Diplômes intégrant cet élément pédagogique :
Descriptif
Optimization and Optimal Control
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1 |
System and Performance |
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Problem formulation; state variables representation; state transition matrix; physical constraints; the optimal control problem. |
2 |
The Performance Measure |
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Performance for optimal control; selecting a performance measure; performance measure for modeling. |
3 |
Dynamic Programming |
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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 |
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Fundamental concepts; problems with fixed/free final time/states; functionals involving several independant variables. |
5 |
The Variational Approach to Optimal Control Problems |
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Necessary conditions for optimal control; boundary conditions; linear regulator problems; Pontryagin's minimum principle and state inequality constraints. |
6 |
Observers and State Estimation |
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State observation; continuous-time optimal filters (Kalman/Bucy, extended); discrete-time estimation. |
7 |
LQG Control |
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Traditional LQG and LQR problems; LQG controller architecture; robustness properties. |
8 |
Optimization with Scilab |
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Optimization and solving nonlinear equations; general optimization; solving nonlinear equations; nonlinear least squares; parameter fitting; linear and quadratic programming; differentiation utilities. |
9 |
Applications |
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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 trajectory tracking with an mBot robot |
Lab 2 |
Optimal control of a biological system |
Multivariable robust control
Lesson |
Topic |
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1 |
Motivation |
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Industrial examples. |
2 |
H&infin norm, stability |
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3 |
Performance analysis/specifications |
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Performances quantifiers, A first robustness criteria |
4 |
H&infin control design |
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Mixed sensitivity problem |
5 |
Uncertainties and robustness |
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Representing uncertainties, Robust stability, Robust performance, Robust control design. |
6 |
Performances limitations |
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Bode and Poisson sensitivity integral. |
Lab |
Robust analysis and control of a magnetic levitation system. |
Bibliographie
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.
Informations complémentaires
Lieu(x) : GrenobleLangue(s) : Anglais