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LionSealWhite Lecture 6 Least squares problems Adjoint operators 1 / 32 LionSealWhite Review: Least Squares Solution to Linear Equations (I) Consider a system of linear equations Ax = b, A ∈ Rm×n, b ∈ Rm with m ≥ n and rank(A) = n (Tall A—more rows than columns, or more equations than unknowns). If b /∈ range(A) then the linear system is inconsistent, i.e., no solution exists. Find x that minimize
ACC 1990 Benchmark Example References ACC 1990, pp. 961-962, The problem ACC 1990, pp. 963-973, Several Solutions ACC 1991, pp. 1931-1932, Mats Liljas design and comments The problem is to design a controller for a scalar linear system consisting of two-mass spring system. There are 4 states.
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/acc90.html - 2025-07-11
ex02.dvi Exercise Session 2 1. Describe your results on Handin 1. 2. Sketch the Nichols curves for the following systems 1 s(s + 1)(s + 10) , 1 1 − s , exp (−s) 1 + s , 1 − s s(1 + s) , 1 s2 + 2ζs + 1 , (ζ small) For what feedback gains is the closed loop system stable? 3. Plot the root-loci for the following systems s s2 − 1 , (s + 1)2 s3 , 1 s(s2 + 2ζs + 1) , (ζ small) 4. Transform the systems i
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex02.pdf - 2025-07-11
Vertical Aerospace Dynamics, Maciejowski example 5.8 References Maciejowski pp. 244-258, Plots on LQGLTR designs Maciejowski pp. Appendix pp 405-406, Describes the model. Hung and MacFarlane, Multivariable Feedback: A quasi-classical Approach , Lecture Notes in Control and Information Sciences, vol 40, Springer-Verlag The problem is to control the vertical-plane dynamics of an aircraft. There are
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/mac58.html - 2025-07-11
Deep-Learning Study Circle: Reinforcement Learning Deep-Learning Study Circle: Reinforcement Learning Gabriel Ingesson 0/46 Reinforcement Learning The problem where an agent has to learn a policy (behavior) by taking actions in an environment, with the goal that the policy should maximize a cumulative reward. Different from supervised and unsupervised learning: No labeled training data. Reward sig
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/RL.pdf - 2025-07-11
Autoencoders Autoencoders Fredrik Bagge Carlson Fredrik Bagge Carlson, Lund University: Autoencoders Introduction General idea Auto: Greek auto- "self, one’s own" Encode: from en- "make, put in" + code: a system of words, letters, figures, or symbols used to represent others Find a useful encoding, h = f(x), of data x in an unsupervised manner. Trained using an encoder h = f(x) and a decoder x̂ =
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/autoencoders.pdf - 2025-07-11
Improving Imputation Using Stacked denoising Autoencoder Improving Imputation Using Stacked denoising Autoencoder Najmeh Abiri November 22, 2016 Computational Biology and Biological Physics Missing Data Pre-processing data Astronomy Outlier? Biology Missing Data? 1 Missing data in Biology Molecular Patterns of Life 2 Missing data in Biology Generate detailed DNA/protein molecular fingerprints and
Untitled 1 Governor s and Stabi li ty Theory Karl Johan Åström Department of Automatic Control LTH Lund University Governor s and Stabi li ty Theory 1. Introduction 2. Maxwell and Routh 3. Vyshnegradskii, Stodola and Hurwitz 4. The Routh-Hurwitz Theorem 5. Lyapunov 6. More recent results 7. Summary Theme: Controlling the speed of mechanical machines and encountering instability. Lectures 1940 1960
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/L02Governorseight.pdf - 2025-07-11
Untitled 1 Ships and Aerospa ce Karl Johan Åström Department of Automatic Control LTH Lund University Ships and Aerospa ce K. J. Åström 1. Introduction 2. Ships 3. Early Autopilots for Aircrafts 4. German Autopilots 5. Missiles 6. Later Developments 7. Summary Theme: Gyroscopes, powerful actuators and mission critical systems. Lectures 1940 1960 2000 1 Introduction 2 Governors | | | 3 Process Cont
