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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Untitled 1 Automatic Cont rol in Lund Karl Johan Åström Department of Automatic Control, LTH Lund University Automatic Cont rol in Lund 1. Introduction 2. System Identification and Adaptive Control 3. Computer Aided Control Engineering 4. Relay Auto-tuning 5. Two Applications 6. Summary Theme: Building a New Department and Samples of Activities. Lectures 1940 1960 2000 1 Introduction 2 Governors |

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A Brief History of Event-Based Control Marcus T. Andrén Department of Automatic Control Lund University Marcus T. Andrén A Brief History of Event-Based Control Concept of Event-Based Example with impulse control [Åström & Bernhardsson, 1999] Periodic Sampling Event-Based Sampling Event-Based: Trigger sampling and actuation based on signal property, e.g |x(t )| >δ (Lebesgue sampling) A.k.a aperiodi

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History of Robotics History of Robotics Martin Karlsson Dept. Automatic Control, Lund University, Lund, Sweden November 25, 2016 Martin Karlsson November 30, 2016 1 / 14 Outline Introduction What is a robot? Early ideas The first robots Modern robots Major organizations Ubiquity of robots Future challenges Martin Karlsson November 30, 2016 2 / 14 Introduction The presenter performs research in rob

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MLGA.key Let's make the lab great! 2017-05-03 Vision • Small & cheap processes, which students can bring home (and perhaps use remotely over internet) • Pedagogic lab manuals, introducing control concepts and encouraging hacking • A PhD course, where we develop the lab together and learn new (control) engineering skills, as well as gain team work experience Let's focus on getting something simple

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/LabDevelopment/2017/intro.pdf - 2025-05-13

Robotics and Human Machine Interaction Lab Prof. Dr.-Ing. Ulrike Thomas Motion Planning - Trajectory calculation, PRM, RRT 1. Trajectory planning a) Lin and ptp are the two most common methods for trajectory planning, de- scribe them briefly. b) The simplest way to calculate a trajectory (ptp) is a 3rd order polynomial. Why shouldn’t this be applied? c) Calculate the progression of a two-axis mani

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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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Lecture 3. The maximum principle In the last lecture, we learned calculus of variation (CoV). The key idea of CoV for the minimization problem min u∈U J(u) can be summarized as follows. 1) Assume u∗ is a minimizer, and choose a one-parameter variation uϵ s.t. u0 = u∗ and uϵ ∈ U for ϵ small. 2) The function ϵ 7→ J(uϵ) has a minimizer at ϵ = 0. Thus it satisfies the first and second order necessary

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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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Exercise for Optimal control – Week 2 Choose one problem to solve. Exercise 1 (Insect control). Let w(t) and r(t) denote, respectively, the worker and reproductive population levels in a colony of insects, e.g. wasps. At any time t, 0 ≤ t ≤ T in the season the colony can devote a fraction u(t) of its effort to enlarging the worker force and the remaining fraction u(t) to producing reproductives. T

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex2.pdf - 2025-05-13

Exercise for Optimal control – Week 3 Choose 1.5 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 by him/herself. Exercise 1. Consider a harmonic oscillator ẍ + x =

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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 - 2025-05-13

Exercise for Optimal control – Week 6 Choose 1.5 problems to solve. Exercise 1. Derive the policy iteration scheme for the LQR problem min u(·) ∞∑ k=1 x⊤ k Qxk + u⊤ k Ruk with Q = Q⊤ ≥ 0 and R = R⊤ > 0 subject to: xk+1 = Axk +Buk. Assume the system is stabilizable. Start the iteration with a stabilizing policy. Run the policy iteration and value iteration on a computer for the following matrices:

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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

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7 Lecture 7. Dynamic programming II 7.1 Policy iteration In previous lecture, we studied dynamic programming for discrete time systems based on Bellman’s principle of optimality. We studied both finite horizon cost J = φ(xN ) + N−1∑ k=1 Lk(xk, uk), uk ∈ Uk and infinite horizon cost J = ∞∑ k=1 L(xk, uk), uk ∈ U(xk). The key ingredients we obtained were the Bellman equations. For finite horizon, J∗

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PowerPoint Presentation Optimal Control and Planning CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 3 is out! • Start early, this one will take a bit longer! Today’s Lecture 1. Introduction to model-based reinforcement learning 2. What if we know the dynamics? How can we make decisions? 3. Stochastic optimization methods 4. Monte Carlo tree

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PowerPoint Presentation Model-Based Reinforcement Learning CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 3 is out! Due next week • Start early, this one will take a bit longer! 1. Basics of model-based RL: learn a model, use model for control • Why does naïve approach not work? • The effect of distributional shift in model-based RL 2. Uncer

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PowerPoint Presentation Deep RL with Q-Functions CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 2 is due next Monday 2. Project proposal due 9/25, that’s today! • Remember to upload to both Gradescope and CMT (see Piazza post) Today’s Lecture 1. How we can make Q-learning work with deep networks 2. A generalized view of Q-learning algorithms

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PowerPoint Presentation Advanced Policy Gradients CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 2 due today (11:59 pm)! • Don’t be late! 2. Homework 3 comes out this week • Start early! Q-learning takes a while to run Today’s Lecture 1. Why does policy gradient work? 2. Policy gradient is a type of policy iteration 3. Policy gradient as a c

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/StudyCircleDeepReinforcementLearning/CS285-Lecture9-AdvancedPolicyGradients.pdf - 2025-05-13

CS285 Deep Reinforcement Learning HW4: Model-Based RL Due November 4th, 11:59 pm 1 Introduction The goal of this assignment is to get experience with model-based reinforcement learning. In general, model-based reinforcement learning consists of two main parts: learning a dynamics function to model observed state transitions, and then using predictions from that model in some way to decide what to

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