Search result: Catalogue data in Autumn Semester 2024
Electrical Engineering and Information Technology Master  | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 Master Studies (Programme Regulations 2018) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Track: Systems and Control The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Systems and Control", see https://www.ee.ethz.ch/studies/main-master/areas-of-specialisation.html. The individual study plan is subject to the tutor's approval. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Specialisation Courses These specialisation courses are particularly recommended for the area of "Systems and Control", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the Master's Programme. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Number | Title | Type | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 227-0102-00L | Discrete Event Systems | W | 6 credits | 4G | L. Vanbever, L. Josipovic, B. Keller, R. Wattenhofer | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Introduction to discrete event systems. We start out by studying popular models of discrete event systems. Then we analyze discrete event systems from an average-case and from a worst-case perspective, and study verification. Topics include: Automata and Languages, Specification Models, Stochastic Discrete Event Systems, Worst-Case Event Systems, Verification, Petri Nets. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Over the past few decades the rapid evolution of computing, communication, and information technologies has brought about the proliferation of new dynamic systems. A significant part of activity in these systems is governed by operational rules designed by humans. The dynamics of these systems are characterized by asynchronous occurrences of discrete events, some controlled (e.g. hitting a keyboard key, sending a message), some not (e.g. spontaneous failure, packet loss). The mathematical arsenal centered around differential equations that has been employed in systems engineering to model and study processes governed by the laws of nature is often inadequate or inappropriate for discrete event systems. The challenge is to develop new modeling frameworks, analysis techniques, design tools, testing methods, and optimization processes for this new generation of systems. In this lecture we give an introduction to discrete event systems. We start out the course by exploring the limits of what is computable and what is not. In doing so, we will consider three distinct models of computation which are often used to model discrete event systems: finite automata, push-down automata and Turing machines (ranked in terms of expressiveness power). In the second part of the course we analyze discrete event systems. We first examine discrete event systems from an average-case perspective: we model discrete events as stochastic processes, and then apply continuous time markov chains and queueing theory for an understanding of the typical behavior of a system. Then we analyze discrete event systems from a worst-case perspective using the theory of online algorithms and adversarial queueing. In the last part of the course we introduce methods that allow to formally verify certain properties of Finite Automata and Petri Nets. These are some typical analysis questions we will look at: Do two given systems behave the same? Does a given system behave as intended? Does the system eventually enter a dangerous state? | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | 1. Regular Languages 2. Non-Regular Languages 3. Markov Chains 4. Stochastic Discrete Event Systems 5. Worst-Case Event Systems 6. Verification of Finite Automata 7. Petri Nets | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Available at https://disco.ethz.ch/courses/des/ | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | [bertsekas] Data Networks Dimitri Bersekas, Robert Gallager Prentice Hall, 1991, ISBN: 0132009161 [borodin] Online Computation and Competitive Analysis Allan Borodin, Ran El-Yaniv. Cambridge University Press, 1998 [burch] Symbolic Model Checking J. R. Burch, E. M. Clarke, K. L. McMillan, D. L. Dill, and L. J. Hwang Inf. Comput. 98, 2 (June 1992), pp. 142-170 [boudec] Network Calculus J.-Y. Le Boudec, P. Thiran Springer, 2001 [cassandras] Introduction to Discrete Event Systems Christos Cassandras, Stéphane Lafortune. Kluwer Academic Publishers, 1999, ISBN 0-7923-8609-4 [fiat] Online Algorithms: The State of the Art A. Fiat and G. Woeginger [hochbaum] Approximation Algorithms for NP-hard Problems (Chapter 13 by S. Irani, A. Karlin) D. Hochbaum [murata] Petri Nets: Properties, Analysis and Applications Tadao Murata Proceedings of the IEEE, vol. 99, issue 4, April 1989. pp. 541-580 [schickinger] Diskrete Strukturen (Band 2: Wahrscheinlichkeitstheorie und Statistik) T. Schickinger, A. Steger Springer, Berlin, 2001 [sipser] Introduction to the Theory of Computation Michael Sipser. PWS Publishing Company, 1996, ISBN 053494728X | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 227-0447-00L | Image Analysis and Computer Vision | W | 6 credits | 3V + 1U | E. Konukoglu, E. Erdil, F. Yu | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Light and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition. Deep learning and Convolutional Neural Networks. