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Session 1 Linear Control Systems. Examples. Linearization. Transition Matrix. Reading Assignment Rugh (1996 edition) chapters 1-4 and scan Chapter 20 until Example 20.7. The main new thing is to do linearization along a trajectory rather than at an equilibrium, and the definition and properties of the transition matrix Φ(t, τ). Exercise 1.1 = Rugh 1.9 Exercise 1.2 = Rugh 1.20 (spectral norm) Exerc
Session 3 Reachability and Controllability. Observability and Reconstructability. Controller and Observer Forms. Reading Assignment Rugh, Ch 9, 13, 14 (only Theorem 14.9) (for continuous-time systems) and Ch 25 (for discrete-time systems). Exercise 3.1 = Rugh 9.1. Exercise 3.2 = Rugh 9.2 Exercise 3.3 = Rugh 9.4 Exercise 3.4 = Rugh 9.5 Exercise 3.5 = Rugh 9.7 Exercise 3.6 a. Show that {A,B} is cont
Session 5 LTV stability. Quadratic Lyapunov functions. Reading Assignment Rugh Ch 6,7,12 (skip proofs of 7.8, 12.6 and 12.7),14 (pp240-247), and (22,23,24,28) Exercise 5.1 = Rugh 6.3 iii+iv Exercise 5.2 = Rugh 6.11 Exercise 5.3 = Rugh 7.3 Exercise 5.4 = Rugh 8.3 Exercise 5.5 = Rugh 7.6 Exercise 5.6 = Rugh 7.11 Exercise 5.7 = Rugh 7.20 Exercise 5.8 = Rugh 23.2 Hand in problems Exercise 5.9 = Rugh 8
Session 7 Polynomial Matrix Descriptions, Poles and Zeros of MIMO systems Reading Assignment Rugh, Ch. 16-17. Exercises Exercise 7.1 Make sure you can handle the Maple routines Matrix, Hermite- Form, SmithForm. Hint: ?MatrixPolynomialAlgebra[HermiteForm] gives some help text. Exercise 7.2 = Rugh 16.1 Exercise 7.3 = Rugh 16.2 Exercise 7.4 Determine the Smith form, i.e. the invariant polynomials, fo
LionSealWhite Linear Systems, 2019 - Lecture 1 Introduction Multivariable Time-varying Systems Transition Matrices Controllability and Observability Realization Theory Stability Theory Linear Feedback Multivariable input/output descriptions Some Bonus Material 1 / 21 LionSealWhite Lecture 1 State equations Linearization Examples Transition matrices Rugh, chapters 1-4 Main news: Linearization aroun
LionSealWhite Linear Systems, 2019 - Lecture 3 Controllability Observability Controller and Observer Forms Balanced Realizations Rugh, chapters 9,13, 14 (only pp 247-249) and (25) 1 / 43 LionSealWhite Controllability How should controllability be defined ? Some (not used) alternatives: By proper choice of control signal u any state x0 can be made an equilibrium any state trajectory x(t) can be obt
LionSealWhite Lecture 5 LTV stability concepts Quadratic Lyapunov functions Feedback, Well-posedness, Internal Stability Rugh Ch 6,7,12 (skip proofs of 12.6 and 12.7),14 (pp240-247) + (22,23,24,28) Zhou, Doyle, Glover pp 117-124 1 / 31 LionSealWhite Stability For LTI systems ẋ = Ax the stability concept was easy, we had the two concepts i) Stability: x(t) remains bounded ii) Asymptotic stability:
LionSealWhite Lecture 7 Theory for polynomial matrices Hermite and Smith normal forms Smith McMillan form Poles and Zeros Rugh Ch 16-17 (can skip proofs of 16.7,17.4,17.5,17.6) 1 / 36 LionSealWhite Polynomial matrix fraction descriptions There are two natural generalisation to the SISO description G(s) = n(s) d(s) Right polyomial matrix fraction description: G(s) = NR(s)DR(s)−1 { DR(s)X(s) = U(s)
Control System Synthesis - Introduction - PhD Class - Fall 2020 Control System Synthesis - Introduction PHD CLASS - FALL 2020 Brief history and motivations The big picture Class overview Content overview 1 Brief history and motivations 2 The big picture 3 Class overview Pauline Kergus - Karl Johan Åström Control System Synthesis 1st September 2020 2/27 Brief history and motivations The big picture
