Compared to classical engineering disciplines, cybernetics is still a young science. In general, cybernetics is the science of control and information of both machines and living beings. Cybernetics deals with the mastery of complex systems by using abstract and systematic approaches. On the one hand, it handles the development and application of methods analysing the system behaviour, on the other hand, it provides syntheses methods for the development of strategies for a controlled change in system behaviour. The interdisciplinary character of cybernetics yields out of the independence of these methods from the application in view, which are already widespread in the engineering field and are more and more extended into biology and economic sciences. Therefore, cybernetics can be divided according to the fields of application into single disciplines of engineering, biological, and economical cybernetics, respectively.

The course of study of Engineering Cybernetics was introduced at the Universität Stuttgart in 1971 and deals with theoretical fundamentals for the description of dynamic behaviour of engineering systems. Furthermore, it procures general methods for the automation of engineering processes in order to operate them more precisely, more reliably, faster, and more sensitive for environmental concerns. Consequently, the studies require a basic engineering interest and understanding of physical relations as well as an inclination to abstract mathematical reasoning.

The duration of studies in Engineering Cybernetics at the Universität Stuttgart is officially 9 semesters plus 12 weeks of internship. Currently, the average duration of studies (incl. internship) is less than 12 semesters.

The course of study of Engineering Cybernetics belongs to the Faculty of Mechanical Engineering. The following institutes are in charge of it:

• Institute A of Mechanics
  [Institut A für Mechanik (Mech A)]
  Director: Prof. Dr.-Ing. L. Gaul
  Prof. Dr.-Ing. A. Kistner
  Prof. Dr.-Ing. H. Sorg
  Phone: 0711-685-6277
  Fax: 0711/685-6282
  Address: Pfaffenwaldring 9, 70550 Stuttgart
  e-mail: {L.Gaul, A.Kistner, H.Sorg}@mecha.uni-stuttgart.de
  Web-page: www.mecha.uni-stuttgart.de
  
  
• Institute of System Dynamics and Control Engineering
  [Institut für Systemdynamik und Regelungstechnik (ISR)]
  Director: Prof. Dr.-Ing. Dr.h.c.mult. E.-D. Gilles
  Prof. Dr.-Ing. H. Wehlan
  Prof. Dr.-Ing. Dr.h.c. M. Zeitz
  Phone: 0711/685-6302, -6304, -6313
  Fax: 0711/685-6371
  Address: Pfaffenwaldring 9, 70550 Stuttgart
  e-mail: {seifert, wehlan, zeitz}@isr.uni-stuttgart.de
  Web-page: www.isr.uni-stuttgart.de
  
  
• Institute for Systems Theory in Engineering
  [Institut für Systemtheorie Technischer Prozesse (IST)]
  Director: Prof. Dr.-Ing. F. Allgöwer
  Phone: 0711/685-7733
  Fax: 0711/685-7735
  Adress: Pfaffenwaldring 9, 70550 Stuttgart
  e-mail: Allgower@ist.uni-stuttgart.de
  Web-page: www.ist.uni-stuttgart.de
  
  

The course of study of Engineering Cybernetics is composed of 2 parts: the Stage 1 and the Stage 2 Studies. The Stage 1 Studies end with the pre-diploma examination ("Vordiplom"). After having successfully passed the pre-diploma examination, students enter into the Stage 2 Studies which are then completed with the (final) diploma examination ("Diplom"). It is only possible to begin the studies in Engineering Cybernetics in the Winter Semester.

Further information can be obtained by:

C2. Course Catalogue/ Engineering Cybernetics

1. Explanation of Terms

Semester: recommended semester:

WS = Winter Semester

SS = Summer Semester

Type: L = Lecture (Vorlesung)

E = Exercise (Übung)

P = Practical work in laboratory (Praktikum)

Prerequisites: The description of the courses contains no further information about the required prerequisites. The courses are structured in a logical way such that the acquired knowledge in each semester is the basis for the next one.

