Level
Baccalaureate +5
ECTS
6 credits
Component
UFR PhITEM (physique, ingénierie, terre, environnement, mécanique)
Semester
Automne
Description
Optimization and Optimal Control (21 h + 15 h labs)
| |
|---|---|
1 | System and Performance |
| Problem formulation; state variables representation; state transition matrix; physical constraints; the optimal control problem. |
2 | The Performance Measure |
| Performance for optimal control; selecting a performance measure; performance measure for modeling. |
3 | Dynamic Programming |
| Optimal control law; principle of optimality; decision making; recurrence relation for DP; characteristics of DP solutions; discrete linear regulators; the Hamilton-Jacobi-Bellman equation; continuous linear regulators. |
4 | Calculus of Variations |
| Fundamental concepts; problems with fixed/free final time/states; functionals involving several independant variables. |
5 | The Variational Approach to Optimal Control Problems |
| Necessary conditions for optimal control; boundary conditions; linear regulator problems; Pontryagin's minimum principle and state inequality constraints. |
6 | Observers and State Estimation |
| State observation; continuous-time optimal filters (Kalman/Bucy, extended); discrete-time estimation. |
7 | LQG Control |
| Traditional LQG and LQR problems; LQG controller architecture; robustness properties. |
8 | Optimization with Scilab |
| Optimization and solving nonlinear equations; general optimization; solving nonlinear equations; nonlinear least squares; parameter fitting; linear and quadratic programming; differentiation utilities. |
9 | Applications |
| A stochastic gradient descent approach to feedback design for network controlled systems; a constrained variational approach using the augmented Lagrangian for optimal diffusivity identification in firns; parametric optimization of a diesel engine model and comparison between numerical methods (trust region, Levenberg-Marquardt, interior point and active sets) and norms. |
Lab 1 | Optimal particle source identification in Tore Supra tokamak |
Lab 2 | Optimal flow control (see the UJF experiment ) |
Multivariable robust control (20 h + 16 h labs)
Lesson | Topic |
|---|---|
1 | Motivation |
| Industrial examples. |
2 | H&infin norm, stability |
|
|
3 | Performance analysis/specifications |
| Performances quantifiers, A first robustness criteria |
4 | H&infin control design |
| Mixed sensitivity problem |
5 | Uncertainties and robustness |
| Representing uncertainties, Robust stability, Robust performance, Robust control design. |
6 | Performances limitations |
| Bode and Poisson sensitivity integral. |
Lab | Robust analysis and control of a flexible transmission system. |
Course parts
- UE Multi-objective control - CMLectures (CM)41h
- UE Multi-objective control - TPPractical work (TP)31h
Period
Semester 9
Bibliography
Optimization and Optimal Control
Class textbook:
- D. Kirk, "Optimal Control Theory: An Introduction", Prentice-Hall Electrical engineering series, 1970 (original edition), Dover, 2004 (reprint).
Additional readings:
- R. Boudarel, J. Delmas and P. Guichet, "Commande Optimale des Processus", Dunod, 1967.
- S. Campbell, J-P. Chancelier and R. Nikoukhah, "Modeling and Simulation in Scilab/Scicos", Springer, 2005.
- U. Jonsson, C. Trygger and P. Ogren, "Optimization and System Theory", Lecture notes, KTH, Sweden 2008.
- J. Mikles and M. Fikar, "Process Modelling, Identification, and Control", Springer, 2007.
Multivariable robust control
- S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, 2nd Ed., Wiley, 2007.
- K. Zhou, Essentials of Robust Control, Prentice Hall, New Jersey, 1998.
- J.C. Doyle, B.A. Francis, and A.R. Tannenbaum, Feedback control theory, Macmillan Publishing Company, New York, 1992.
- G.C. Goodwin, S.F. Graebe, and M.E. Salgado, Control System Design, Prentice Hall, New Jersey, 2001.
- G. Duc et S. Font, Commande Hinf et analyse: des outils pour la robustesse, Hermès, France, 1999.
- D. Alazard, C. Cumer, P. Apkarian, M. Gauvrit, et G. Ferreres, Robustesse et commande optimale, Cépadues Editions, 1999.