UE Multi-objective control

Degrees incorporating this pedagocial element :


 Optimization and Optimal Control (21 h + 15 h labs)

System and Performance 
 Problem formulation; state variables representation; state transition matrix; physical constraints; the optimal control problem.
The Performance Measure 
 Performance for optimal control; selecting a performance measure; performance measure for modeling.
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.
Calculus of Variations 
 Fundamental concepts; problems with fixed/free final time/states; functionals involving several independant variables.
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. 
Observers and State Estimation 
 State observation; continuous-time optimal filters (Kalman/Bucy, extended); discrete-time estimation. 
LQG Control 
 Traditional LQG and LQR problems; LQG controller architecture; robustness properties. 
Optimization with Scilab 
 Optimization and solving nonlinear equations; general optimization; solving nonlinear equations; nonlinear least squares; parameter fitting; linear and quadratic programming; differentiation utilities. 
 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 1Optimal particle source identification in Tore Supra tokamak
Lab 2Optimal flow control (see the UJF experiment )

Multivariable robust control (20 h + 16 h labs)

Lesson Topic 
 Industrial examples. 
H&infin norm, stability
Performance analysis/specifications
 Performances quantifiers, A first robustness criteria 
H&infin control design
 Mixed sensitivity problem 
Uncertainties and robustness
 Representing uncertainties, Robust stability, Robust performance, Robust control design. 
Performances limitations
 Bode and Poisson sensitivity integral. 
Lab Robust analysis and control of a flexible transmission system.



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 DesignPrentice 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.