() Control System Design - LQG Bo Bernhardsson, K. J. Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson, K. J. Åström Control System Design - LQG Lecture - LQG Design Introduction The H2-norm Formula for the optimal LQG controller Software, Examples Properties of the LQ and LQG controller Design tricks, how to tune the knobs What do the “technical conditions” mean? How to

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/lqg.pdf - 2025-07-11

() Control System Design - LQG Part 2 Bo Bernhardsson, K. J. Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson, K. J. Åström Control System Design - LQG Part 2 Lecture - LQG Design What do the “technical conditions” mean? Introducing integral action, etc Loop Transfer Recovery (LTR) Examples For theory and more information, see PhD course on LQG Reading tip: Ch 5 in Macie

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/lqg2.pdf - 2025-07-11

Fundamental Limitations in MIMO Systems Fundamental Limitations in MIMO Systems M.T Andrén J. Berner Control System Synthesis, 2016 M.T Andrén, J. Berner Fundamental Limitations in MIMO Systems Control System Synthesis, 2016 1 / 21 Outline 1 Some concepts Singular values Pole and zero directions Sensitivity functions 2 Bode’s Integral Theorem 3 RHP Poles & Zeros Interpolation Constraints Specifi

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/mimolimitations_marcusJosefine.pdf - 2025-07-11

Mixed H/H2-synthesis and Youla-parametrization Mixed H∞/H2-synthesis and Youla-parametrization Olof Troeng 2016-05-25 Motivation (1/2) Control of electric field in accelerator cavity. Very simple process P(s) = 1 1 + sT e−sτ , Optimal controller? : P(I)(D), LQG, Smith Predictor, (MPC) Inspiration from (Garpinger 2009). Motivation (1/2) Control of electric field in accelerator cavity. Very simple p

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Discrete time mixed H2 / H control Discrete time mixed H2/H∞ control Yang Xu Department of Automatic Control Lund University May 25, 2016 Introduction Continuous time mixed H2/H∞ control problem: ◮ Zhou, Kemin, et al. ”Mixed H2 and H∞ performance objectives. I. Robust performance analysis.” Automatic Control, IEEE Transactions on 39.8 (1994): 1564-1574. ◮ Doyle, John, et al. ”Mixed H2 and H∞ perfo

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Lateral Dynamics of Aeroplane References Anderson, Moore, Optimal Control, Linear quadratic methods, 2nd ed , Prentice Hall 1990, Sec 6.2 Harvey and Stein, Quadratic Weights for Regulator Properties , IEEE AC 1978, pp 378-387 Friedland, Control System Design , pp. 40-47. Nice description of Aerodynamics for control The problem is to design a state feedback controller u = -Lx. There are two input s

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Monotone Operators and Fixed-Point Iterations Monotone Operators and Fixed-Point Iterations Pontus Giselsson 1 Today’s lecture • operators and their properties • monotone operators • Lipschitz continuous operators • averaged operators • cocoercive operators • relation between properties • monotone inclusion problems • special case: composite convex optimization • resolvents and reflected resolvent

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ConvexOptimization/2015/monotone_fp.pdf - 2025-07-11

IntroductionDeep Learning - Study Circle Deep Learning - Study Circle Bo Bernhardsson, Kalle Åström, Magnus Fontes, Fredrik Bagge Carlsson, Martin Karlsson Agenda Intro by me, Fontes FredrikB Kalle all Decide weekly meeting date Decide upon the first topics and responsible About the course Engineering perspective Hands on experience and intuition Use existing material Structure 1-2 persons respons

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Session 1 — Readings and exercises limit cycles, existence/uniqueness, Lyapunov, regions of attraction Reading assignment Khalil Chapter 1–3.1, (not 2.7), 4–4.6 Comments on chapter 2.6 The main topic is about existance of periodic orbits for planar systems and the most important subjects are the Poincaré-Bendixson Criterion and the Bendixson Criterion. Lemma 2.3 and Corollary 2.1 can also be used

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E1.pdf - 2025-07-11

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 - 2025-07-11

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 - 2025-07-11

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 - 2025-07-11

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 - 2025-07-11

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 - 2025-07-11

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 - 2025-07-11

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 - 2025-07-11

Exercise for Optimal control – Week 1 Choose two problems to solve. Disclaimer This is not a complete solution manual. For some of the exercises, we provide only partial answers, especially those involving numerical problems. If one is willing to use the solution manual, one should judge whether the solutions are correct or wrong him/herself. Exercise 1 (Fundamental lemma of CoV). Let f be a real

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PowerPoint Presentation Equation and Object-oriented Modeling Modeling Course – Automatic Control Hilding Elmqvist Mogram AB and Modelon AB In collaboration with: Martin Otter, Gerhard Hippman, Andrea Neumayr, Oskar Åström Assistants: Karl Johan Åström and Oskar Åström Content • Introduction • Part 1: Equation Oriented Modeling (Modia) • structural and symbolic algorithms • DAE index reduction • e

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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 - 2025-07-11