How to use

This repository contains regularly updated course materials. You can use lecture slides for self study (they are written as lecture notes). Lecture recordings from this and last year offerings are linked below. The links in the Self-study with Colab section are both for self-study and reviewing the practical sessions. Refer to the book and resourses suggestions at the bottom of the page.

Lecture slides

• Lecture 1 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Introduction.pdf
• Lecture 2 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Stability.pdf
• Lecture 3 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Control.pdf
• Lecture 4 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Laplace.pdf
• Lecture 5 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Bode.pdf
• Lecture 6 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Discrete.pdf
• Lecture 7 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/HJB_LQR.pdf
• Lecture 8 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Observer.pdf
• Lecture 9 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/ControllabilityObservability.pdf
• Lecture 10 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Kalman.pdf
• Lecture 11 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/LyapunovTheory.pdf
• Lecture 12 - https://github.com/SergeiSa/Control-Theory-2024/blob/main/Slides/Linearization.pdf

Lecture videos:

playlist

• Lecture 1 (State Space) - https://youtu.be/sgc9bQ7ao3A
• Lecture 2 (Stability) - https://youtu.be/ZCjeTW4jjW8
• Lecture 3 (Stabilizing control) - https://youtu.be/XFO02Z2W0Rs
• Lecture 4 (Laplace, Transfer functions) - https://youtu.be/ow9sWpSf_YI
• Lecture 5 (Bode) - https://youtu.be/U8szIWSVf6E
• Lecture 6 (Discrete) - https://youtu.be/k4QQXFkcthw
• Lecture 7 (LQR, Riccati) -
• Lecture 8 (Observers) -
• Lecture 9 (Controllability, Observability) -
• Lecture 10 (Kalman) -

Assignments (labs)

• Assignment / lab / submission / gradable item # 1:
• • PDF: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment1.pdf
• • Colab: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment1.ipynb
• Assignment / lab / submission / gradable item # 2:
• • PDF: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment2.pdf
• • Colab: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment2.ipynb
• Assignment / lab / submission / gradable item # 3:
• • PDF: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment3.pdf
• • Colab: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment3.ipynb

Practice sessions with Colab

• Practice 1 (State Space) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_1_ODE_to_StateSpace.ipynb
• Practice 2 (Stability) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_2_Stability.ipynb
• Practice 3 (Laplace, Transfer functions) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_3_Laplace_TransferFunctions.ipynb
• Practice 4 (Bode) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_4_Bode.ipynb
• Practice 5 (Feedback control) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_5_FeedbackControl.ipynb
• Practice 6 (Trajectory tracking) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_6_TrajectoryTracking.ipynb
• Practice 7 (Discrete) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_7_Discrete.ipynb
• Practice 8 (Lyapunov) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_8_Lyapunov.ipynb

Book suggestions

Lecture 1. State-Space, ODE

• Control Systems Engineering Norman S. Nise
  • Chapter 3.3: The General State-Space Representation
  • Chapter 3.4: Applying the State-Space Representation
• Systems of First Order Linear Differential Equations. Download

Lecture 2. Stability

• Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y
  • 4.4 STABILITY
• Control Systems Engineering Norman S. Nise (chapters 3.3, 3.4)
• Paul's Online Notes (systems of linear ODE, solutions for them):
  • http://tutorial.math.lamar.edu/Classes/DE/SystemsDE.aspx
  • http://tutorial.math.lamar.edu/Classes/DE/SolutionsToSystems.aspx
• Astolfi, A., 2006. Systems and Control Theory: An Introduction. Imperial College London lecture notes. - 2.3.1 Linear systems (on equilibrioum of linear systems): http://www3.imperial.ac.uk/pls/portallive/docs/1/31851696.PDF
• Videos:
  • State Space Stability (Linear Systems Theory EECS 221a, Berkeley) - https://youtu.be/7GarcEQ0uk8

Lecture 3. Stabilizing control

• Control theory by S. Simrock - sections 5, 6 (stability discussed in terms of TF): https://cds.cern.ch/record/1100534/files/p73.pdf
• Module 9: State Feedback Control Design, Lecture Note 1: https://nptel.ac.in/content/storage2/courses/108103008/PDF/module9/m9_lec1.pdf
• 16.31 Feedback Control Systems https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-30-feedback-control-systems-fall-2010/lecture-notes/MIT16_30F10_lec11.pdf
• Chapter 6 State Feedback - http://www.cds.caltech.edu/~murray/books/AM05/pdf/am06-statefbk_16Sep06.pdf

