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)

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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 - 2025-02-07

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

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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 - 2025-02-07

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

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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 - 2025-02-07

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 - 2025-02-07

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 - 2025-02-07

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 - 2025-02-07

From motion capture to real-time virtual reality | Historia 7 feb From motion capture to real-time virtual reality 7 februari 2025 12:00 till 20:15 Workshop FULLY BOOKED- SIGN UP TO BE ON THE WAITING LIST! Join us for an exciting workshop hosted by Lund University Humanities Lab, inspired by CREA’s captivating performance of The Ghost of Canterville. This event is perfect for anyone curious about

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Spöket på Canterville | Historia 7 feb Spöket på Canterville 7 februari 2025 19:00 till 9 februari 2025 16:15 Teater Från rörelsedetektering till virtuell verklighet i realtid. Det började som en fråga från Riksteaters teckenspråksensemble CREA : - Kan ni hjälpa oss göra en animerad figur som talar teckenspråk i realtid på scenen i vår kommande föreställning om Spöket på Canterville? Det har gjort

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Upplysningens pietistiska paradox. Henric Schartau i internationell kontext - föreläsning av prof. em. Anders Jarlert | Historia 6 feb Upplysningens pietistiska paradox. Henric Schartau i internationell kontext - föreläsning av prof. em. Anders Jarlert 6 februari 2025 17:15 Föreläsning Med anledning av att det den 3 februari gått tvåhundra år sedan den mycket inflytelserike prästen och teologen He

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NEWS | Division of Physical Chemistry Faculty of Science Search Division of Physical Chemistry Department of Chemistry Department of Chemistry Kemicentrum Safety and security Contact About Education News and events Research People Instruments COMMONS Center Center for Scattering Methods Home  >  COMMONS Center  >  NEWS Denna sida på svenska This page in English NEWS Jan 30: Minisymposium om Biomol

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Research school | Division of Physical Chemistry Faculty of Science Search Division of Physical Chemistry Department of Chemistry Department of Chemistry Kemicentrum Safety and security Contact About Education News and events Research People Instruments COMMONS Center Center for Scattering Methods Home  >  COMMONS Center  >  Research school Denna sida på svenska This page in English Research schoo

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Diffusive wave spectrometer (DWS) | Division of Physical Chemistry Faculty of Science Search Division of Physical Chemistry Department of Chemistry Department of Chemistry Kemicentrum Safety and security Contact About Education News and events Research People Instruments COMMONS Center Center for Scattering Methods Home  >  Instruments  >  Scattering techniques  >  Diffusive wave spectrometer (DWS

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SAXS (pinhole system) | Division of Physical Chemistry Faculty of Science Search Division of Physical Chemistry Department of Chemistry Department of Chemistry Kemicentrum Safety and security Contact About Education News and events Research People Instruments COMMONS Center Center for Scattering Methods Home  >  Instruments  >  Scattering techniques  >  SAXS pinhole system Denna sida på svenska Th

https://www.physchem.lu.se/instruments/scattering-techniques/saxs-pinhole-system/news/instruments/microscopy/ - 2025-02-07

SAXS (pinhole system) | Division of Physical Chemistry Faculty of Science Search Division of Physical Chemistry Department of Chemistry Department of Chemistry Kemicentrum Safety and security Contact About Education News and events Research People Instruments COMMONS Center Center for Scattering Methods Home  >  Instruments  >  Scattering techniques  >  SAXS pinhole system Denna sida på svenska Th

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Control System Synthesis - Basics - PhD Class - Fall 2020 Control System Synthesis - Basics PHD CLASS - FALL 2020 Representation of feedback systems Block diagrams System description Feedback fundamentals Static analysis Design issues The Gang of Four Stability and Nyquist plots Performances and Bode plots About feedforward Conclusions 1 Introduction 2 Fundamentals: problem formulation System repr

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/Control_System_Synthesis_Basics.pdf - 2025-02-07