Session 3 Density functions and sum-of-squares methods Reading assignment Check the main results and examples of these papers. • Rantzer, Systems & Control Letters, 42:3 (2001). • Prajna/Parrilo/Rantzer, TAC 49:2 (2004). • SOSTOOLS and its Control Applications, Prajna/P/S/P (2005) Exercise 3.1 a. Draw a phase plot for the system[ ẋ1 ẋ2 ] = [ −εx1 + x2 1 − x2 2 −εx2 + 2x1x2 ] for ε = 1. b. Prove

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E3.pdf - 2025-07-25

Session 5 Relaxed dynamic programming and Q-learning Reading assignment Check the main results and examples of these papers. • Lincoln/Rantzer, TAC 51:8 (2006) • Rantzer, IEE Proc on Control Theory and Appl. 153:5 (2006) • Geramifard et.al, Found. & Trends in Machine Learn. 6:4 (2013) Exercise 5.1Consider the linear quadratic control problem Minimize ∞∑ t=0 x(t)2 + u(t)2 subject to x(t+ 1) = x(t)

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E5.pdf - 2025-07-25

Reading instructions and problem set 7 Feedback linearization, zero-dynamics, Lyapunov re-design, backtep- ping Reading assignment Khalil [3rd ed.] Ch 13. Khalil [3rd ed.] Ch.14.(1) 2-4 + "The joy of feedback" by P. Kokotović (handout) (Extra reading: • “Constructive Nonlinear Control” by R. Sepulchre et al, Springer, 1997) • “Nonlinear & Adaptive Control Design” by M. Krstić et al, Wiley, (1995)

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E7.pdf - 2025-07-25

Nonlinear Control Theory 2017 Anders Rantzer m.fl. Nonlinear Control Theory 2017 L1 Nonlinear phenomena and Lyapunov theory L2 Absolute stability theory, dissipativity and IQCs L3 Density functions and computational methods L4 Piecewise linear systems, jump linear systems L5 Relaxed dynamic programming and Q-learning L6 Controllability and Lie brackets L7 Synthesis: Exact linearization, backsteppi

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec01_2017eight.pdf - 2025-07-25

L3: Density functions and sum-of-squares methods ○ Lyapunov Stabilization Computationally Untractable ○ Density Functions ○ “Almost” Stabilization Computationally Convex ○ Duality Between Cost and Flow ○ Sum-of-squares Optimization ○ Examples Literature. Density functions: Rantzer, Systems & Control Letters, 42:3 (2001) Synthesis: Prajna/Parrilo/Rantzer, TAC 49:2 (2004) SOSTOOLS and its Control Ap

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec03_2017eight.pdf - 2025-07-25

RLbob_4slides L5: Relaxed dynamic programming and Q-learning • Relaxed Dynamic Programming ○ Application to switching systems ○ Application to Model Predictive Control Literature: [Lincoln and Rantzer, Relaxing Dynamic Programming, TAC 51:8, 2006] [Rantzer, Relaxing Dynamic Programming in Switching Systems, IEE Proceeding on Control Theory and Applications, 153:5, 2006] Who decides the price of a

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec05_2017all.pdf - 2025-07-25

lie2017 Lecture 6 – Nonlinear controllability Nonlinear Controllability Material Lecture slides Handout from Nonlinear Control Theory, Torkel Glad (Linköping) Handout about Inverse function theorem by Hörmander Nonlinear System ẋ = f(x, u) y = h(x, u) Important special affine case: ẋ = f(x) + g(x)u y = h(x) f : drift term g : input term(s) What you will learn today (spoiler alert) New mathemat

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec06_2017nine.pdf - 2025-07-25

Synthesis, Nonlinear design ◮ Introduction ◮ Relative degree & zero-dynamics (rev.) ◮ Exact Linearization (intro) ◮ Control Lyapunov functions ◮ Lyapunov redesign ◮ Nonlinear damping ◮ Backstepping ◮ Control Lyapunov functions (CLFs) ◮ passivity ◮ robust/adaptive Ch 13.1-13.2, 14.1-14.3 Nonlinear Systems, Khalil The Joy of Feedback, P V Kokotovic Why nonlinear design methods? ◮ Linear design degra

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/funonlin_lec07_synthesis_2017_eight.pdf - 2025-07-25

Session 1 Reading assignment Liberzon chapters 1 – 2.4. Exercises 1.1. = Liberzon Exercise 1.1 1.2. = Liberzon Exercise 1.5 1.3. = Liberzon Exercise 2.2 1.4. = Liberzon Exercise 2.3 1.5. Read Liberzon Chap.2.3.3 and explain how we can avoid assuming y ∈ C2. Prove Lemma 2.2 (Liberzon Exercise 2.4). 1.6. = Liberzon Exercise 2.5 (State the brachistochrone problem first.) 1.7. = Liberzon Exercise 2.6

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise1.pdf - 2025-07-25

Session 3 Reading assignment Liberzon chapters 4.1, 4.3 – 4.5. Exercises 3.1. = Liberzon Exercise 4.1. (Deriving the Euler-Lagrange equation for brachistochrone is enough. No need to derive that its solutions are cycloids.) 3.2. = Liberzon Exercise 4.8 3.3. = Liberzon Exercise 4.10 3.4. = Liberzon Exercise 4.11 3.5. = Liberzon Exercise 4.12 3.6. = Liberzon Exercise 4.15 3.7. = Liberzon Exercise 4.

