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 Ă¨ 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 â€“Jacobi â€“ 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", BirkhĂ¤user, 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", BirkhĂ¤user, 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 â€“Jacobi â€“ 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 VenerdĂ¬ 13 Dicembre 2019 12:26