Examination: certificate = course certificate (Schein)

oral = oral exam (mündliche Prüfung)

written = written exam (Klausur)

(More detailed descriptions regarding the presentation of course credits can be found in the examination regulations. Examinations in some courses of the Stage 1 Studies are combined in blocks.)

Credits: Number of credits

The credit system is based on 60 credits per academic year.

2. Stage 1 Studies

2.1 Structure of Stage 1 Studies

A broad basic knowledge in the classic engineering disciplines (Mechanical Engineering, Technical Thermodynamics, Electrical Engineering) is offered during the Stage 1 Studies, largely in accordance with the courses of study of Mechanical Engineering and Chemical Engineering. In our case, however, emphasis is put on Mathematics and Computer Science.

Table I shows the weekly hours of courses of the Stage 1 Studies during the first 4 semesters.

Table I:

As a rule, the Stage 1 Studies are completed with the pre-diploma examination ("Vordiplom") at the end of the fourth semester. The student is considered to have passed the pre-diploma examination as soon as he or she is registered at the examination office as having passed all the demanded exams.

2.2 Survey of Courses of Stage 1 Studies

Advanced Mathematics I

Höhere Mathematik I

Vector calculus, analytic geometry, matrices, determinants, systems of linear equations, complex numbers, sequences, power series, elementary functions, differentiation, mean-value theorem, Taylor’s formula.

Advanced Mathematics II

Höhere Mathematik II

Indefinite integrals, linear differential equations with constant coefficients, definite integrals, improper integrals, functions of two or more variables, partial differential equations, Taylor’s formula, extrema.

Advanced Mathematics III

Höhere Mathematik III

Volume integrals, surface integrals, vector analysis, theorems of Gauss and Stokes, some special differential equations, introduction to complex analysis.

Technical Mechanics I

Technische Mechanik I

Fundamentals of static: vector calculus, forces and moments, centre of gravity, necessary conditions of equilibrium, types of support, statically determinate systems. Statics of rigid beams: types of support, axial and shearing forces, bending moments. Fundamentals of elastic bodies: bars with axial loads, bending of beams without and with shearing forces, torsion of bars. Introduction to kinematics: trajectory, velocity and acceleration of a particle, infinitesimal and finite rotation of a rigid body, angular velocity and acceleration, kinematics of relative motions.

Technical Mechanics II

Technische Mechanik II

Fundamentals of dynamics: laws of momentum, law of angular momentum, kinetics of rigid bodies, tensor of inertia, kinetic energy, law of conservation of energy, principle of virtual work, Lagrange’s equations of the second kind. Mechanical oscillations: free and forced oscillations of a linear damped system with one degree of freedom, parametrically excited oscillations. Impact problems: assumptions of technical impact theory, central impacts, eccentric impacts, multiple impacts.

Technical Mechanics III

Technische Mechanik III

Fundamentals of elasticity: stress vector and stress tensor, displacements, strain tensor, state of stress and strain at a point, Hooke’s law, strain energy. Fundamentals of fluid dynamics: particle acceleration, stress tensor at a point, tensor of the rate of strain at a point, continuity equation, viscosity, Navier-Stokes’ equation.

Hydrostatics: fluids and gases in the gravitational field, pressure on walls, hydrostatic lift, stability of swimming bodies. Applied fluid dynamics: ideal fluids, stream lines, Bernoulli’s equation, incompressible flows, potential flows, Bernoulli’s equation for potential flows, Laplace’s equation, momentum equation, one-dimensional flows of viscous fluids, laminar and turbulent flow in pipes of circular cross-section, drag of solid bodies.

