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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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

Exercise 1 1. Use MATLAB to find the generalized plant of the following diagram: Plant: G = [ 1 s , 1 s ] ∈ C1×2, controller: K = [ −1 −1 −1 1 ] , uncertainty: ∆ = [ ∆1 ∆2 ] ∈ C4×4 with ∆1,∆2 ∈ C2×2 Controller input: y = [ y1 y2 ] ∈ R2, controller ouput u ∈ R2. Controlled signal: z = [ z1 z2 ] ∈ R2 Exogenous signal: w = dr n  ∈ R3 The weighting functions Wr, Wrf , Wz1 , Wd, Wn are tunable real

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/RobustControl2025/ExercisePDF/Exercise1.pdf - 2026-04-24

Exercise 3 1. a) Let M = [ 0 A B 0 ] where A, B ∈ Cn×n are two constant square matrices. Compute the structured singular value µS(M) for S = {∆ : δI2n, δ ∈ C} S = { ∆ : ∆ ∈ C2n×2n } S = { ∆ = [ ∆1 0 0 ∆2 ] : ∆1,∆2 ∈ Cn×n } Hint : Use Schur’s formula for determinant. The results can be expressed in terms of ρ(AB), σ̄(A) and σ̄(B). b) Given a structured uncertainty S. Show that µS(M) = 1 min{σ̄(∆) |

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/RobustControl2025/ExercisePDF/Exercise3.pdf - 2026-04-24

I propose that for the exercise session the students solve the following from 'essentials of robust control' •Problem 16.5 •Problem 16.11 And also try and solve the loopshaping task in exercise 3 of the attached (the last page) using the H-infinity loopshaping method from the lecture. When solving the task rather than trying to find the w_c that minimises ||S||_\infty they should instead investiga

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/RobustControl2025/ExercisePDF/Exercise5.pdf - 2026-04-24

Robust Control Lecture 1 Dongjun Wu Course Information ~ 7 Lectures (Monday 13h15), ~ 7 exercises (Thursday 13h15) Textbooks: Essentials of Robust Control etc. Schedule and material: see course page Examination: Handins + Exam Exercises: fill in the google sheets before solving Handins are due before the exercise session, email to: dongjun.wu@control.lth.se with subject Robust control handin X Syl

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/RobustControl2025/SlidesPDF/Lec1.pdf - 2026-04-24

Robust Control Lecture 3 Dongjun Wu Uncertainty modeling Nyquist-Bode plots. e.g. for P̃ = (1+w∆)P , ∥∆∥∞ ≤ 1, choose w such that ∣∣∣∣ P̃ −P P ( jω) ∣∣∣∣≤ |w( jω)|, ∀ω. Parametric uncertainties. e.g. for ẍ + c m ẋ + k m x = F m nominal value error actual mass normalized error m m̄ ±10% m̄(1+0.1δm) |δm | ≤ 1 c c̄ ±20% c̄(1+0.2δc ) |δc | ≤ 1 k k̄ ±30% k̄(1+0.3δk ) |δk | ≤ 1 All can be put as wz ηv

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/RobustControl2025/SlidesPDF/Lec3.pdf - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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 - 2026-04-24

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

https://www.control.lth.se/personnel-old/charlotta-johnsson/research-projects/research-projects-passed/pic-lu/ - 2026-04-24