Technische Universität Ilmenau

# Systems Optimization - Modultafeln of TU Ilmenau

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module properties Systems Optimization in degree program Master Research in Computer & Systems Engineering 2012
module number100965
examination number2200416
departmentDepartment of Computer Science and Automation
ID of group 2212 (Simulation and Optimal Processes)
term winter term only
languageEnglisch
credit points5
on-campus program (h)45
self-study (h)105
obligationobligatory module
examwritten examination performance, 90 minutes
details of the certificate
signup details for alternative examinations
maximum number of participants30
previous knowledge and experience<p><span id="part1"><span dir="none">Fundamentals of Mathematics and Control Engineering</span></span></p>
learning outcome<p>• to model and classify optimization problems</p><p>• to identify relevant optimization algorithms and solve real-life engineering optimization problems</p><p>• to enable the student solve practical optimization problems using modern software tools</p><p><span dir="none">• to enable the student analyze the viability of optimization solutions for practical use</span></p><p> </p>
content

PRELIMINARIES
1. Introduction, Motivation, and Preliminaries
- Importance of Systems Optimization
- Mathematical Preliminaries
- Convex sets and Convex Functions

PART - I : Steady-State Optimization Problems and Applications

Methods of Unconstrained Optimization Problems
2.1. First- and Second-Order Optimality Conditions
2.2. The Method of Steepest Descent
2.3. The Newton Method
2.4. The Levenberg-Marquardt Method
2.5. Quasi-Newton Methods
2.6. Line-search Methods
2.7. System of Nonlinear Equations
2.7a. Numerical Algorithms for Systems of Nonlinear Equations
2.7b. Numerical Solution Methods for Differential Algebraic Equations: backward differentiation formula (BDF), Single and Multiple-shooting, collocation methods

Methods of Constrained Optimization Problems
3.1. The Karush-Kuhn-Tucker Optimality Conditions
3.2. Convex Optimization Problems
3.3. Penalty Methods
3.4. Barrier and Interior-Point Methods
3.5. The Sequential Quadratic Programming (SQP) Method

Part-II: Dynamic Optimization Problems and Applications

4. Introduction to Dynamic Optimization
5. Direct Methods for Dynamic Optimization Problems
5.1. Collocation Methods for Dynamics Optimization Problems
5.2. Costate estimation
6. Introduction to Model-Predictive Control

Appendix
• A review on numerical linear algebra methods
• Introduction to 1D quadrature rules and orthogonal polynomial collocation
• A review on numerical methods of Ordinary Differential Equations (ODEs): numerical methods of initial value and boundary value ordinary differential equations - Euler method, Runge-Kutta, BDF, implicit Runge-Kutta,
• A brief introduction differential Algebraic Equations (DAEs) and Applications: The concept of Index in DAEs, Consistent Initialization, etc.
• A summary of the Classical Theory of Optimal Control Problems - the Pontryagin Principle - Indirect Methods

media of instruction<p><span id="part1"><span dir="none">Presentation, Lecture slides script, blackboard presentation</span></span></p><p><a href="https://www.tu-ilmenau.de/prozessoptimierung/lehre/vorlesungen-seminare-und-praktika/wintersemester">https://www.tu-ilmenau.de/prozessoptimierung/lehre/vorlesungen-seminare-und-praktika/wintersemester</a><a>/</a></p><p>Link zum Moodle-Kurs:</p><p><span dir="none"><a href="https://moodle2.tu-ilmenau.de/course/view.php?id=3138">https://moodle2.tu-ilmenau.de/course/view.php?id=3139</a></span></p>
literature / references<p><span id="part1"><span dir="none">• J.T. Betts: Practical methods for optimal control using nonlinear programing, SIAM 2001.<br />• A. E. Bryson, Y.-C. Ho: Applied optimal control : optimization, estimation, and control, Taylor & Francis, 1975.<br />• C. Chiang: Elements of dynamic optimization. McGraw-Hill, 1992.<br />• E. Eich-Soellner, C. Führer: Numerical methods in multibody dynamics. B.G Teubner, 1998.<br />• M. Gerdts: Optimal control of ODEs and DAEs. De Gruyter, 2012.<br />• D.R. Kirk: Optimal Control theory: an introduction. Dover Publisher, 2004.<br />• J. Nocedal, S.J. Wright: Numerical methods of optimization. 2nd ed. Springer Verlag 2006.<br />• R.D. Rabinet III et al.: Applied dynamic programming for optimization of dynamical systems. SIAM 2005.<br />• S.S. Rao: Engineering optimization - theory and practice. Wiley, 1996.</span></span></p>
evaluation of teaching

Plichtevaluation:

WS 2018/19 (Fach)

Freiwillige Evaluation:

WS 2015/16 (Vorlesung)

WS 2017/18 (Vorlesung)

Hospitation:

WS 2018/19