Technical Thermodynamics I

Technische Thermodynamik I

Task and basic concepts for thermodynamics. Thermodynamic equilibrium and the empirical temperature. The first law of thermodynamics: work, internal energy, heat, application of the first law to closed systems, application of the first law to open systems, the caloric equation of state and the specific heat capacities, simple processes with ideal gases. The second law of thermodynamics: the principle of irreversibility, entropy and the absolute temperature, general formulation of the second law, calculation of entropy, diagrams with entropy, special irreversible processes, application of the second law to transformation of energy, exergy (availability). Thermodynamic processes with gases: the Carnot cycle and the reversed Carnot cycle, the gas turbine, the Stirling cycle, the Otto- and the Diesel-engines, the air compressor.

Technical Thermodynamics II

Technische Thermodynamik II

Thermodynamic properties of pure substances: gases and vapours, diagrams, solidification and the solid state, equation of Clausius and Clapeyron. Thermodynamic processes with vapours: the Clausius-Rankine process and its reversal. Introduction to thermodynamics of mixtures: definitions, mixtures of ideal gases, mixtures of gases and vapours, h_1+X,X-diagram, applications (cooling tower, air condition processes, drying). Combustion: stoichiometry, gross calorific value, net calorific value, adiabatic flame temperature. Real gases: the Van der Waals equation, enthalpy as a function of p and T, entropy as a function of p and T, throttling of real gases, Thomson Joule effect. Thermodynamics of fluid flow: flow processes without work, adiabatic flow, Fanno line, velocity of sound, normal shock, flow in diffusers and nozzles.

Introduction to Electrical Engineering I

Einführung in die Elektrotechnik I

Direct current: definitions, electrical quantities, Ohm’s law, calculation of direct current circuits. Electric and magnetic fields: electric field, capacitor, magnetic field, forces and voltage generation in magnetic fields.

Alternating current: alternating current resistance, vector representation of alternating current quantities, representation of alternating-current quantities in the complex plane and calculation of alternating current circuits, oscillating circuits, compensation of reactive currents, three-phase current.

Introduction to Electrical Engineering II

Einführung in die Elektrotechnik II

Rotating electrical machines: direct current machines, alternating current machines, three-phase asynchronous machines, one-phase alternating current motors, variable speed motors. Electric drives: fundamental principles, start-up of electric drives. Static converters (power electronics): fundamentals, semiconductors, controlled converters and applications. Basic elements of electronics for communication engineering: electronic components: diodes, transistors, circuits, integrated circuits, analogue circuits, digital circuits, logic circuits.

(3): one common exam, all courses have to be attended

Metrology I

Meßtechnik I

Measuring chain, compensation method, errors of measuring components, calculation of measurement uncertainty, international system of units, measuring of mechanical quantities (length, force, time, speed of rotation, torque, power, pressure), measuring of thermal quantities (temperature, net calorific value, humidity), volumetric flow measurements, flow rate measurements, technical gas analysis, measuring of concentrations in fluids, measuring of electrical quantities (measurement devices, measurement principles), radiation measurements, mechanical vibrations, balancing, acoustic measurements.

Metrology II

Meßtechnik II

Fundamentals, measuring microscope, measuring telescope, angle and linear encoders, interferometric metrology, application of Moiré phenomena, triangulation sensors, testing of optical components.

Systems with Distributed Parameters

Systeme mit verteilten Parametern

Fundamentals of system theory, mathematical models of systems with lumped and with distributed parameters. Solution of differential equations: Fourier series, Fourier transformation and Laplace transformation. Modal transformation and Green’s function for boundary-value problems and partial differential equations. Separation of variables and method of characteristics for partial differential equations.

Probability Theory and Statistics

Wahrscheinlichkeitstheorie und Statistik

Random events, probabilities, conditional probabilities, discrete random variables, discrete probability distributions, geometric distribution, binomial distribution, Poisson distribution, continuous random variables, continuous probability distributions, uniform distribution, Gaussian distribution, law of large numbers, central limit theorem, linear regression, multi-linear regression, fundamental principles of statistics, point estimation, maximum likelihood method, confidence intervals, statistical tests.

