Technische Universität Ilmenau

Systems Optimization - Modultafeln der TU Ilmenau

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Fachinformationen zu Fachnummer 100965 - allgemeine Informationen
Fachnummer100965
FakultätFakultät für Informatik und Automatisierung
Fachgebietsnummer2212 (Prozessoptimierung)
Fachverantwortliche(r)Prof. Dr. Pu Li
SpracheEnglisch
TurnusWintersemester
Vorkenntnisse<p><span id="part1"><span dir="none">Fundamentals of Mathematics and Control Engineering</span></span></p>
Lernergebnisse<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>
Inhalt

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

 

Medienformen<p><span id="part1"><span dir="none">Presentation, Lecture slides script, blackboard presentation</span></span></p>
Literatur<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>
Lehrevaluation

Plichtevaluation:

Freiwillige Evaluation:

WS 2015/16 (Vorlesung)

WS 2017/18 (Vorlesung)

Hospitation:

WS 2018/19

Spezifik im Studiengang Master Research in Computer & Systems Engineering 2012, Master Research in Computer & Systems Engineering 2016
FachnameSystems Optimization
Prüfungsnummer2200416
Leistungspunkte5
Präsenzstudium (h)45
Selbststudium (h)105
VerpflichtungPflicht
Abschlussschriftliche Prüfungsleistung, 120 Minuten
Details zum Abschluss

Oral examination, 30 min.

Anmeldemodalitäten für alternative PL oder SL

Plichtevaluation:


Freiwillige Evaluation:


WS 2015/16 (Vorlesung)


WS 2017/18 (Vorlesung)


Hospitation:


WS 2018/19

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