Suchergebnis: Katalogdaten im Frühjahrssemester 2018

Mathematik Master Information
Anwendungsgebiet
Nur für das Master-Diplom in Angewandter Mathematik erforderlich und anrechenbar.
In der Kategorie Anwendungsgebiet für den Master in Angewandter Mathematik muss eines der zur Auswahl stehenden Anwendungsgebiete gewählt werden. Im gewählten Anwendungsgebiet müssen mindestens 8 KP erworben werden.
Control and Automation
NummerTitelTypECTSUmfangDozierende
151-0660-00LModel Predictive Control Information W4 KP2V + 1UM. Zeilinger
KurzbeschreibungModel predictive control is a flexible paradigm that defines the control law as an optimization problem, enabling the specification of time-domain objectives, high performance control of complex multivariable systems and the ability to explicitly enforce constraints on system behavior. This course provides an introduction to the theory and practice of MPC and covers advanced topics.
LernzielDesign and implement Model Predictive Controllers (MPC) for various system classes to provide high performance controllers with desired properties (stability, tracking, robustness,..) for constrained systems.
Inhalt- Review of required optimal control theory
- Basics on optimization
- Receding-horizon control (MPC) for constrained linear systems
- Theoretical properties of MPC: Constraint satisfaction and stability
- Computation: Explicit and online MPC
- Practical issues: Tracking and offset-free control of constrained systems, soft constraints
- Robust MPC: Robust constraint satisfaction
- Nonlinear MPC: Theory and computation
- Hybrid MPC: Modeling hybrid systems and logic, mixed-integer optimization
- Simulation-based project providing practical experience with MPC
SkriptScript / lecture notes will be provided.
Voraussetzungen / BesonderesOne semester course on automatic control, Matlab, linear algebra.
Courses on signals and systems and system modeling are recommended. Important concepts to start the course: State-space modeling, basic concepts of stability, linear quadratic regulation / unconstrained optimal control.

Expected student activities: Participation in lectures, exercises and course project; homework (~2hrs/week).
227-0207-00LNonlinear Systems and Control Information
Voraussetzung: Control Systems (227-0103-00L)
W6 KP4GE. Gallestey Alvarez, P. F. Al Hokayem
KurzbeschreibungIntroduce students to the area of nonlinear systems and their control. Familiarize them with tools for modelling and analysis of nonlinear systems. Provide an overview of the various nonlinear controller design methods.
LernzielOn completion of the course, students understand the difference between linear and nonlinear systems, know the the mathematical techniques for modeling and analysing these systems, and have learnt various methods for designing controllers for these systems.
Course puts the student in the position to deploy nonlinear control techniques in real applications. Theory and exercises are combined for better understanding of virtues and drawbacks in the different methods.
InhaltVirtually all practical control problems are of nonlinear nature. In some cases the application of linear control methods will lead to satisfying controller performance. In many other cases however, only application of nonlinear analysis and synthesis methods will guarantee achievement of the desired objectives. During the past decades a number of mature nonlinear controller design methods have been developed and have proven themselves in applications. After an introduction of the basic methods for modelling and analysing nonlinear systems, these methods will be introduced together with a critical discussion of their pros and cons, and the students will be familiarized with the basic concepts of nonlinear control theory.

This course is designed as an introduction to the nonlinear control field and thus no prior knowledge of this area is required. The course builds, however, on a good knowledge of the basic concepts of linear control.
SkriptAn english manuscript will be made available on the course homepage during the course.
LiteraturH.K. Khalil: Nonlinear Systems, Prentice Hall, 2001.
Voraussetzungen / BesonderesPrerequisites: Linear Control Systems, or equivalent.
227-0224-00LStochastic Systems Information W4 KP2V + 1UF. Herzog
KurzbeschreibungProbability. Stochastic processes. Stochastic differential equations. Ito. Kalman filters. St Stochastic optimal control. Applications in financial engineering.
LernzielStochastic dynamic systems. Optimal control and filtering of stochastic systems. Examples in technology and finance.
Inhalt- Stochastic processes
- Stochastic calculus (Ito)
- Stochastic differential equations
- Discrete time stochastic difference equations
- Stochastic processes AR, MA, ARMA, ARMAX, GARCH
- Kalman filter
- Stochastic optimal control
- Applications in finance and engineering
SkriptH. P. Geering et al., Stochastic Systems, Measurement and Control Laboratory, 2007 and handouts
151-0530-00LNonlinear Dynamics and Chaos II Information W4 KP4GG. Haller
KurzbeschreibungThe internal structure of chaos; Hamiltonian dynamical systems; Normally hyperbolic invariant manifolds; Geometric singular perturbation theory; Finite-time dynamical systems
LernzielThe course introduces the student to advanced, comtemporary concepts of nonlinear dynamical systems analysis.
InhaltI. The internal structure of chaos: symbolic dynamics, Bernoulli shift map, sub-shifts of finite type; chaos is numerical iterations.

II.Hamiltonian dynamical systems: conservation and recurrence, stability of fixed points, integrable systems, invariant tori, Liouville-Arnold-Jost Theorem, KAM theory.

III. Normally hyperbolic invariant manifolds: Crash course on differentiable manifolds, existence, persistence, and smoothness, applications.
IV. Geometric singular perturbation theory: slow manifolds and their stability, physical examples. V. Finite-time dynamical system; detecting Invariant manifolds and coherent structures in finite-time flows
SkriptStudents have to prepare their own lecture notes
LiteraturBooks will be recommended in class
Voraussetzungen / BesonderesNonlinear Dynamics I (151-0532-00) or equivalent
151-0566-00LRecursive Estimation Information W4 KP2V + 1UR. D'Andrea
KurzbeschreibungEstimation of the state of a dynamic system based on a model and observations in a computationally efficient way.
LernzielLearn the basic recursive estimation methods and their underlying principles.
InhaltIntroduction to state estimation; probability review; Bayes' theorem; Bayesian tracking; extracting estimates from probability distributions; Kalman filter; extended Kalman filter; particle filter; observer-based control and the separation principle.
SkriptLecture notes available on course website: Link
Voraussetzungen / BesonderesRequirements: Introductory probability theory and matrix-vector algebra.
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