https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/M_C_History.pdf - 2025-03-18

governors.dvi ON GOVERNORS J.C. MAXWELL From the Proceedings of the Royal Society, No.100, 1868. A GOVERNOR is a part of a machine by means of which the velocity of the machine is kept nearly uniform, notwithstanding variations in the driving-power or the resistance. Most governors depend on the centrifugal force of a piece connected with a shaft of the machine. When the velocity increases, this f

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https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/ProfosOnStodola.pdf - 2025-03-18

History of Real Time Systems History of Real Time Systems Gautham Department of Automatic Control, Lund University 1/14 Gautham: History of Real Time Systems Overview Introduction 1940s 1950s 1960s RTOS A look at RTSS Cloud. The future? 2/14 Gautham: History of Real Time Systems Real Time Systems I Real Time Systems describes hardware and software systems subject to a ”real-time constraint”, for e

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1 Lecture 1: Introduction (Karl Johan) 2 Lecture 2: Calculus of variation (CoV) and the Maximum principle In this lecture, we are going to learn the maximum principle. The MP is a type of CoV, so we will first study the classical theory of CoV. Then we will try to move from the classical CoV theory to the optimal control setting, there we will immediately encounter some essential difficulties that

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4 Lecture 4. Misc topics on MP and the proof of the MP In the previous lecture, we studied the maximum principle. The main result is the following theorem. Theorem 1. Consider the system ẋ = f(x, u) with cost function J(u) = φ(x(tf )) + ∫ tf 0 L(x, u)dt and boundary constraint x(tf ) ∈ M ⊆ Rn Assume f , φ and L are C1 in x. Let (x∗(·), u∗(·)) correspond to the optimal solution to the minimiza- ti

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/Lecture4.pdf - 2025-03-18

Optimal Control Introduction Karl Johan Åström Department of Automatic Control LTH Lund University Optimal Control K. J. Åström 1. Introduction 2. Calculus of Variations 3. Optimal Control 4. Computations 5. Stochastic Optimal Control 6. Conclusions Theme: Subspecialities A Brief History Early beginning: Bernoulli, Newton, Euler, Lagrange The Golden Era 1930-39: Department of Mathematics at Univer

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Exercise for Optimal control – Week 1 Choose two problems to solve. Exercise 1 (Fundamental lemma of CoV). Let f be a real valued function defined on open interval (a, b) and f satisfies ∫ b a f(x)h(x)dx = 0 for all h ∈ Cc(a, b), i.e., h is continuous on (a, b) and its support, i.e., the closure of {x : h(x) ̸= 0} is contained in (a, b). 1) Show that f is identically zero if f is continuous. If f

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex1.pdf - 2025-03-18

Exercise for Optimal control – Week 2 Choose one problem 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 (Insect control). Let w(t) and r(t) denote

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Exercise for Optimal control – Week 3 Choose 1.5 problems to solve. Exercise 1. Consider a harmonic oscillator ẍ + x = u whose control is constrained in the interval [−1, 1]. Find an optimal controller u which drives the system at initial state (x(0), ẋ(0)) = (X1, X2) to the origin in minimal time. Draw the phase plot. Exercise 2. Consider a rocket, modeled as a particle of constant mass m movin

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex3.pdf - 2025-03-18

Exercise for Optimal control – Week 4 Choose one problem 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. Use tent method to derive the KKT conditi

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex4-sol.pdf - 2025-03-18

Exercise for Optimal control – Week 5 Choose 2 problems to solve. Exercise 1. A public company has in year k profits amounting to xk SEK. The management then distributes uk to the shareholders and invests xk − uk in the company itself. Each SEK invested in such way will increase the company profit by θ > 0 the following year so that xk+1 = xk + θ(xk − uk). Suppose x0 ≥ 0 and 0 ≤ uk ≤ xk so that xk

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex5.pdf - 2025-03-18

Exercise for Optimal control – Week 6 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. Derive the policy iteration scheme for t

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex6_sol.pdf - 2025-03-18

6 Lecture 6. Final step of the proof of MP and a start of DP 6.1 The proof of the maximum principle (finally!) In our previous lecture, we started proving the maximum principle for the Mayer problem ẋ = f(x, u) with cost J = φ(x(tf )) under the constraint u(t) ∈ U , x(tf ) ∈ M . The basic tool for the proof is the method of tent. To that end, we defined the following tents: Ω0 = {x1} ∪ {x : φ(x)

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/lec6.pdf - 2025-03-18

PII: S0005-1098(99)00171-5 Automatica 36 (2000) 363}378 Drum-boiler dynamicsq K.J. As stroK m!,*, R.D. Bell" !Department of Automatic Control, Lund Institute of Technology, Box 118, S-221 00 Lund, Sweden "Department of Computing, School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2109, Australia Received 2 October 1998; revised 7 March 1999; received i

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/Astrom-Bell.pdf - 2025-03-18

Compartment Models K. J. Åström 1. Introduction 2. Compartment Models 3. Flow Systems 4. Measurement of Volumes and Flows 5. Summary 6. References Introduction ◮ Early work by Teorell and Widmark on propagation of alcohol in the body 1920 ◮ Teorell coined the term compartment model around 1937 ◮ Extensive application in pharmacokinetics Dost 1953 Models required for FDA approval of new drugs Shepp

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/Compartmentseight.pdf - 2025-03-18

Fluid Dynamics Modeling K. J. Åstr{öm 1. Introduction 2. Review of Fluid Dynamics 3. Simple Water Tank 4. Simple Gas Tank 5. Tanks, Pipes and Turbines 6. Summary Historical Remarks ◮ Hydroelectric power ◮ Control of dams and turbines ◮ Founded in civil engineering A not so well recognized base of automatic control Evangelisti (an IFAC founder) in Italy Many others in civil engineering Vattenfalls

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/Fluidseight.pdf - 2025-03-18

Ships and Aerospace Karl Johan Åström Department of Automatic Control LTH Lund University Ships and Aerospace K. J. Åström 1. Introduction 2. A Little History 3. Sensing and actuation 4. Stability and Manoevrability 5. Autopilots 6. Dynamic Modeling Ships 7. Dynamic Modeling Aircrafts 8. Summary Ships and Aerospace ◮ Cutting edge technology ◮ Technology driver ◮ Driving forces: Emerging technologi

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A Modeling Methodology 1. Introduction 2. Representation of Models 3. Units 4. Schematic Diagrams 5. A Water Tank 6. Electrical Circuits 7. Summary A Modeling Methodology ◮ Purpose of modeling: understanding, control design, diagnostics, ... ◮ Cut a system into subsystems ◮ Write mass, momentum and energy balances for each subsystem ◮ Discretize partial differential equations ◮ Add constitutive eq

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/L3-Methodologyeight.pdf - 2025-03-18

Differential Algebraic Equations Contents: 1. Introduction 2. Differential Algebraic Equations 3. Linear DAE 4. The Notion of Index 5. Numerical Methods 6. Summary Goal: ◮ To develop a basic understanding of differential-algebraic equations Introduction ◮ Cut a system into subsystems ◮ Use object orientation to structure the system ◮ Write mass, momentum and energy balances for each subsystem ◮ As

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