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Overview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | This course aims at offering a self-contained account of computer vision and its underlying concepts, including the recent use of deep learning. The first part starts with an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First the interaction of light with matter is considered. The most important hardware components such as cameras and illumination sources are also discussed. The course then turns to image discretization, necessary to process images by computer. The next part describes necessary pre-processing steps, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and 3D shape as two important examples. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed. A major part at the end is devoted to deep learning and AI-based approaches to image analysis. Its main focus is on object recognition, but also other examples of image processing using deep neural nets are given. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Course material Script, computer demonstrations, exercises and problem solutions | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Prerequisites: Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Python and Linux. The course language is English. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0526-00L | Power System Analysis | W | 6 credits | 4G | G. Hug, G. Valverde Mora | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | The goal of this course is understanding the stationary dependencies in electrical power systems. The course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power networks. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The goal of this course is understanding the stationary dependencies in electrical power systems and the application of analysis tools in normal but also in faulty state. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | The course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power grids. Approaches such as the Newton-Raphson algorithm applied to power flow equations, superposition technique for short-circuit analysis and symmetrical components are discussed as well as power flow computation techniques for distribution grids and state estimation. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lecture notes. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 227-0689-00L | System Identification | W | 4 credits | 2V + 1U | R. Smith | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Theory and techniques for the identification of dynamic models from experimentally obtained system input-output data. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | To provide a series of practical techniques for the development of dynamical models from experimental data, with the emphasis being on the development of models suitable for feedback control design purposes. To provide sufficient theory to enable the practitioner to understand the trade-offs between model accuracy, data quality and data quantity. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Introduction to modeling: Black-box and grey-box models; Parametric and non-parametric models; ARX, ARMAX (etc.) models. Predictive, open-loop, black-box identification methods. Time and frequency domain methods. Subspace identification methods. Optimal experimental design, Cramer-Rao bounds, input signal design. Parametric identification methods. On-line and batch approaches. Closed-loop identification strategies. Trade-off between controller performance and information available for identification. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | "System Identification; Theory for the User" Lennart Ljung, Prentice Hall (2nd Ed), 1999. Additional papers will be available via the course Moodle. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Control systems (227-0216-00L) or equivalent. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 151-0532-00L | Nonlinear Dynamics and Chaos I | W | 4 credits | 4G | G. Haller | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Basic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | This course is intended for Masters and Ph.D. students in engineering sciences, physics and applied mathematics who are interested in the behavior of nonlinear dynamical systems. It offers an introduction to the qualitative study of nonlinear physical phenomena modeled by differential equations or discrete maps. We discuss applications in classical mechanics, electrical engineering, fluid mechanics, and biology. A more advanced Part II of this class is offered every other year. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | (1) Basic facts about nonlinear systems: Existence, uniqueness, and dependence on initial data. (2) Near equilibrium dynamics: Linear and Lyapunov stability (3) Bifurcations of equilibria: Center manifolds, normal forms, and elementary bifurcations (4) Nonlinear dynamical systems on the plane: Phase plane techniques, limit sets, and limit cycles. (5) Time-dependent dynamical systems: Floquet theory, Poincare maps, averaging methods, resonance | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Written and typed lecture notes are available in Moodle, as well as recorded lecture videos from an earlier year. