Session 4 Hybrid systems Reading assignment Check the main results and examples of these papers. • Johansson/Rantzer, IEEE TAC, 43:4 (1998). • Chizeck/Willsky/Castanon, Int. J. on Control, 43:1 (1986) Exercise 4.1Consider two pendula[ ẋ1 ẋ2 ] = [ x2 1− x1 ] [ ẋ1 ẋ2 ] = [ x2 −1− x1 ] which are swinging around x1 = 1 and x1 = −1 respectively. a. Find a control law that brings the state to (0, 0)

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E4.pdf - 2025-08-10

Session 6 Nonlinear Controllability Reading assignment • Glad, Nonlinear Control Theory, Ch. 8 + Hörmander handout Exercises marked with a “*” are more difficult Exercise 6.1 Consider a car with N trailers. The front-wheels of the car can be controlled, and the car can drive forwards and backwards. Describe a manifold that can be used as state-space. Show that its dimension is N + 4. Exercise 6.2

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E6.pdf - 2025-08-10

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, backstepping, forwarding Exercise sessions: Solve 50% of prob

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec02_2017eight.pdf - 2025-08-10

L4: Hybrid systems and dynamic programming • Hybrid Systems ○ Piecewise Linear Systems ○ Piecewise Quadratic Lyapunov Functions ○ Value Iteration ○ Policy Iteration ○ Jump Linear Systems Literature: Piecewise Quadratic: Johansson/Rantzer, IEEE TAC, 43:4 (1998) Networked Control Example: Nilsson/B/W, Automatica 34:1 (1998) Value and policy iteration: web.mit.edu/dimitrib/www/Det_Opt_Control_Lewis_V

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec04_2017eight.pdf - 2025-08-10

Session 2 Reading assignment Liberzon chapters 2.5 – 3. Exercises 2.1. = Liberzon Exercise 2.9. Reading the discussion in Chapter 1.2.2 will be helpful. 2.2. = Liberzon Exercise 2.10 2.3. = Liberzon Exercise 2.14 2.4. = Liberzon Exercise 3.2 2.5. = Liberzon Exercise 3.5 2.6. = Liberzon Exercise 3.6 for k = 1 and n = 2. 2.7. = Liberzon Exercise 3.8 1

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise2.pdf - 2025-08-10

Session 4 Reading assignment Liberzon chapter 4.2. Exercises 4.1. = Liberzon Exercise 4.2 4.2. = Liberzon Exercise 4.3 4.3. = Liberzon Exercise 4.4 4.4. = Liberzon Exercise 4.5 4.5. = Liberzon Exercise 4.6 1

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise4.pdf - 2025-08-10

Session 6 Reading assignment Liberzon chapter 6. Exercises 6.1. = Liberzon Exercise 6.1 6.2. = Liberzon Exercise 6.2 6.3. = Liberzon Exercise 6.3 6.4. = Liberzon Exercise 6.4 6.5. = Liberzon Exercise 6.5 6.6. = Linerzon Exercise 6.6 1

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise6.pdf - 2025-08-10

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 L4: Maximum principle, Existence of optimal control L5: Dynamic programming, Hamilton-Jacobi-Bellman equation L6: Linear quadratic regulator L7: Numerical methods for optimal control problems Exercise

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/lecture1eight.pdf - 2025-08-10

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/lecture3eight.pdf - 2025-08-10

Optimal Control 2018 LionSealGrey Optimal Control 2018 Yury Orlov 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

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/lecture4.pdf - 2025-08-10

Discrete Systems Karl-Erik Årzén Material • The material comes from • PhD course “Discrete Event Systems”, 1998 • PhD course “Discrete & Hybrid Systems”, 2004 • Lecture on Discrete Event Systems from the Market-Driven Systems course • Lecture on Discrete Event Systems from Real-Time Systems Course • Disclaimer: • A lot of material comes from old pdf slides for which I do not have the source any mo

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/DiscreteSystems_x4.pdf - 2025-08-10

Generate code for lasso problem QPgen Home Examples Installation Documentation Licence Authors Citing Generate code for lasso problem % set problem dimensions q = 2000; n = 10000; % generate sparse data matrix F = sprandn(q,n,10/n); % regenerate until all columns are non zero while not(isempty(find(sum(F,2) == 0))) F = sprandn(q,n,10/n); end % store data in QP struct QP.H = F'*F; QP.G = F'; QP.C =

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/gen_lasso.html - 2025-08-10

Help file for run_code_gen_MPC QPgen Home Examples Installation Documentation Licence Authors Citing Help file for run_code_gen_MPC % ------------------------------------------------------- % [QP_reform,alg_data] = run_code_gen_MPC(MPC,opts) % Actions: % - reformulates MPC problem in struct MPC to QP problem in struct QP % - runs: run_code_gen(QP,opts) % -------------------------------------------

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/help_run_code_gen_MPC.html - 2025-08-10

Simulate aircraft MPC system QPgen Home Examples Installation Documentation Licence Authors Citing Simulate aircraft MPC system % nbr of time steps nbr_steps = 100; % create reference trajectory r_y1 = 0.25; r_y2 = 10; g1 = repmat(MPC.Q*[0;-r_y2;0;-r_y2],10,1); g1 = [g1;zeros(20,1)]; g2 = zeros(60,1); % time instance when reference is changed change_ref = 50; % initial condition X0 = zeros(4,1); %

https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/sim_aircraft_mpc.html - 2025-08-10

Pauline Kergus – Pauline Kergus Born November 25, 1992 H +33 (0)6 68 87 95 87 B pauline.kergus@control.lth.se Education 2016–2019 PhD in Automatic Control, ONERA, Toulouse, France. Supervision: Charles Poussot-Vassal and Fabrice Demourant. Title: "Data-driven model reference control in the frequency-domain: From model reference selection to controller validation." Thesis available at tel-3084374 2

https://www.control.lth.se/fileadmin/control/staff/PaulineKergus/CV_KERGUS.pdf - 2025-08-10

LISA2 | 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  >  LISA2 Denna sida på svenska This page in English LISA2 Future manufacturing system need to be more flex

https://www.control.lth.se/personnel-old/charlotta-johnsson/research-projects/research-projects-passed/lisa2/ - 2025-08-10

Curriculum Vitae | 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  >  Curriculum Vitae Denna sida på svenska This page in English Curriculum Vitae Curriculum Vitae Karl J. Åström was born in Östersund, Sweden on Augu

https://www.control.lth.se/personnel-old/karl-johan-aastroem/curriculum-vitae/ - 2025-08-10

Publications before 1970 | 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 before 1970 Denna sida på svenska This page in English Publications before 1970 Books Karl Johan Åström: Reglerteori . Almqvi

https://www.control.lth.se/personnel-old/karl-johan-aastroem/publications-before-1970/ - 2025-08-10

Misc | 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  >  Pontus Giselsson  >  Misc Denna sida på svenska This page in English Misc Software QPgen : A C code generator for quadratic optimization problems Pendulum Movies Time-optimal path

https://www.control.lth.se/personnel-old/pontus-giselsson/misc/ - 2025-08-10

Automotive Systems | 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  >  Rolf Johansson  >  Automotive Systems Denna sida på svenska This page in English Automotive Systems Research Publications of Prof. Rolf Johansson   Publications in Au

https://www.control.lth.se/personnel-old/rolf-johansson/automotive-systems/ - 2025-08-10