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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Untitled 1 The Feedback Ampl ifier Karl Johan Åström Department of Automatic Control LTH Lund University The Feedback Ampl ifier K. J. Åström 1. Introduction 2. Black’s Invention 3. Bode 4. Nyquist 5. More Recent Developments 6. Summary Theme: Pure feedback. Lectures 1940 1960 2000 1 Introduction 2 Governors | | | 3 Process Control | | | 4 Feedback Amplifiers | | | 5 Harry Nyquist | | | 6 Aerospac

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L08TheSecondWave.pdf The Second Wave K. J. Åström Department of Automatic Control LTH Lund University History of Control – The Second Wave 1.  Introduction 2.  Major Advances 3.  Computing 4.  Control Everywhere 5. Summary History of Control – The Second Wave Introduction !  Use of control in widely different areas unified into a single framework by 1960 !  Education mushrooming, more than 36 text

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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 - 2025-07-22

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 - 2025-07-22

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 - 2025-07-22

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

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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 - 2025-07-22

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 - 2025-07-22

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 - 2025-07-22

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 - 2025-07-22

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

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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 - 2025-07-22

A Course in Optimal Control and Optimal Transport Dongjun Wu dongjun.wu@control.lth.se August, 2023 i CONTENTS Contents 1 1 Dynamic Programming 5 1.1 Discrete time systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.1 Shortest path problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Optimal control on finite horizon .

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Exercise for Optimal control – Week 5 Choose one problem to solve. Exercise 1. Use tent method to derive the KKT condition (google it if you don’t know) for the nonlinear optimization problem: min f(x) subject to gi(x) ≤ 0, i = 1, · · · ,m hj(x) = 0, j = 1, · · · , l where f , gi, hj are continuously differentiable real-valued functions on Rn. Exercise 2. Find a variation of inputs uϵ near u∗ that

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex4.pdf - 2025-07-22

5 Lecture 5. Proof of the maximum principle 5.1 The tent method We continue with the static nonlinear optimization problem: min g0(x) subject to gi(x) ≤ 0, i = 1, · · · ,m (LM) in which {gi}mi=0 ∈ C1(Rn;R). Suppose that the problem is feasible, i.e., there exists an admissible x∗ which minimizes g0(x). Recall that we defined the following sets: Ωi = {x ∈ Rn : gi(x) ≤ 0}, i = 1, · · · ,m and for x1

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/lec5.pdf - 2025-07-22

Neurons and Neuroscience 1. Introduction 2. Neurobiology 3. Simple models of a single neuron 4. Systems with a few neurons 5. Silicon neurons 6. Event based control 7. Summary Introduction ◮ A major challenge ◮ Golgi staining 1885 ◮ Cajal 1911 Mapping of the neurons using Golgi staining ◮ McCulloch and Pitts 1943 ◮ Wiener 1948 Cybernetics - Control and Communication in the Animal and the Machine ◮

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/neuronseight.pdf - 2025-07-22