Ph. D. Project
Observers and control design of non linear systems under constraints. Application to cable robots
2019/10/01 - 2022/09/30
Other supervisor(s):
JAMMAZI Chaker (
This research topic, which is part of the scientific collaboration between the CRAN and the LIM, relates to the observation and the control of nonlinear
systems under constraints. One of the main motivations concerns the application of these approaches to the state estimation and the control of cable robots.

For twenty years, we have developed several analysis and synthesis techniques for a broad class of dynamic systems with many applications, below some
references since 2012 [1] - [10] ]. The purpose of this thesis is twofold: first, establish a generic methodology to address the issue of observation and control
under constraints for a large class of non linear systems. Stability conditions must be established in terms of linear matrix inequalities (LMI), thus allowing
us to supply both the synthesis matrices and the performances that can be achieved directly. The second goal concerns the application of this methodology to
the state estimation and control of cable robots.

Indeed challenges are multiple. The dynamic behavior of the cable robot is described by complex non-linear differential equations with six degrees of
freedom and very strong constraints on the cables. The first part is to validate the model through experimental data. The second phase, will focus on the
development of control laws taking into account the constraints on the cables continuously in time while ensuring trajectories tracking. Given the
complexity of the system and the limited number of sensors used, the control laws will have to guarantee a robustness compared to the uncertainties and
delays of transmission. The results obtained must be validated by a simulation code through performance evaluation in terms of trajectory tracking,
accuracy, robustness and computation time. The last phase concerns the implementation of these techniques to a cable robot developed by CRAN-LORIA.

[1] Benallouch M., Boutayeb M., Zasadzinski M. Observers design for one sided Lipschitz discrète time systems. Systems and Control Letters 61-9, pp.
879-886, 2012.
[2] Zemouche A., Boutayeb M. On LMI conditions to design observers for Lipschitz non linear systems. Automatica 49-2, pp. 585-591, 2013.
[3] Grandvallet B., Zemouche A., Souley Ali H., Boutayeb M. New LMI condition for observer based Hinf stabilization for a class of non linear discrete
time systems. SIAM Journal on Optimization and Control 51-1, pp. 584-800, 2013.
[4] Drouot A., Richard E., Boutayeb M. An approximate backstepping based trajectory tracking control of a gun-launched micro aerial vehicle in
crosswind. Journal of Intelligent and Robotic Systems 70-1-4, pp. 133-150, 2013.
[5] Hassan L., Zemouche A., Boutayeb M. Robust unknown input observers for non linear time delay systems. SIAM Journal on Optimization and Control
51-4, pp. 2735-2752, 2013.
[6] L. Hassan, A. Zemouche, M. Boutayeb. Robust observer and observer-based controller for time-delay singular systems. Asian Journal of Control, 16
(1), pp.80-94, 2014.
[7] Benallouch M., M. Boutayeb, H. Trinh. Hinfinity observer-based control for discrete-time one-sided Lipschitz systems with unknown inputs. SIAM
Journal on Control and Optimization, 52 (6), pp.3751-3775, 2014.
[8] A. Drouot, E. Richard, M. Boutayeb. Hierarchical backstepping-based control of a gun launched MAV in crosswinds: theory and experiment. Control
Engineering Practice, 25, pp.16-25, 2014.
[9] Thabet A., Boutayeb M., Abdelkrim N. « Real-time fault-voltage estimation for nonlinear dynamic power systems » Int. J. Adapt. Control Signal
Process. pp. 284-296, Février 2016
[10] Jammazi Ch., Zaghdoudi M., Boutayeb «On the global polynomial stabilization of non linear dynamical systems» Non Linear Analysis : Real World
Applications, Elsevier, pp. 29-42, 2019.
Non linear systems - State observers - Control design - Cable robots
Control Identification Diagnosis