Untitled 1 Automatic Cont rol in Sweden Karl Johan Åström Department of Automatic Control, LTH Lund University Lectures 1940 1960 2000 1 Introduction 2 Governors | | | 3 Process Control | | | 4 Feedback Amplifiers | | | 5 Harry Nyquist | | | 6 Aerospace | | | 7 Automatic Control Emerges ← | | 8 The Second Phase ← ← | 9 Automatic Control in Sweden | | | 10 Automatic Control in Lund | | 11 The Futur
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/L09Swedeneight.pdf - 2025-07-11
L4: Hybrid systems and dynamic programming • Hybrid Systems ○ Piecewise Linear Systems ○ Piecewise Quadratic Lyapunov Functions ○ Value Iteration ○ Policy Iteration ○ Jump Linear Systems Literature: Piecewise Quadratic: Johansson/Rantzer, IEEE TAC, 43:4 (1998) Networked Control Example: Nilsson/B/W, Automatica 34:1 (1998) Value and policy iteration: web.mit.edu/dimitrib/www/Det_Opt_Control_Lewis_V
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec04_2017eight.pdf - 2025-07-11
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
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex2-sol.pdf - 2025-07-11
Discrete Systems Karl-Erik Årzén Material • The material comes from • PhD course “Discrete Event Systems”, 1998 • PhD course “Discrete & Hybrid Systems”, 2004 • Lecture on Discrete Event Systems from the Market-Driven Systems course • Lecture on Discrete Event Systems from Real-Time Systems Course • Disclaimer: • A lot of material comes from old pdf slides for which I do not have the source any mo
Deep RL Assignment 1: Imitation Learning Fall 2019 due September 16th, 11:59 pm The goal of this assignment is to experiment with imitation learning, including direct behavior cloning and the DAgger algorithm. In lieu of a human demonstrator, demonstrations will be provided via an expert policy that we have trained for you. Your goals will be to set up behavior cloning and DAgger, and compare thei
FRT090projektkurs.dvi REGLERTEKNIK LTH KURSINFORMATION PROJEKT I REGLERTEKNIK FRT090 Modellbaserad reglerdesign I ett industriellt reglerprojekt tar ofta modelle- ringsarbete en stor del av tiden. Det gäller också att beskriva de prestandabegränsingar som ges av dynamik i givare och ställdon och av mätbrus och styrsignalmättning. Kursprojekten genomförs före- trädesvis på verkliga modellprocesser
FRTN10flervar.dvi REGLERTEKNIK LTH KURSINFORMATION FLERVARIABEL REGLERING FRTN10 Design av reglersystem Hur reglerar man en kemisk process, spårföljning- en i en DVD-spelare eller bränsleinsprutningen i en bil? Systemen är mycket olika, men har ändå många gemensamma drag. Ett sådant drag är att komplexa samband ökar behovet av systematiska verktyg för modellering och optimering. För att kla- ra de
manual.dvi MPCtools 1.0 — Reference Manual Johan Åkesson Department of Automatic Control Lund Institute of Technology January 2006 Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Model Predictive Control – Background . . . . . . . . . . . . . 6 4. Linear Model Predictive Contr
https://www.control.lth.se/fileadmin/control/Research/MPCtools/MPCtools-1.0-manual.pdf - 2025-07-11
Generate code for lasso problem QPgen Home Examples Installation Documentation Licence Authors Citing Generate code for lasso problem % set problem dimensions q = 2000; n = 10000; % generate sparse data matrix F = sprandn(q,n,10/n); % regenerate until all columns are non zero while not(isempty(find(sum(F,2) == 0))) F = sprandn(q,n,10/n); end % store data in QP struct QP.H = F'*F; QP.G = F'; QP.C =
https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/gen_lasso.html - 2025-07-11
Licence QPgen Home Examples Installation Documentation Licence Authors Citing Licence QPgen and its generated code is licenced under the GNU Affero GPL v3 licence. By using QPgen and/or its generated code, you agree to the terms in the licence. If this licence is not suitable for your purposes, please contact the authors for a different licence agreement. Page generated 2015-12-09 10:07:10 CET, by
https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/licence.html - 2025-07-11
