UE Multi-objective control

Diplômes intégrant cet élément pédagogique :


 Optimization and Optimal Control


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 1

Optimal trajectory tracking with an mBot robot

Lab 2

Optimal control of a biological system

Multivariable robust control





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. 


Robust analysis and control of a magnetic levitation 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.

Informations complémentaires

Lieu(x) : Grenoble
Langue(s) : Anglais