Trainee Project
Title:
Identification of nonlinear systems based on deep learning. Application on an autonomous vehicle model.
Dates:
2024/03/01 - 2024/08/31
Student:
Supervisor(s):
Other supervisor(s):
, Hichem BESSEFA (hichem.bessafa@univ-lorraine.fr)
Description:
I) Context of the internship subject

The aim of this master 2 internship is to identify the parameters of a class of nonlinear dynamic systems using artificial intelligence methods, in
particular approaches based on deep learning, drawing on the work developed in [MaB21,Nad23].

The considered nonlinear system has a following state model

x(k+1)=f(x(k),u(k)),
y(k)=h(x(k),u(k))+w(k),

where x(k) is the state vector, u(k) is the vector of measured inputs, y(k) is the vector of measured outputs and w(k) is the vector of measurement
noises. The functions f and h are assumed to be unknown.

Using a set of measured input/output data {u(0),y(0),u(1),y(1),...,u(N),y(N)}, the candidate will have to estimate a recursive state model linking
inputs u(k) to outputs y(k) using approaches based on deep learning, drawing in particular on the work developed in [MaB21,Nad23].

The nonlinear model on which the identification of parameters will be carried out is that of an autonomous vehicle for which input/output data will be
generated and used for deep learning. The nonlinear model of the autonomous vehicle and the software to simulate the input/output data will be
provided by the supervisors.

The estimated state model must be recursive, that is to say it must be able to provide realistic estimated outputs \hat{y(1)}, ..., \hat{y(N)} in using
only the initialization of the state x(0) and the inputs u(0), ...., u(N). Thus, the estimate \hat{y(k)} of the output y(k) will be generated without
needing the outputs measured at previous times (i.e. without needing y(0), y(1), ..., y(k-1).

II) Work to be done

The work to be carried out during this internship is as follows.

a) Study the approach proposed in [MaB21,Nad23].
b) Simulate autonomous vehicle models on MATLAB/SIMULINK.
c) Generate input/output data sets with CARLA Simulation and/or CARSIM.
d) Develop a MATLAB code for the identification of nonlinear state model parameters.
e) Implement deep learning methods on input/output data sets using \cite[MaB21,Nad23].
f) Validate the estimated nonlinear state model in simulation.

- Duration: 5 to 6 months

- Bonus: around 550 euros/month.

- Supervisors: Hichem Bessefa (hichem.bessafa@univ-lorraine.fr), Hugues Rafaralahy (hugues.rafaralahy@univ-lorraine.fr) and Michel Zasadzinski