Identification, Data Assimilation & Robust control

Presentation

Identification.

Examples of inverse problms : optimal command optimale, parameter identification, data assimilation, optimum design.

Reviews of: functional analysis, differential calculus, optimisation.

Optimal control:

PDE non-linear, adjoint equations, optimality system, Lagrangien.

Variational Data Assimilation.

Examples. Models – errors

Cost function, regularisations. Sensitivities.

Global algorithms, minimisation, 4D-Var.

Linear case : links with BLUE & sequential methods / filtering.

Practical (Python-Fenics or FreeFem++): advection-diffusion phenomena or Burgers equation.

Automatic- Robust control

This course provides the main mathematical results on system control. It covers the core areas that are: controllability, observability, Lyapunov stability, static and dynamic regulator, Linear quadratic control, dynamic programming, A control design application on landing gear is presented.

Organisation:

Identification

8 videos (SPOC-MOOC) + manuscript (140 pages)

Flipped classes. Tutorials + lab tutorials.

Modeling of a simplified industrial problem (in Python- Fenics  or FreeFem++ software).

Automatic-Robust control

Classes, exercises derived from real world problems (in aeronautics, space, finances).

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

Identification:

- Setting up a complete modeling problem: data – models - errors ; inverse modelling.

- The optimal control of ODE and PDE systems,

- Sensitivity analysis, an identification-calibration process, a  data assimilation process.

- Links between Variational Data Assimilation & BLUE – Kalman filtering.

Automatic-Robust Control:

The main concepts  for controlling a system in a view of engineering applications are:

-       Stability

-       Performance

-       Robustness

The student will be able to:

Identification: Set up the equations and the complete modeling chain to perform numeriocal identification / calibration / Variational Data Assimilation for PDE models.

Automatic-Robust Control :

Design a feedback control law that is able to optimize objectives and fulfilled constraints. These objectives and constraints functions can be: cost, stability, performances, robustness, reliability,……

Needed prerequisite

Identification.

PDE & ODE Models, differential calculus, functional analysis, optimisation, numerical schemes, programming.

Robust control

ODE, Optimization, Numerical Schemes, Linear Algebra, Programming

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...