Research interests

My main research interest concernes the nonlinear control theory and its application. I'm more concerned in three specific fields:

Analysis of nonlinear systems :

The problem is to characterize the behavior of the trajectories of a nonlinear system subject to nonlinearities ( such as hysteresis or other nonlinearities).

Keywords : Lyapunov function, dissipativity, Homogeneous approximation, Hysteresis, backlash, small-gain arguments, LMI

Main publications related to the topic :

  1. B. Jayawardhana, R. Ouyang, V. Andrieu, On the construction of storage functions for the Duhem models.
    1. Automatica, Volume 48, Issue 10, Pages 2657–2662, October 2012.
  2. V. Andrieu, L. Praly, A. Astolfi,Homogeneous approximation, recursive observer design and output feedback,
    1. SIAM J. Control and Optimization, Vol.47, Issue 4, Pages 1814-1850, June 2008. [Hal]

Feedback control of nonlinear systems :

In this topic the problem is to design an algorithm which gives online a control input such that the trajectories of the closed loop system follow some prescribed behavior (stability, tracking of trajectories, optimal control...).

Keywords : Lyapunov design, High-gain techniques, Homogeneous designs, backstepping, forwarding, optimal control, LMI, Sector conditions, Output feedback

Main publications related to the topic :

  1. V. Andrieu, C. Prieur, S. Tarbouriech, D. Arzelier, Global asymptotic stabilization of systems satisfying two different sector conditions.
    1. Submitted to Systems & Control Letters
  2. V. Andrieu, C. Prieur,Uniting two control Lyapunov functions for affine systems.
    1. IEEE Transactions on Automatic Control, Volume 55, Issue 8, Pages 1923-1927, August 2010. [Hal]
  3. V. Andrieu, L. Praly, A. Astolfi, Asymptotic tracking of a reference trajectory by output-feedback for a class of non linear systems.
    1. Systems & Control Letters, Vol 58, Issue 9, Pages 652-663, September 2009.[Hal]
  4. V. Andrieu, H. Piet-Lahanier, Exoatmospheric interception problem solved using output feedback law.
    1. Systems & Control Letters, Volume 55, Issue 8, Pages 633-639, August 2006.[Hal]
  5. V. Andrieu, L. Praly,Global asymptotic stabilization for non-minimum phase non linear systems admitting a strict normal form.
    1. IEEE Transactions on Automatic Control, Volume 53, Issue 5, Pages 1120-1132, June 2008. [Hal]
  6. V. Andrieu, L. Praly, A. Astolfi, Homogeneous approximation, recursive observer design and output feedback,
    1. SIAM J. Control and Optimization, Vol.47, Issue 4, Pages 1814-1850, June 2008 . [Hal]
  7. V. Andrieu, L. Praly, A Unifying point of view on output feedback designs for global asymptotic stabilization.
    1. Automatica, Survey paper, Vol. 45, Issue 8, Pages 1789-1798, August 2009. [Hal]

State estimation and observer design for non linear systems with outputs :

In this topic, the problem is to give an algorithm which provides an estimate of the state from the measured outputs.

Keywords : high-gain observer, Luenberger observer, Homogeneous observer.

Main publications related to the topic :

  1. V. Andrieu, L. Praly. On the existence of Kazantzis-Kravaris / Luenberger Observers.
    1. SIAM J. Control and Optimization, Vol. 45, Issue 2, Pages 432–456, 2006. [Hal]
  2. V. Andrieu, L. Praly, A. Astolfi,Homogeneous approximation, recursive observer design and output feedback,
    1. SIAM J. Control and Optimization, Vol.47, Issue 4, Pages 1814-1850, June 2008. [Hal]
  3. V. Andrieu, M. Nadri, Observer design for Lipschitz systems with discrete-time measurements,
    1. IEEE Conference on Decision and Control,, Atlanta (2010). [HAL]
  4. V. Andrieu, L. Praly, A. Astolfi, High gain observers with updated high-gain and homogeneous correction terms.
    1. Automatica, Volume 45, Issue 2, Pages 422-428, February 2009. [Hal]
  5. V. Andrieu, L. Praly, A. Astolfi, High-gain observer with uniform in the initial condition finite-time convergence.
    1. HAL/00412585, August 2009

Research Report:

  1. 2006-2009.
  2. 2010-2015.