Lecture 4. Laplace Transform, Transfer functions

• Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y
  • 3.4 SOLUTION BY THE LAPLACE TRANSFORM: THE RESOLVENT
  • 3.5 INPUT-OUTPUT RELATIONS: TRANSFER FUNCTIONS
• Control Systems Engineering, by Norman S. Nise
  • chapter 2.2 Laplace Transform Review
  • chapter 2.3 The Transfer Function (optional)
• Cho W. S. To, Introduction to Dynamics and Control in Mechanical Engineering Systems.
  • 2 Review of Laplace Transforms
  • 8.3 Transfer Functions
• Control theory by S. Simrock - sections 2, 3 and 4: https://cds.cern.ch/record/1100534/files/p73.pdf
• Videos:
  • Control Systems Lectures - Transfer Functions, Brian Douglas: https://youtu.be/RJleGwXorUk
  • The Laplace Transform - A Graphical Approach, Brian Douglas: https://youtu.be/ZGPtPkTft8g

Lecture 5. Frequency response, Bode plot

• Control System Lectures - Bode Plots, Introduction, by Brian Douglas: https://youtu.be/_eh1conN6YM
• Bode Plots by Hand, Real Constants, by Brian Douglas: https://youtu.be/CSAp9ooQRT0

Lecture 6. Discrete Systems

• Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y
  • 3.1 DIFFERENTIAL EQUATIONS REVISITED
  • 3.2 SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN STATE-SPACE FORM
• MIT 2.14, State Space response https://web.mit.edu/2.14/www/Handouts/StateSpaceResponse.pdf
  • 2 State-Variable Response of Linear Systems
• Astolfi, A., 2006. Systems and Control Theory: An Introduction. Imperial College London lecture notes:
  • 1.2.9 Approximate discrete-time models;
  • Proposition 2.3 (Trajectories of linear, discrete-time, systems) - on Controllability: http://www3.imperial.ac.uk/pls/portallive/docs/1/31851696.PDF
• Dahleh, M., Dahleh, M.A. and Verghese, G., 2004. Lectures on dynamic systems and control. A+ A, 4(100), pp.1-100. (goes to z-transform, which is outside the scope of our course): https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-241j-dynamic-systems-and-control-spring-2011/readings/MIT6_241JS11_chap10.pdf

Lecture 7 LQR

• Underactuated robotics. Linear Quadratic Regulators - http://underactuated.mit.edu/lqr.html
• Discrete LQR (slides) - https://stanford.edu/class/ee363/lectures/dlqr.pdf
• Discrete LQR, infinite horizon (slides) - https://web.stanford.edu/class/ee363/lectures/dlqr-ss.pdf
• F.L. Lewis, lecture notes - https://lewisgroup.uta.edu/ee5321/2013%20notes/2%20lqr%20dt%20and%20sampling.pdf
• University of Freiburg, lecture notes - https://www.syscop.de/files/2019ss/sscs/summary/chap3c.pdf
• Optimal Control: Discrete-Time LQR (slides, Cristian Mahulea) - https://webdiis.unizar.es/~cmahulea/course/lecture4.pdf
• Videos:
  • Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart, Steve Brunton https://youtu.be/1_UobILf3cc

Lecture 8 Observers

• Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y
  • LINEAR OBSERVERS
• Videos:
  • Motivation for Full-State Estimation, Steve Brunton https://youtu.be/LTNMf8X21cY

Lecture 9 Controllability, Observability

• Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y
  • 5.4 ALGEBRAIC CONDITIONS FOR CONTROLLABILITY AND OBSERVABILITY
• Invariant subspaces, Sylvester equation, PBH https://stanford.edu/class/ee363/sessions/s2notes.pdf
• EE363 Winter 2008-09 Lecture 6 Invariant subspaces https://web.stanford.edu/class/ee363/lectures/inv-sub.pdf
• Videos:
  • Degrees of Controllability and Gramians, Steve Brunton - https://youtu.be/ZNHx62HbKNA
  • Controllability and the PBH Test, Steve Brunton - https://youtu.be/0XJHgLrcPeA

Lecture 10 Kalman Filter

• Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y
  • RANDOM PROCESSES
  • KALMAN FILTERS: OPTIMUM OBSERVERS

Lyapunov Theory

• 3.9 Liapunov’s direct method - https://folk.uib.no/nmagb/m2142002l3.pdf
• Universita degli studi di Padova Dipartimento di Ingegneria dell'Informazione, Nicoletta Bof, Ruggero Carli, Luca Schenato, Technical Report, Lyapunov Theory for Discrete Time Systems - https://arxiv.org/abs/1809.05289

For contributors

Pull requests with suggestions and improvements, however small or big, are welcome!

The changes in lecture slides are going through an automated check.

The PDFs are compiled and updated automatically when PR is merged (thanks to k1rill-fedoseev from the 2020 Linear Control class!). You don't need to update them manually. They are also uploaded as workflow artifacts for every new commit pushed into this repository. You can use them to see your changes.

Consider adding *.pdf to the .git/info/exclude file on your local repo. Here is the overy long but helpful description why it works