System Identification and Optimal Control

 

   System Identification and Optimal Control 2018/2019

Prof. Stefano Battilotti (coordinator) and Prof.Daniela Iacoviello 

 

The course, which gives 12 ECTS credits, is organized in the following 2 modules:

Module 1 (September - December  2019):

Optimal Control (Prof. Daniela Iacoviello)

 

Module 2 (February  - May, 2020): 

System Identification and Filtering (Prof. Stefano Battilotti).

 

 ==================================

2019-2020

=========

 Information Module 1 (Optimal control)

====================================

SEPTEMBER 24   2019 -   December  (6 ECTS)

Tuersday      10:00-12:00 (Room A7)

Wednesday  10:00-12:00 (Room A7)

Friday           11:00-13:00 (Room A5)

 Office hours: send me an e-mail ( Questo indirizzo e-mail è protetto dallo spam bot. Abilita Javascript per vederlo. )

====================================

GRADING

Exams: send an email to Prof. Iacoviello.

The exam must be held in one of these periods:

  • January-February
  •  June- July
  • September

 

 

Project+ oral exam

 

Example of project (1-3 Students):-

Read a paper on an optimal control problem

-Study: background, motivations, model, optimal control, solution, results-

- Simulations

-Conclusions

-References-

The Students must give me, before the date of the exam (about a week):

-A .doc document

-A power point presentation

-Matlab simulation files

Oral exam: Discussion of the project AND on the topics of the lectures

  

PROGRAM  2019-2020

Introduction to optimal Control and motivations

Definitions: local minimum, strict local minimum, global minimum.

Unconstrained optimization: first order necessary conditions; second order conditions

Weierstrass theorem

Constrained optimization; the Lagrangian; first order necessary conditions,

second order sufficient conditions; convexity hypothesis.

Calculus of variations; the Lagrange problem; the Euler equation; the augmented lagrangian;

necessary conditions; necessary and sufficient conditions

Calculus of variations and optimal control; the Hamiltonian function

The Pontryagin minimum principle; necessary conditions; necessary and sufficient conditions

The Hamilton –Jacobi – Bellman equation

The principle of optimality

The regulator problem: the optimal regulator problem on finite time interval; the optimal regulator problem

on infinite time interval; the steady state linear optimal regulator problem; the optimal tracking problem;

the optimal regulator problem with null final error; the optimal regulator problem with limited control

The minimum time problem; the minimum time problem for steady state system

Singular solutions

The armonic oscillator ; the double integrator

The LQG problem

 

REFERENCES

Textbooks available in the DIAG library

 B.D.O.Anderson, J.B.Moore, Linear Optimal Control, Prentice Hall, 2000

 C. Bruni, G. Di Pillo, "Metodi variazionali per il controllo ottimo", Aracne, 2007

 L. Evans, An Introduction to Mathematical Optimal control Theory, Berkeley, 1983

 How, Jonathan. 16.323  Principles of Optimal Control, Spring 2008. 

 (MIT OpenCourseWare: Massachusetts Institute of Technology). License: Creative Commons BY-NC-SA.

 D. E. Kirk, "Optimal Control Theory: An Introduction, New York, NY: Dover, 2004 

 D. Liberzon, "Calculus of Variations and Optimal Control Theory: A Concise Introduction", Princeton University Press, 2011

 A. Locatelli, "Optimal Control: An Introduction", Birkhäuser, 2001Sc

...................... 

SLIDES of the LECTURES

THESE SLIDES ARE NOT SUFFICIENT FOR THE EXAM

YOU MUST STUDY ON THE BOOKS


Lecture 1 (September 24, 25, 27),  last update September 26 

 

Lecture 2 (October 1,2, 4, 8, 9),  last update October 8

 

Lecture  (The Brachistochrone problem)  (October 11),  last update October 10

 

Lecture 3   (October 11, 22), last update October 21

 

Lecture (Examples)  (October 23)

 

Lecture 4 (October 24,  29, 30), last update November 6


Lecture 5 (October 30)

 

Lecture (Moonlanding)

 

Lecture 6  (November 5, 6, 8,12), last update November 11

 

Lecture 7 (November 13, 15, 19 ) last update November 18

 

Lecture (double integrator, harmonic oscillator) (November 19, 20)

 

Lecture (examples) (November 26, 27)

 

LQG (November 29 (3 h), 3, 4, 6 (3h) ) last update December 4

 

Lecture ( grading- general overview of the course with the most important results)

 

=============================================================================== 

WEEK OCTOBER 14 - 18, 2019 (Lectures of October 15, 16, 18) :

NO CLASSES NOR OFFICE HOURS OF OPTIMAL CONTROL

November 22: no class 

December 17 - 18- 20 : no class

 

 ===============================================================================

===============================================================================

 