Fundamentals of Machine Design I

Grundzüge der Maschinenkonstruktion I

Fundamentals, definitions, working methods, design tasks, basic functions and components. Defining requirements, specification list, evaluation and control of design. Engineering drawing: standards of drawing, free-hand drafting. Tolerances: manufacturing tolerances, systems of fits. Springs: types and characteristics, load-deformation diagrams, composed spring systems. Structural forces and reactions, strength of materials, strain: fundamentals of static, bearing reactions, virtual cut stress calculation. Form and strength, design of frames. Mechanical connections, rigid connections: welding, soldering and brazing, adhesive bonding.

Fundamentals of Machine Design II

Grundzüge der Maschinenkonstruktion II

Mechanical connections: frictional fits: bolted joints, clamping elements, interference fits. Positive fits: locking elements, circlips. Bearing of movable machine components: rolling and sliding shaft bearings, guiding elements. Static and dynamic sealing: container seals, hydraulic seals, sealing of rotating shafts. Driving elements and units, axles and shafts, shaft couplings. Fundamentals of gearing technology. Principles of optimum design on basis of optimum force transmission, producibility (‘productivity’ gemeint?), cost.

(4): one common exam, all courses have to be attended

Introduction to Computer Science I

Einführung in die Informatik I

Computer system principles; principles of high level programming; introduction to OBERON language: notation systems, data types, control structures, procedures, structured data types, pointer data types, object orientation.

Introduction to Computer Science II

Einführung in die Informatik II

Formal concepts: sets, relations, structures, graphs; algorithms for numeric applications, searching and storing; graph algorithms; structure and programme design principles; boolean algebra; logic circuits; sequential circuits; computer system components; computer organisation.

(5): one common exam, all courses have to be attended

Electrical Signal Processing

Elektrische Signalverarbeitung

Fundamentals: signals, spectra, power, levels, two-poles, networks, four-poles. Components: R, C, L, transformers, diodes, transistors, integrated circuits, operational amplifiers. Circuits: transistor circuits, applications of operational amplifiers, electronic switches, sample and hold. Filters: filter types, filter characteristics, filter approximations, frequency transformations, filter realisations. Modulation: AM, PM, FM. Signal acquisition. Power amplifiers.

Introduction to Cybernetics

[Einführung in die Kybernetik]

Lecture given by different teachers and institutes in order to introduce into the wide spread areas of cybernetics.

3. Stage 2 Studies

3.1 Structure of Stage 2 Studies

During the Stage 2 Studies, the subjects directly pertaining to the area of Engineering Cybernetics are taught. Due to their common characteristics concerning their dynamic behaviour, different engineering and non-engineering systems can be studied by the same mathematical methods.

Table II shows the weekly hours of courses from the 5th to the 8th semester.

Table II:

* = several courses are offered alternatively (see also next page)

Concerning the compulsory subject "Systems Theory", students can choose from the following list of courses:

• Adaptive and Learning Systems
• Control of Distributed Parameter Systems
• Control of Nonlinear Systems
• Discrete-time Control Systems
• Dynamic Filtering Methods
• Fuzzy Methods
• Identification of Dynamic Systems
• LMIs in Control (taught in English)
• Optimization Methods with Applications
• Research Methods in Control Engineering (taught in English)
• Robust Control (taught in English)

However, not all of these lectures are offered every year.

The list of courses of the compulsory subject "Advanced Computer Science" is updated every year. A summary of the lectures related to that subject can be found in the plans of study of Computer Science and Electrical Engineering.

The current details and deadlines can be seen on the corresponding noticeboards and are published in the respective course catalogue. The current lists of courses of the subjects "Systems Theory" and "Advanced Computer Science" are also on the corresponding noticeboard at the beginning of every semester.

