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 - 2025-05-13

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 - 2025-05-13

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 - 2025-05-13

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 - 2025-05-13

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 - 2025-05-13

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 - 2025-05-13

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

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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

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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 - 2025-05-13

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 - 2025-05-13

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 - 2025-05-13

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 - 2025-05-13

  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

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Citing QPgen Home Examples Installation Documentation Licence Authors Citing Citing Documentation or a paper describing QPgen is not finished yet. However, QPgen relies on the following publications. Therefore, if you use QPgen in an academic work, you could cite: P. Giselsson and S. Boyd , Diagonal Scaling in Douglas-Rachford Splitting and ADMM . In 53rd IEEE Conference on Decision and Control .

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/citing.html - 2025-05-13

Generate C code for aircraft MPC problem QPgen Home Examples Installation Documentation Licence Authors Citing Generate C code for aircraft MPC problem % specify dynamics (sampled with 50 ms sampling time) MPC.Adyn = [0.9993 -3.0083 -0.1131 -1.6081; -0.0000 0.9862 0.0478 0.0000; 0.0000 2.0833 1.0089 -0.0000; 0.0000 0.0526 0.0498 1.0000]; MPC.Bdyn = [-0.0804 -0.6347;-0.0291 -0.0143; -0.8679 -0.0917

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/gen_aircraft_mpc.html - 2025-05-13

Help file for run_code_gen QPgen Home Examples Installation Documentation Licence Authors Citing Help file for run_code_gen % ------------------------------------------------------- % [QP_reform,alg_data] = run_code_gen(QP,opts) % ------------------------------------------------------- % Generate C code to solve parametric QP:s of the form % % minimize 1/2 x'Hx + g'x + h(Cx) % subject to Ax = b %

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/help_run_code_gen.html - 2025-05-13

Releases QPgen Home Examples Installation Documentation Licence Authors Citing Releases QPgen v0.0.2 [2014-12-19] Added features Bug fixes Efficiency improvements QPgen v0.0.1 [2014-12-11] Page generated 2015-12-09 10:07:11 CET, by jemdoc+MathJax .

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/releases.html - 2025-05-13

Solve sequence of lasso problems QPgen Home Examples Installation Documentation Licence Authors Citing Solve sequence of lasso problems % store problem dimension n = 10000; m = 2000; % store nbr of iterations and execution times nbr_iters = []; exec_times = []; iter = 0; % run 50 different lasso problems for jj = 1:50 % aquire new data (returns random vector) g = acquire_data(m); % solve problem t

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/solve_lasso.html - 2025-05-13

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

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