===============================================================================

===============================================================================

2018-2019

==========

Information Module 1 (Optimal control) 

(4ECTS)

 ====================================

SEPTEMBER 25 2018 - December  (4ECTS)

Tuersday 10:00-12:00 (Room A6)

Wednesday 10:00-12:00 (Room A6)

====================================

 

THESE SLIDES ARE NOT SUFFICIENT FOR THE EXAM: 

YOU MUST STUDY ON THE BOOKS

Lecture 1 (September 25 and 26)

 Lecture 2 (September 26, October 2, 16)

Lecture 3 (October  17, 23)

Lecture Applications (October 24)

Lecture 4 (October 24, 30, 31)

Lecture moon landing (October 31)

  OPTIMAL CONTROL- SCHEDULE (week november 5-9 2018)

Monday 5 November: 12:00-14:00 Room A7

Tuesday 6 November: 12:00-14:00 Room A6


Wednesday 7 November: 10:15-12:00 Room A6 (confirmed)

Wednesday 7 November: 12:00-14:00 Room A6

 Lecture 5 (November 5)

 

Lecture 6 (November 5,6,7)

 

 Lecture 7 (November 13, 14)

Lecture 8 (November  20, 21)
Lecture 9 (December 4,5)

 ======================================================================

  Reference material 

 Textbooks available in the DIAG library

 B.D.O.Anderson, J.B.Moore, Linear Optimal Control, Prentice Hall, 2000

 C. Bruni, G. Di Pillo, "Metodi variazionali per il controllo ottimo", Aracne, 2007

 L. Evans, An Introduction to Mathematical Optimal control Theory, Berkeley, 1983

 How, Jonathan. 16.323  Principles of Optimal Control, Spring 2008. 

 (MIT OpenCourseWare: Massachusetts Institute of Technology). License: Creative Commons BY-NC-SA.

 D. E. Kirk, "Optimal Control Theory: An Introduction, New York, NY: Dover, 2004 

 D. Liberzon, "Calculus of Variations and Optimal Control Theory: A Concise Introduction", Princeton University Press, 2011

 A. Locatelli, "Optimal Control: An Introduction", Birkhäuser, 2001Sc

 ============================================================

 Some projects discussed since 2014

 Application Of Optimal Control To Malaria: Strategies And Simulations

 Performance Compare Between Lqr And Pid Control Of Dc Motor

 Optimal Low-thrust Leo (Low-earth Orbit) To Geo (Geosynchronous-earth Orbit)

 Circular Orbit Transfer

 Controllo Ottimo Di Una Turbina Eolica A VelocitĂ  Variabile Attraverso Il Metodo

 dell'inseguimento Ottimo A Regime Permanente

 Optimalcontrol In Dielectrophoresis

 On The Design Of P.I.D. Controllers Using Optimal Linear Regulator Theory

 Rocket Railroad Car

 Optimal Control Of Quadrotor Altitude Using Linear Quadratic Regulator

 Optimal Control Of An Inverted Pendulum

 Glucose Optimal Control System In Diabetes Treatment 

 Optimal Control Of Shell And Tube Heat Exchanger

 Optimal Control Analysis Of A Mathematical Model For Unemployment

 Time optimal control of an automatic Cableway

 Optimal Control Of An Inverted Pendulum

 Glucose Optimal Control System In Diabetes Treatment

 Optimal Control Of Shell And Tube Heat Exchanger

 Optimal Control Analysis Of A Mathematical Model For Unemployment

 Time Optimal Control Of An Automatic Cableway

 Optimal Control Project On Arduino Managed Module For Automatic Ventilation Of

 Vehicle Interiors

 Optimal Control For A Suspension Of A Quarter Car Model

 

============================================================

PROGRAM  2018-2019

Introduction to optimal Control and motivations

Definitions: local minimum, strict local minimum, global minimum.

Unconstrained optimization: first order necessary conditions; second order conditions

Weierstrass theorem

Constrained optimization; the Lagrangian; first order necessary conditions,

second order sufficient conditions; convexity hypothesis.

Calculus of variations; the Lagrange problem; the Euler equation; the augmented lagrangian;

necessary conditions; necessary and sufficient conditions

Calculus of variations and optimal control; the Hamiltonian function

The Pontryagin minimum principle; necessary conditions; necessary and sufficient conditions

The Hamilton –Jacobi – Bellman equation

The principle of optimality

The regulator problem: the optimal regulator problem on finite time interval; the optimal regulator problem

on infinite time interval; the steady state linear optimal regulator problem; the optimal tracking problem;

the optimal regulator problem with null final error; the optimal regulator problem with limited control

The minimum time problem; the minimum time problem for steady state system

Singular solutions

The armonic oscillator ; the double integrator

 

 

Ultimo aggiornamento Venerdì 13 Dicembre 2019 12:26
 
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