In the practice related subject, the students should acquire a profund knowledge of one possible application area of Engineering Cybernetics. Since there is a diversified offer of application areas, the student has the possibility to choose in accordance with his or her interests. The practice related subject can be chosen from the following areas:

• Power Engineering
• Manufacturing Engineering
• Aerospace Engineering
• Non-technical Systems
• Process Engineering
• Traffic Engineering

A description of courses belonging to the practice related subject can be found in the corresponding plans of studies. Out of these courses, the students have to attend at least 12 SWS [SWS = Semesterwochenstunden (weekly hours per semester) of lectures and exercises.

The electives give the students the possibility to choose some of the examination subjects on their own. They have to attend a minimum of 6 SWS ["Semesterwochenstunden" (weekly hours per semester)] of lectures and exercises. Besides the courses from the field of Engineering Cybernetics, students can also choose other courses which represent a sensible complement to the course of study of Engineering Cybernetics.

In the Humanities which can be freely chosen by the students, a minimum of 2 SWS (lectures, exercises, seminars) is required.

During the Stage 2 Studies and in order to qualify for the diploma examination, the following requirements have to be met:

1) examinations in the following compulsory subjects:

• Dynamics of Mechanical Systems
• Dynamics of Chemical Processes
• Dynamics of Non-Engineering Systems
• Real-time Data Processing
• Advanced Computer Science
• Metrology III
• Automatic Control I
• Automatic Control II
• Stochastic Systems
• Simulation Engineering
• Control Technology I
• Systems Theory
• Thermodynamics of Mixtures, or (alt.) Dynamics of Discrete Event Systems

2) examinations in the practice related subject and the electives

3) project work ("Studienarbeit")

4) project work (diploma thesis) ("Diplomarbeit")

The project work ("Studienarbeit") should show that the student is able to apply the knowledge acquired to solve a proposed research task. As a rule, it is carried out under the supervision of a member of the academic staff who is in charge of teaching activities within the scope of Engineering Cybernetics. The project work should be concluded after 300 hours of work and within a maximum period of 6 months. An oral presentation of the project work is part of the examination.

The diploma thesis ("Diplomarbeit") should demonstrate that the student is capable of handling a research work on his or her own, to a large extent, applying scientific methods. As a rule, the diploma thesis is completed under the guidance of an university teacher who works in the field of Engineering Cybernetics.

3.2 Survey of Courses of Stage 2 Studies

Dynamics of Mechanical Systems

Dynamik Mechanischer Systeme

Kinematics of a rigid body in space: location and orientation, relative motion, holonomic and nonholonomic constraints, virtual displacement, degree of freedom. Fundamental dynamic equations: laws of momentum, law of angular momentum, d’Alembert’s principle, Lagrange’s equations of the first kind, kinetic energy. Dynamics of holonomic systems: equations of motion in minimal coordinates derived from d’Alembert’s principle, Lagrange’s equations of the second kind, Hamilton’s canonical equations. Dynamics of nonholonomic systems: equations of motion in minimal coordinates and minimal velocities derived from d’Alembert’s principle, equations of Gibbs-Appell. Linearized equations of motion: linearization, solution of linear systems, stability, free and forced vibrations of linear holonomic systems. Non-linear systems: analysis in the phase plane, stability.

Dynamics of Chemical Processes

Dynamik verfahrenstechnischer Systeme

Fundamental principles of thermodynamics of mixtures, introduction to irreversible thermodynamics, entropy and stability. Formulation of balance equations (energy balance, mass balance, momentum balance), single-phase systems (CSTR), two-phase systems (tray of a distillation column), systems with distributed parameters (catalytic reactor).

Dynamics of Non-Engineering Systems

Dynamik nichttechnischer Systeme

Applications of cybernetics in non-engineering areas, e.g. economics, biology, sociology, ecology, and medicine. Methods and techniques for the mathematical modelling of non-engineering systems. Analysis of nonlinear dynamic models.

