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UE Multi-objective control

Degrees incorporating this pedagocial element :

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.

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.