# Advanced Automation and Control

### Corso di Laurea Specialistica

Università degli Studi di Pavia, sede di Pavia

From Academic Year 2016/2017 onwards

Prof. Raimondo Davide M. and Prof. Ferrara Antonella

### Office hours: upon appointment

Office location: Dipartimento di Ingegneria Industriale e dell'Informazione

- Prof. Raimondo, floor F

- Prof. Ferrara, floor F

### Handouts

- Prof. FerraraSliding Mode Control

Slides Prof. Stratis Kanarachos

Slides Prof. Anuradha Annaswamy

- Prof. Raimondo

Introduction (update)

Duality (updated)

Properties of linear programming

(optional, the same content is also available in the Scripts on Linear Programming)

Prof. Ciaramella will teach the next 6 lectures at the blackboard

Scripts on Linear Programming

Linear Programming: examples

Slides Lecture 5 - Lecture 8 provide the details for solving an LP using the

simplex algorithm through the tableu. This approach should be used during the exam.

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9 Not done (2018/2019)

Lecture 10

Lecture 11

Link to slides on branch and bound algorithm

Solved exercise: milp example with branch and bound.

Note : Phase 1 of the problem above could be solved with no iterations

since we had in the basis elements that were not y1, y2..

Lecture 12

Cutting Plane Method for Integer Programs

Branch and Bound for Integer Programs

Link to material for integer programming

(optional, please consider only the examples at this link)

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18 Not done (2018/2019)

Lecture 19 Not done (2018/2019)

Lecture 20 Not done (2018/2019)

Lecture 21

Solved MILP

Another solved MILP (errata corrige)

New exercise: translation of a problem into the corresponding MILP

Solution of the problem above

Solved MILP Phase 1-2

A very long MILP Phase 1-2 which requires to explore all nodes

Exercises on duality and convexity (updated). For the duality case please substitute

to the matrices the values of matrices and vectors in order to complete the exercise.

### Previous examination texts (recent ones)

- Prof. Ferrara20-01-2017

05-07-2017

09-02-2017

13-06-2017

08-09-2017

22-09-2017

- Prof. Raimondo

20-01-2017

09-02-2017

13-06-2017

05-07-2017

08-09-2017

06-04-2018

19-06-2018

Solution to the 1st exercise of the 19-06-2018

Solution to the 2nd exercise of the 19-06-2018

Solution to the 3rd exercise of the 19-06-2018

Solution to the 4th exercise of the 19-06-2018

11-07-2018

Solution to the 1st exercise of the 11-07-2018

Solution to the exercises 2-4 of the 11-07-2018

14-09-2018

28-09-2018

25-01-2019

Solution to the 1st exercise of the 25-01-2019 (update)

21-06-2019

Solution exam 21-06-2019

11-07-2019

11-07-2019 File where to report the results

### Laboratory

- Prof. Raimondo### Laboratory 1

Laboratory 1: problem descriptionMatlab script: linear programming example with function linprog

Matlab script: linear programming example with yalmip

The scripts require the MPT toolbox

To execute the scripts try

[x,fval,exitflag]=LP_example_linprog(800,0,'max')

[x,fval,exitflag]=LP_example_yalmip(800,0,'max')

Check the comments in the script to understand the meaning of the inputs

of the functions and to try different inputs

### Laboratory 2

Laboratory 2: problem descriptionMatlab script: mixed integer linear programming example with function glpk

Matlab script: mixed integer linear programming example with yalmip

The scripts require the MPT toolbox

To execute the scripts try

[x_out,delta_out,fval,exitflag]=MILP_example_glpk(1)

[x_out,delta_out,fval,exitflag]=MILP_example_yalmip(1)

Check the comments in the script to understand the meaning of the inputs

of the functions

### Laboratory 3

Script for dynamic programming for mobile robotics (single robot)Script for dynamic programming for mobile robotics (two robots)

Robot image (download in the same directory)

Robot image 2 (download in the same directory)

### Exams

- Closed-books closed-notes written exam on all course topics
- Date/time/room will be published on the website of the Faculty of Engineering
- No graphic or programmable calculators are allowed
- Registration
to exams must be done through the University website and ends 7 days before the exam
date

### Grade registration

Grades will be notified to each students by email. Students will have 5 days to accept or reject the grade: this has to be done only through the university account (and not sending an email to the Professor). After 5 days all grades that will have not been rejected will be registered in the student curriculum.

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