Thermodynamics of Mixtures

Thermodynamik der Gemische

Definitions. The chemical potential and the first law: the chemical potential, Gibb’s fundamental equation of mixtures, properties of the chemical potential, the first law for systems with varying number of particles and the relation between entropy and heat. Equation of state, Euler’s equation and the equation of Gibbs-Duhem. Phase rule and phase diagrams. Thermodynamic potentials and quantities for describing the behaviour of mixtures: thermodynamic potentials, partial molar quantities, fugacity and fugacity coefficient, activity and activity coefficient, quantities of mixing and excess quantities, empirical correlations for the free excess enthalpy. Phase splitting and phase equilibrium.

Dynamics of Descrete Event Systems

Dynamik Ereignisdiskreter Systeme

Introduction and Overview, Automata, Formal Languages, Petri Nets, Behavioural Systems Theory, Supervisory Control Theory, Ramadge-Wonham Theory)

Automatic Control I

Regelungstechnik I

Basic concepts of automatic control engineering, formulation of differential equations for loop elements, time and frequency domain analysis of linear systems, Laplace transformation, transfer function, frequency response, Bode diagram, criteria for stability, Nyquist stability criterion, root locus technique, design of closed loop systems, non-linear control (describing function).

Automatic Control II

Regelungstechnik II

State space description for dynamic systems, non-linear controller design in the state space, Ljapunow’s criterion of stability, design of control strategies in the state space (pole placement, modal control, deadbeat controller), optimal control, Hamiltonian theory, Pontryagin’s maximum principle, state observers.

Control Technology I

Steuerungstechnik I

Historical review on automation technology. Classification of control systems with respect to different energy sources: mechanical/ hydraulic/ pneumatic/ electrical control systems. Systematic circuit design: combinatorial and sequential networks. Programmable logic controllers (PLC): mode of operation and hardware structure, programming methods, project engineering and commissioning.

Metrology III

Meßtechnik III

Supplement to the courses Metrology I + II. Topics: electro-chemical measuring principles, digital image processing, non-destructive material inspection.

Simulation Engineering

Simulationstechnik

Introduction to digital simulation of dynamic systems; iterative methods for solving algebraic equations; numerical integration methods for solving ordinary differential equations, differential and algebraic equations and boundary value problems; numerical solution of partial differential equations; simulation tools ISRSIM and ACSL; discrete-event systems; simulation tool SIMAN for discrete-event systems. The practical computer work gives students the chance to work on tasks studied in the exercises using personal computers and the simulation tools ISRSIM, MATLAB, ACSL, and SIMAN.

Real-time Data Processing

Echtzeit-Datenverarbeitung

Digital electronics: Boolean algebra, gates, integrated circuits, logic families, memories, coding, sequential logic, dependency notation, PLDs, areas of application of digital VLSI circuits. Process interfaces: D/A and A/D converters, application of converters in sampled data systems (quantization noise, sampling theorem, oversampling), frequency converters (VFC, FVC, PLL). Systems for real-time data processing: structural elements (LIFO, FIFO, interrupts, DMA, memory management, cache), interfaces (synchronization, error protection, example: IEC bus), system examples (digital signal processors, FFT, distributed process control systems). Software: processes, real-time languages, real-time operating systems, synchronization (busy waiting, semaphore, rendezvous, clock synchronization), communication (pipe, mailbox, shared memory), process and experiment automation, real-time language PEARL. Digital filters: overview, examples, Z-transform, bilinear transform, structure of FIR filters, design of FIR filters, filter order, interpolation, digital PID controller.

Stochastic Systems

Stochastische Systeme

Random signals, mean value function, correlation function, spectral density, white noise, form filters, stationary Gaussian random signals in linear systems, stochastic differential equations, covariance equation, Kalman-Bucy-Filter, optimal control of linear stochastic systems.