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | - Prerequisites: Analysis, linear algebra and a basic course in differential equations. . | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 151-0563-01L | Dynamic Programming and Optimal Control | W | 4 credits | 2V + 1U | R. D'Andrea | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Introduction to Dynamic Programming and Optimal Control. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Covers the fundamental concepts of Dynamic Programming & Optimal Control. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Dynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Dynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Requirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 376-1219-00L | Rehabilitation Engineering II: Rehabilitation of Sensory and Vegetative Functions | W | 3 credits | 2V | R. Riener, O. Lambercy | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Rehabilitation Engng is the application of science and technology to ameliorate the handicaps of individuals with disabilities to reintegrate them into society.The goal is to present classical and new rehabilitation engineering principles applied to compensate or enhance motor, sensory, and cognitive deficits. Focus is on the restoration and treatment of the human sensory and vegetative system. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Provide knowledge on the anatomy and physiology of the human sensory system, related dysfunctions and pathologies, and how rehabilitation engineering can provide sensory restoration and substitution. This lecture is independent from Rehabilitation Engineering I. Thus, both lectures can be visited in arbitrary order. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Introduction, problem definition, overview Rehabilitation of visual function - Anatomy and physiology of the visual sense - Technical aids (glasses, sensor substitution) - Retina and cortex implants Rehabilitation of hearing function - Anatomy and physiology of the auditory sense - Hearing aids - Cochlea Implants Rehabilitation and use of kinesthetic and tactile function - Anatomy and physiology of the kinesthetic and tactile sense - Tactile/haptic displays for motion therapy (incl. electrical stimulation) - Role of displays in motor learning Rehabilitation of vestibular function - Anatomy and physiology of the vestibular sense - Rehabilitation strategies and devices (e.g. BrainPort) Rehabilitation of vegetative Functions - Cardiac Pacemaker - Phrenic stimulation, artificial breathing aids - Bladder stimulation, artificial sphincter Brain stimulation and recording - Deep brain stimulation for patients with Parkinson, epilepsy, depression - Brain-Computer Interfaces | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Introductory Books: An Introduction to Rehabilitation Engineering. R. A. Cooper, H. Ohnabe, D. A. Hobson (Eds.). Taylor & Francis, 2007. Principles of Neural Science. E. R. Kandel, J. H. Schwartz, T. M Jessell (Eds.). Mc Graw Hill, New York, 2000. Force and Touch Feedback for Virtual Reality. G. C. Burdea (Ed.). Wiley, New York, 1996 (available on NEBIS). Human Haptic Perception, Basics and Applications. M. Grunwald (Ed.). Birkhäuser, Basel, 2008. The Sense of Touch and Its Rendering, Springer Tracts in Advanced Robotics 45, A. Bicchi et al.(Eds). Springer-Verlag Berlin, 2008. Interaktive und autonome Systeme der Medizintechnik - Funktionswiederherstellung und Organersatz. Herausgeber: J. Werner, Oldenbourg Wissenschaftsverlag 2005. Neural prostheses - replacing motor function after desease or disability. Eds.: R. Stein, H. Peckham, D. Popovic. New York and Oxford: Oxford University Press. Advances in Rehabilitation Robotics - Human-Friendly Technologies on Movement Assistance and Restoration for People with Disabilities. Eds: Z.Z. Bien, D. Stefanov (Lecture Notes in Control and Information Science, No. 306). Springer Verlag Berlin 2004. Intelligent Systems and Technologies in Rehabilitation Engineering. Eds: H.N.L. Teodorescu, L.C. Jain (International Series on Computational Intelligence). CRC Press Boca Raton, 2001. Selected Journal Articles and Web Links: Abbas, J., Riener, R. (2001) Using mathematical models and advanced control systems techniques to enhance neuroprosthesis function. Neuromodulation 4, pp. 187-195. Bach-y-Rita P., Tyler M., and Kaczmarek K (2003). Seeing with the brain. International journal of human-computer-interaction, 15(2):285-295. Burdea, G., Popescu, V., Hentz, V., and Colbert, K. (2000): Virtual reality-based orthopedic telerehabilitation, IEEE Trans. Rehab. Eng., 8, pp. 430-432 Colombo, G., Jörg, M., Schreier, R., Dietz, V. (2000) Treadmill training of paraplegic patients using a robotic orthosis. Journal of Rehabilitation Research and Development, vol. 37, pp. 693-700. Hayward, V. (2008): A Brief Taxonomy of Tactile Illusions and Demonstrations That Can Be Done In a Hardware Store. Brain Research Bulletin, Vol 75, No 6, pp 742-752 Krebs, H.I., Hogan, N., Aisen, M.L., Volpe, B.T. (1998): Robot-aided neurorehabilitation, IEEE Trans. Rehab. Eng., 6, pp. 75-87 Levesque. V. (2005). Blindness, technology and haptics. Technical report, McGill University. Available at: http://www.cim.mcgill.ca/~vleves/docs/VL-CIM-TR-05.08.pdf Quintern, J. (1998) Application of functional electrical stimulation in paraplegic patients. NeuroRehabilitation 10, pp. 205-250. Riener, R., Nef, T., Colombo, G. (2005) Robot-aided neurorehabilitation for the upper extremities. Medical & Biological Engineering & Computing 43(1), pp. 2-10. Riener, R. (1999) Model-based development of neuroprostheses for paraplegic patients. Royal Philosophical Transactions: Biological Sciences 354, pp. 877-894. The vOICe. http://www.seeingwithsound.com. VideoTact, ForeThought Development, LLC. http://my.execpc.com/?dwysocki/videotac.html | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Target Group: Students of higher semesters and PhD students of - D-MAVT, D-ITET, D-INFK, D-HEST - Biomedical Engineering, Robotics, Systems and Control - Medical Faculty, University of Zurich Students of other departments, faculties, courses are also welcome This lecture is independent from Rehabilitation Engineering I. Thus, both lectures can be visited in arbitrary order. