Optimization and Optimal Control

Mirko FIACCHINI ( ).

Class schedule

Lesson Topic
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 UGA experiment )

References

Class textbook:
  • D. Kirk, "Optimal Control Theory: An Introduction", Prentice-Hall Electrical engineering series, 1970 (original edition), Dover, 2004 (reprint).
Additional readings:
  • A.E. Bryson, Jr., "Applied Optimal Control", John Wiley & Sons, 1975. [Online]
  • 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.
  • R. D'Andrea, "Dynamic Programming and Optimal Control", Lecture notes.

Grading Policy

Homeworks: 20 %
Final Exam: 80 %

Handouts

Restricted access area