Adaptive and Learning Systems

Adaptive und lernende Systeme

Introduction. Decision processes; performance measures; explicit and implicit evaluation of performance measures. Model-reference adaptive systems; (strict) positivity; hyperstability. Self-tuning regulators; adaptive pole placement. Neural networks; neural controllers.

Control of Distributed Parameter Systems

Regelung verteilter Systeme

Technical and non-technical examples of plants with distributed parameters. Mathematical modelling, solution techniques for partial differential equations, input/ output behaviour, measurement and control devices. Structure of closed loop. Controller design. State-space description. Stability. Controllability. Observability. Optimal control. Observers. Simulation techniques for systems described by partial differential equations.

Control of Nonlinear Systems

Regelung nichtlinearer Systeme

Fundamentals of non-linear systems. Analysis and synthesis of time variant systems. Lie derivatives and non-linear systems. Stability and centre manifold theorem. Controllability. Observability. Non-linear normal forms. Asymptotic tracking. Exact input/ output and input/ state linearization. Decoupling, flat systems, non-linear observers. Sliding mode control.

Discrete-time Control Systems

Diskrete Regelsysteme

Discrete digital control (using process control computers), difference equations, sampling theorem, z-transform, state-space equations, online-identification, deterministic and stochastic signals, correlation analysis, parameter estimation, design of discrete control systems, optimal control algorithms.

Dynamic Filtering Methods

Dynamische Filterverfahren

Kalman-Bucy filters for time-continuous, time-discrete and continuous-discrete problems; factorization methods. Non-linear filtering methods; linearized and extended Kalman filters; point mass filters. Adaptive filtering methods; covariance matching method; correlation method. Multiple filtering methods.

Fuzzy Methods

Fuzzy Methoden

Introduction. Fuzzy sets; fuzzy numbers; fuzzy arithmetic; linguistic variables; fuzzy relations; fuzzy logic. Fuzzy controllers; design methods. Case studies.

Identification of Dynamic Systems

Identifikation dynamischer Systeme

Signals, systems and their description; identifiability. Parametric identification; (weighted) least squares methods; minimum variance estimation; instrumental-variable method; stochastic approximation methods; covariance methods. Non-parametric identification; correlation methods; fast Fourier transform. Combined parameter and state estimation; quasi-linearization method; extended Kalman filter.

LMIs in Control

This course will focus on system analysis and controller synthesis for linear (parameter varying) systems based on recent developments in the area of Linear Matrix Inequalitys (LMIs). LMIs allow to recast many control and analysis problems in a unifying way and to combine several control objectives (multi-objective design). Additionally, LMIS can be solved in a numerically efficient way. In the second part we deal with the problem of model reduction for large-scale linear system.

Optimization Methods with Applications

Optimierungsverfahren mit Anwendungen

Optimization of functions with and without constraints; Lagrange multipliers; Kuhn-Tucker conditions; numerical methods. Optimization of functionals; Euler differential equation; Ritz-Galerkin method. Dynamic optimization; Bellman’s principle of optimality; dynamic programming; Pontryagin’s maximum principle; Riccati controllers.

Research Methods in Control Engineering

The objective of this course is to present an introduction to the major considerations and tasks involved in conducting a research project, and in particular in conducting a research project in the area of control engineering. Some of the topics to be covered include:

- Gathering the necessary information to guide you through your research project.

- Critically evaluate your own research and research carried out by others.

- Presenting scientific results (writing of a thesis, paper, report or research proposal;

oral presentations).

- Project management skills.

The course is intended for students with good working knowledge and interest in control engineering and may serve, for example, as preparation for carrying out research for a diploma thesis.

Robust Control

The course focuses on the analysis and controller synthesis of linear multivariable systems under special consideration of robustness aspects. Among the controller design methods treated are: H-infinity control, mu- optimal control, LQG techniques, Loop Transfer Recovery and open loop shaping methods. The exercises comprise of small projects in which the design and analysis methods are applied to practical control problems.