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 :
- B. Jayawardhana, R. Ouyang, V. Andrieu, On the construction of storage functions for the Duhem models.
- Automatica, Volume 48, Issue 10, Pages 2657–2662, October 2012.
- V. Andrieu, L. Praly, A. Astolfi,Homogeneous approximation, recursive observer design and output feedback,
- 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 :
- V. Andrieu, C. Prieur, S. Tarbouriech, D. Arzelier, Global asymptotic stabilization of systems satisfying two different sector conditions.
- Submitted to Systems & Control Letters
- V. Andrieu, C. Prieur,Uniting two control Lyapunov functions for affine systems.
- IEEE Transactions on Automatic Control, Volume 55, Issue 8, Pages 1923-1927, August 2010. [Hal]
- V. Andrieu, L. Praly, A. Astolfi, Asymptotic tracking of a reference trajectory by output-feedback for a class of non linear systems.
- Systems & Control Letters, Vol 58, Issue 9, Pages 652-663, September 2009.[Hal]
- V. Andrieu, H. Piet-Lahanier, Exoatmospheric interception problem solved using output feedback law.
- Systems & Control Letters, Volume 55, Issue 8, Pages 633-639, August 2006.[Hal]
- V. Andrieu, L. Praly,Global asymptotic stabilization for non-minimum phase non linear systems admitting a strict normal form.
- IEEE Transactions on Automatic Control, Volume 53, Issue 5, Pages 1120-1132, June 2008. [Hal]
- V. Andrieu, L. Praly, A. Astolfi, Homogeneous approximation, recursive observer design and output feedback,
- SIAM J. Control and Optimization, Vol.47, Issue 4, Pages 1814-1850, June 2008 . [Hal]
- V. Andrieu, L. Praly, A Unifying point of view on output feedback designs for global asymptotic stabilization.
- 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 :
- V. Andrieu, L. Praly. On the existence of Kazantzis-Kravaris / Luenberger Observers.
- SIAM J. Control and Optimization, Vol. 45, Issue 2, Pages 432–456, 2006. [Hal]
- V. Andrieu, L. Praly, A. Astolfi,Homogeneous approximation, recursive observer design and output feedback,
- SIAM J. Control and Optimization, Vol.47, Issue 4, Pages 1814-1850, June 2008. [Hal]
- V. Andrieu, M. Nadri, Observer design for Lipschitz systems with discrete-time measurements,
- IEEE Conference on Decision and Control,, Atlanta (2010). [HAL]
- V. Andrieu, L. Praly, A. Astolfi, High gain observers with updated high-gain and homogeneous correction terms.
- Automatica, Volume 45, Issue 2, Pages 422-428, February 2009. [Hal]
- V. Andrieu, L. Praly, A. Astolfi, High-gain observer with uniform in the initial condition finite-time convergence.
- HAL/00412585, August 2009