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise3.pdf - 2025-07-25

Session 5 Reading assignment Liberzon chapter 5. Exercises 5.1. = Liberzon Exercise 5.2 5.2. = Liberzon Exercise 5.3 5.3. = Liberzon Exercise 5.4 5.4. = Liberzon Exercise 5.5 5.5. = Liberzon Exercise 5.6 5.6. = Linerzon Exercise 5.7 1

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise5.pdf - 2025-07-25

Optimal Control 2018 Kaoru Yamamoto Optimal Control 2018 L1: Functional minimization, Calculus of variations (CV) problem L2: Constrained CV problems, From CV to optimal control L3: Maximum principle, Existence of optimal control L4: Maximum principle (proof) L5: Dynamic programming, Hamilton-Jacobi-Bellman equation L6: Linear quadratic regulator L7: Numerical methods for optimal control problems

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/lecture2eight.pdf - 2025-07-25

  Start of video. If t<1s, previous video. Start of slide. If t<1s, previous slide. Skip 15s back. Auto forward to next video on finish. Play. Pause. Toggle speedup (if possible). Skip 15s ahead. Next slide. Next video. Use full browser width. Exit use full browser width. Toggle 16:9 and 4:3 aspect ratio. Toggle 16:9 and 4:3 aspect ratio. Created by Pontus Giselsson

https://www.control.lth.se/fileadmin/control/Education/EngineeringProgram/FRTN50/VideoPlatform/VideoLecturePlatform.html - 2025-07-25

QPgen QPgen Home Examples Installation Documentation Licence Authors Citing QPgen What it does QPgen is a MATLAB toolbox that generates C code that solve convex parametric problems of the form: minimize \(\tfrac{1}{2}x^THx+g^Tx+h(Cx)\) subject to \(Ax=b\), where: \(x\in\mathbf{R}^n\) is the variable to be decided \(H\in\mathbf{R}^{n\times n}\) is a positive semi definite real data matrix \(C\in\ma

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/index.html - 2025-07-25

PIC-LU | Department of Automatic Control Faculty of Engineering, LTH Search Department of Automatic Control LTH, Faculty of Engineering Education Research External Engagement Personnel Publications About, Contact Home  >  Charlotta Johnsson  >  Research projects  >  Research Projects - Passed  >  PIC-LU Denna sida på svenska This page in English PIC-LU Page Manager: Mika Nishimura 2018-12-05 Sidöv

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PIC-opic | Department of Automatic Control Faculty of Engineering, LTH Search Department of Automatic Control LTH, Faculty of Engineering Education Research External Engagement Personnel Publications About, Contact Home  >  Charlotta Johnsson  >  Research projects  >  Research Projects - Passed  >  PIC-opic Denna sida på svenska This page in English PIC-opic PIC-opic: Process Industry Centre - Opt

https://www.control.lth.se/personnel-old/charlotta-johnsson/research-projects/research-projects-passed/pic-opic/ - 2025-07-25

PIC | Department of Automatic Control Faculty of Engineering, LTH Search Department of Automatic Control LTH, Faculty of Engineering Education Research External Engagement Personnel Publications About, Contact Home  >  Charlotta Johnsson  >  Research projects  >  Research Projects - Passed  >  PIC Denna sida på svenska This page in English PIC Page Manager: Mika Nishimura 2018-12-05 Sidöversikt De

https://www.control.lth.se/personnel-old/charlotta-johnsson/research-projects/research-projects-passed/pic/ - 2025-07-25

Publications 1970 – 1979 | Department of Automatic Control Faculty of Engineering, LTH Search Department of Automatic Control LTH, Faculty of Engineering Education Research External Engagement Personnel Publications About, Contact Home  >  Karl Johan Åström  >  Publications 1970 – 1979 Denna sida på svenska This page in English Publications 1970 – 1979 Books Karl Johan Åström: Introduction to stoc

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Publications 1980 – 1989 | Department of Automatic Control Faculty of Engineering, LTH Search Department of Automatic Control LTH, Faculty of Engineering Education Research External Engagement Personnel Publications About, Contact Home  >  Karl Johan Åström  >  Publications 1980 – 1989 Denna sida på svenska This page in English Publications 1980 – 1989 Books Karl Johan Åström, Björn Wittenmark: Ad

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Publications 1990 – 1999 | Department of Automatic Control Faculty of Engineering, LTH Search Department of Automatic Control LTH, Faculty of Engineering Education Research External Engagement Personnel Publications About, Contact Home  >  Karl Johan Åström  >  Publications 1990 – 1999 Denna sida på svenska This page in English Publications 1990 – 1999 Books Karl Johan Åström, Björn Wittenmark: Co

https://www.control.lth.se/personnel-old/karl-johan-aastroem/publications-1990-1999/ - 2025-07-25