Control System Synthesis - Basics - PhD Class - Fall 2020 Control System Synthesis - Basics PHD CLASS - FALL 2020 Performance specifications Driving example: Cruise control Design trade-offs Expression in the frequency-domain Loopshaping Fundamental limitations System design considerations Sensitivity minimization Bode’s integral formula Gain crossover frequency inequality Internal stability Summa
Control System Synthesis - Model Predictive Control - PhD Class - Fall 2020 Control System Synthesis - Model Predictive Control PHD CLASS - FALL 2020 MPC design Basic idea How does MPC work? Design parameters Important issues Going further Robust MPC Stochastic MPC Running MPC faster and explicit MPC Adaptive and Gain-scheduled MPC Nonlinear MPC Data-driven MPC 1 Introduction 2 Fundamentals 3 Desi
DARC: Dynamic Adaptation of Real-time Control Systems DARC: Dynamic Adaptation of Realtime Control Systems Nils Vreman1, Claudio Mandrioli1 Control Systems Synthesis Project November 30, 2020 1{nils.vreman,claudio.mandrioli}@control.lth.se Dept. of Automatic Control Lund University { nils.vreman, claudio.mandrioli } @control.lth.se This story starts with... Vreman, Mandrioli DARC CSS Project 1
Neighborhood Heat Control Comfort Control and Peak Load Reduction Neighborhood Heat Control Comfort Control and Peak Load Reduction Felix Agner, Johan Lindberg November 30, 2020 Felix Agner, Johan Lindberg Neighborhood Heat Control November 30, 2020 1 / 13 Presentation Outline Problem: Control indoor temperature and peak electricity consumption in domestic buildings Problem formulation Results Dis
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/Felix-JohanL.pdf - 2025-11-21
Control System Synthesis - PhD Class Exercise session 1 24/09/2020 1 The X-29 aircraft The X-29 aircraft has an unusual configuration, designed to enhance its maneuverability. It has a right half-plane pole at approximately p = 6rad/s and a right half-plane zero at z = 26rad/s. The non-minimum phase factor then writes: Pnmp(s) = z − s z + s s+ p s− p . What are the fundamental limitations ? 1. App
Deep Learning Tubes for Tube MPC Deep Learning Tubes for Tube MPC Johan Gronqvist Introduction MPC Tubes Three Problems Deep Learning Summary Deep Learning Tubes for Tube MPC Johan Gronqvist 2020-11-30 Deep Learning Tubes for Tube MPC Johan Gronqvist Introduction MPC Tubes Three Problems Deep Learning Summary Overview Contents I MPC I Tubes I Problems I Deep Learning I Summary Reference I Based on
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/tubes-JohanG.pdf - 2025-11-21
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 - 2025-11-21
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
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/BoB-coursestart.pptx - 2025-11-21
Image deconvolution using Neural Networks Deconvolution Neural Network for Semantic Segmentation Deconvolution Networks Johan Brynolfsson Mathematical Statistics Centre for Mathematical Sciences Lund University December 6th 2016 1 / 27 Image deconvolution using Neural Networks Deconvolution Neural Network for Semantic Segmentation Deconvolution Neural Networks 2 / 27 Image deconvolution using Neur
Deep Learning - Study Circle Sequence Modeling: Recurrent and Recursive Nets Deep Learning - Study Circle Sequence Modeling: Recurrent and Recursive Nets Martin Karlsson Dept. Automatic Control, Lund University, Lund, Sweden October 26, 2016 Martin Karlsson RNN Structure Martin Karlsson Warm-up examples Recurrent neural network to generate new first names I also added two unstructured sequences. C
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/dl_rnn.pdf - 2025-11-21
Exercise in Convolutional Neural Networks for Classification * Choose a dataset, e g MNIST (0-1), MNIST (0-9), OCR (a-z) * Choose a framework * Choose a network topology * Train a convolutional neural network for classification * Think about a few or all of the following questions. Evaluate how well it performs. Try to run it on a few images, where you examine the values of a few different layers.
