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Trainee Project

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

(michel.zasadzinski@univ-lorraine.fr)

- Location: CRAN premises at the IUT Henri Poincaré de Nancy, 186 rue de Lorraine, 54400 Cosnes et Romain.

References

[MaB21] D. Masti and A. Bemporad. Learning nonlinear state-space models using autoencoders. Automatica, vol. 129. ID 109666, 2021.

[Nad23] Mr. Nadri. How control theory learned to stop worrying and succumbing to AI? Talk. October 20, 2023. Second Workshop on Intelligent

Estimation Algorithms for Smart Mobility, ANR ArtISMo, Longwy, France.

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

(michel.zasadzinski@univ-lorraine.fr)

- Location: CRAN premises at the IUT Henri Poincaré de Nancy, 186 rue de Lorraine, 54400 Cosnes et Romain.

References

[MaB21] D. Masti and A. Bemporad. Learning nonlinear state-space models using autoencoders. Automatica, vol. 129. ID 109666, 2021.

[Nad23] Mr. Nadri. How control theory learned to stop worrying and succumbing to AI? Talk. October 20, 2023. Second Workshop on Intelligent

Estimation Algorithms for Smart Mobility, ANR ArtISMo, Longwy, France.

Keywords:

Identification, nonlinear systems, deep learning, autonomous vehicle

Department(s):

Control Identification Diagnosis |