PhD Position F/M Nonlinear observer design using AI tools

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The Inria University of Lille centre, created in 2008, employs 360 people including 305 scientists in 15 research teams. Recognised for its strong involvement in the socio-economic development of the Hauts-De-France region, the Inria University of Lille centre pursues a close relationship with large companies and SMEs. By promoting synergies between researchers and industrialists, Inria participates in the transfer of skills and expertise in digital technologies and provides access to the best European and international research for the benefit of innovation and companies, particularly in the region.

For more than 10 years, the Inria University of Lille centre has been located at the heart of Lille's university and scientific ecosystem, as well as at the heart of Frenchtech, with a technology showroom based on Avenue de Bretagne in Lille, on the EuraTechnologies site of economic excellence dedicated to information and communication technologies (ICT).


This thesis project is devoted to solution of a localization problem for mobile robots using the conventional and modern approaches, based on AI tools.

The conventional problem of bearings-only target motion analysis (BOTMA) is studied in the project. It assumes that the two mobile agents, monitor and target, are on the same plane and that they (or at least target) have a constant speed during the observation time period. The goal is to estimate the position of a target, namely two coordinates of geographical location and the projections of the speed on two axes, from a set of available perturbed bearing measurements collected by the monitor.

This project is performed in collaboration with IIT Delhi.

Main activities

Development of various state and/or parameter estimation algorithms for linear dynamical systems subjected to nonlinear noisy measurements by combining modern methods from the theories of control, estimation, and artificial intelligence.

Physics-informed neural networks (PINNs) can be used to approximate the behavior of the target, or an alternative implementation of an observer. This recently developed framework allows one to use neural networks for nonparametric estimation by simultaneously approximating a system model, an observer (or a controller) and the respective Lyapunov function, which can be used to verify the stability and convergence of the estimation error.


  • Perez, A.-C. Contribution à la trajectographie passive sous-marine. HDR, Toulon, 2021.
  • Le Cadre, J. P. and Jauffret, C. Discrete-time observability and estimability analysis for bearings-only target motion analysis. IEEE Transactions on Aerospace and Electronic Systems, 33, 1 (Jan. 1997), 178--201.
  • Ristic, B. and Sanjeev, A. M. Tracking a manoeuvring target using angle-only measurements: Algorithms and performance. Signal Processing, 83 (June 2003), 1223--1238.
  • Schiassi E., D’Ambrosio A., Drozd K., Curti F., Furfaro R. Physics-Informed Neural Networks for Optimal Planar Orbit Transfers. Journal of Spacecraft and Rockets. 59(3), 2022, pp. 834--849.
  • Umar B. Niazi M., Cao J., Sun X., Das A., Johansson K.H. Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems. arXiv:2210.01476, 2022.
  • Aranovskiy S., Efimov D., Sokolov D., Wang J., Ryadchikov I., Bobtsov A. Switched Observer Design For a Class of Locally Unobservable Time-Varying Systems. Automatica, 130(8), 2021, pp. 109715.
  • Ballesteros-Escamilla M., Polyakov A., Efimov D., Chairez I., Poznyak A.S. Non-parametric Identification of Homogeneous Dynamical Systems. Automatica, 129(6), 2021, pp. 109600.



The candidate should have experience in analysis of nonlinear dynamical systems and/or theory of control and estimation. The main mission will be analysis of existing results on the topic of the thesis, development of new theories and its practical verification. It is in general desirable to have a solid background in applied mathematics. The candidate should also be comfortable with English (oral and written).

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


1st and 2nd year: 2100€ gross per month

3rd year: 2190€ gross per month