scientific Computing

Course Description

This course consists of two topics, Optimisation and Control. In the Control portion of the course you will become familiar with the modern state-space description of dynamic systems, and how feedback can be used to modify dynamic response. You will gain an understanding of the basic concepts of stability, observability and controllability of systems and learn how to verify performance using the simulation software package MATLAB. The Optimisation portion of the course gives an introduction to the main ideas behind the optimisation algorithms which are used to solve problems which arise in many areas of engineering, science, economic modelling, resource modelling and operations research. We consider what leads to convergence and efficiency for various algorithms. MATLAB code and C-programming is developed to illustrate these principles.

Objectives/Learning Outcomes/Capability Development

On successful completion of this course, you will be able to
• set up mathematical models of linear dynamic systems in state-space format,
• convert a system model to transfer function form,
• take a the Laplace transform or Z—transform of a wide class of functions and be able to invert these transforms,
• solve linear constant coefficient differential and difference equations using Laplace and Z-transforms,
• establish whether a dynamical system is stable, marginally stable or unstable,
• analyse the input-output behaviour of a system using the MATLAB software package,
• develop an optimization problem, formulated in appropriate mathematical language, whose solution will provide an answer to a real world problem
• formulate appropriate optimality conditions for a given problem.
• reformulate constrained problems using Lagrangian and Wolfe duality.
• identify the reasons for poor convergence behaviour of an algorithm. Work with and (if needed) modify the appropriate code for an optimization algorithm and problem.
• use some basic techniques for handling constraints such as penalty methods and augmented Lagrangian.
• describe the various optimization problem classes and explain which optimization solver is suitable for each class of problem.

This course contributes to the development of the following Program Learning Outcomes:

Knowledge and technical competence

• The ability to use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.

Problem-solving

• The ability to bring together and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
• An understanding of the balance between the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.

Overview of Learning Activities

There will be a series of structured written assignments and laboratory exercises that will develop the ability to apply the mathematical theory to a range of applications. There will also be supervised computer laboratory classes where you will learn Matlab syntax and run Matlab programs. The underlying theory will be presented in lectures.

Overview of Learning Resources

You will have access to course material on Blackboard, including lecture notes and a detailed study program.

Overview of Assessment

The assessment for this course includes assignments, lab-based assessment and a final exam. Feedback on labs and assignments will be provided to you during the semester.