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 401-0647-00L | Introduction to Mathematical Optimization | W | 5 credits | 2V + 1U | D. Adjiashvili | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Introduction to basic techniques and problems in mathematical optimization, and their applications to a variety of problems in engineering. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The goal of the course is to obtain a good understanding of some of the most fundamental mathematical optimization techniques used to solve linear programs and basic combinatorial optimization problems. The students will also practice applying the learned models to problems in engineering. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Topics covered in this course include: - Linear programming (simplex method, duality theory, shadow prices, ...). - Basic combinatorial optimization problems (spanning trees, shortest paths, network flows, ...). - Modelling with mathematical optimization: applications of mathematical programming in engineering. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Information about relevant literature will be given in the lecture. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | This course is meant for students who did not already attend the course "Linear & Combinatorial Optimization", which is a more advance lecture covering similar topics. Compared to "Linear & Combinatorial Optimization", this course has a stronger focus on modeling and applications. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 401-3901-00L | Linear & Combinatorial Optimization | W | 10 credits | 4V + 2U | R. Zenklusen | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Mathematical treatment of optimization techniques for linear and combinatorial optimization problems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The goal of this course is to get a thorough understanding of various classical mathematical optimization techniques for linear and combinatorial optimization problems, with an emphasis on polyhedral approaches. In particular, we want students to develop a good understanding of some important problem classes in the field, of structural mathematical results linked to these problems, and of solution approaches based on such structural insights. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Key topics include: - Linear programming and polyhedra; - Flows and cuts; - Combinatorial optimization problems and polyhedral techniques; - Equivalence between optimization and separation. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | - Bernhard Korte, Jens Vygen: Combinatorial Optimization. 6th edition, Springer, 2018. - Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003. This work has 3 volumes. - Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993. - Alexander Schrijver: Theory of Linear and Integer Programming. John Wiley, 1986. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Solid background in linear algebra. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 636-0007-00L | Computational Systems Biology | W | 6 credits | 3V + 2U | J. Stelling | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Study of fundamental concepts, models and computational methods for the analysis of complex biological networks. Topics: Systems approaches in biology, biology and reaction network fundamentals, modeling and simulation approaches (topological, probabilistic, stoichiometric, qualitative, linear / nonlinear ODEs, stochastic), and systems analysis (complexity reduction, stability, identification). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The aim of this course is to provide an introductory overview of mathematical and computational methods for the modeling, simulation and analysis of biological networks. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Biology has witnessed an unprecedented increase in experimental data and, correspondingly, an increased need for computational methods to analyze this data. The explosion of sequenced genomes, and subsequently, of bioinformatics methods for the storage, analysis and comparison of genetic sequences provides a prominent example. Recently, however, an additional area of research, captured by the label "Systems Biology", focuses on how networks, which are more than the mere sum of their parts' properties, establish biological functions. This is essentially a task of reverse engineering. The aim of this course is to provide an introductory overview of corresponding computational methods for the modeling, simulation and analysis of biological networks. We will start with an introduction into the basic units, functions and design principles that are relevant for biology at the level of individual cells. Making extensive use of example systems, the course will then focus on methods and algorithms that allow for the investigation of biological networks with increasing detail. These include (i) graph theoretical approaches for revealing large-scale network organization, (ii) probabilistic (Bayesian) network representations, (iii) structural network analysis based on reaction stoichiometries, (iv) qualitative methods for dynamic modeling and simulation (Boolean and piece-wise linear approaches), (v) mechanistic modeling using ordinary differential equations (ODEs) and finally (vi) stochastic simulation methods. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | http://www.csb.ethz.ch/education/lectures.html | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | U. Alon, An introduction to systems biology. Chapman & Hall / CRC, 2006. Z. Szallasi et al. (eds.), System modeling in cellular biology. MIT Press, 2010. B. Ingalls, Mathematical modeling in systems biology: an introduction. MIT Press, 2013 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 401-3055-64L | Algebraic Methods in Combinatorics Does not take place this semester. | W | 5 credits | 2V + 1U | not available | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The students will get an overview of various algebraic methods for solving combinatorial problems. We expect them to understand the proof techniques and to use them autonomously on related problems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage and often relies on deep, well-developed tools. One of the main general techniques that played a crucial role in the development of Combinatorics was the application of algebraic methods. The most fruitful such tool is the dimension argument. Roughly speaking, the method can be described as follows. In order to bound the cardinality of of a discrete structure A one maps its elements to vectors in a linear space, and shows that the set A is mapped to linearly independent vectors. It then follows that the cardinality of A is bounded by the dimension of the corresponding linear space. This simple idea is surprisingly powerful and has many famous applications. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. The topics covered in the class will include (but are not limited to): Basic dimension arguments, Spaces of polynomials and tensor product methods, Eigenvalues of graphs and their application, the Combinatorial Nullstellensatz and the Chevalley-Warning theorem. Applications such as: Solution of Kakeya problem in finite fields, counterexample to Borsuk's conjecture, chromatic number of the unit distance graph of Euclidean space, explicit constructions of Ramsey graphs and many others. The course website can be found at https://moodle-app2.let.ethz.ch/course/view.php?id=15757 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lectures will be on the blackboard only, but there will be a set of typeset lecture notes which follow the class closely. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Students are expected to have a mathematical background and should be able to write rigorous proofs. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0694-00L | Game Theory and Control | W | 4 credits | 2V + 2U | S. Bolognani | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Game Theory is the study of strategic decision making, and was originally used to solve problems in economics. We study concepts and methods in non-cooperative game theory and show how these can be used to solve control design problems, emphasizing their possible use in control, robotics, and engineering applications. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Recognize control problems that can be formalized as noncooperative dynamic games, analyze these games to compute their Nash equilibria and to identify their most important properties. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Introduction to game theory, mathematical tools including convex optimization and dynamic programming, zero sum games in matrix and extensive form, pure and mixed strategies, nonzero sum games in normal and extensive form, numerical computation of mixed equilibrium strategies, Nash and Stackelberg equilibria, potential games, convex games, multi-stage games, behavioral strategies and informational properties for dynamic games, auction and VCG mechanisms, evolutionary games. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lecture notes will be made available via Moodle. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Basar, T. and Olsder, G. "Dynamic Noncooperative Game Theory," 2nd Edition, Society for Industrial and Applied Mathematics, 1998. Joao Hespanha "Noncooperative Game Theory: An introduction for engineers and computer scientists," Princeton University Press, 2017. Both books are available online and can be a useful reference during the course, but will not be strictly followed. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Control Systems I (or equivalent). Necessary methods and concepts from optimization will be covered in the course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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