Ph. D. Project
Title:
On Estimation and Observer Design in Nonlinear Systems. Theory and Application
Dates:
2020/11/01 - 2022/04/30
Supervisor(s): 
Other supervisor(s):
HAMAZ Abdelghani (hamaz.ghani@gmail.com)
Description:
1. Introduction:
Observer design for nonlinear systems with discrete-time measurements or under event triggering conditions is widely investigated in
the recent literature [7]-[10]. Beyond its practical advantages and network applications, this issue gives rise to complex mathematical
challenges. Indeed, the convergence analysis of the observer is more complicated due to the availability of the measurements only at
sampling times or subject to event triggering conditions. This thesis fits into this context and aims to solve some fundamental issues on
the development of new design procedures.

2. Objectives:
In this thesis we aim to apply our recent results on state observers established in the literature for nonlinear systems. We particularly
extend the results presented in [1], [2], [4], and [6] to systems with sampled measurements, and outputs under event triggering
conditions. The overall objective consists in developing a systematic link between the conditions ensuring exponential convergence of
the observer and the sampling period, or the triggering conditions. The theoretical results will then be applied to water desalination
models provided by our collaborator from KAUST.

- Nonlinear observers based on sampled measurements: This issue consists in extending the recent results we established in [1], [2], [4],
and [6] to systems with sampled measurements. Indeed, recently, we proposed in [1] a kind of smart high-gain observer, which allows
reducing significantly the values of the gain. Then in this thesis, we will investigate the impact of the sampling time on the conditions
guaranteeing the design of this observer or vice-versa. Similarly, we will study the effect of the output sampling period on the hybrid
observer proposed in [4] and [6]. Indeed, in [4] and [6], we have demonstrated that all the LMI-based observer techniques available in
the literature fail for systems where all the nonlinearities in the process or all the output nonlinearities are non-monotonic. We then
proposed a switched gain approach to overcome this obstacle. In this thesis, we will study the influence of the sampling time on the
switching rule and the dwell time condition.

- Nonlinear observers based on event-triggered measurements: The same problem for event-triggered observers. We plan to study the
relation between triggering conditions and the sufficient LMI conditions or high-gain conditions ensuring exponential convergence of
the observer with continuous-time measurements.

- Sophisticated estimation algorithms: Recently we have developed a new finite-time and exact estimation algorithm for some classes of
discrete-time systems. The algorithm is based on the use of two connected observers, which lead to exact estimation in finite-time [5].
However, this algorithm is not applicable for nonlinear systems. Such an idea led us to think on extending the results to nonlinear
systems and investigate their link to sampling period, or event triggered condition.

- Application to water desalination: The theoretical results will be applied to water desalination models. The models we will tackle are
nonlinear with complex behavior. The methods will be tested using real data, which will be provided by our collaborator from KAUST.

References
[1] A. Zemouche, F. Zhang, F. Mazenc and R. Rajamani, "High Gain Nonlinear Observer with Lower Tuning Parameter. IEEE Transactions
on Automatic Control, vol. 64, n°8: 3194-3209, 2019.
[2] A. Zemouche, R. Rajamani, G. Phanomchoeng, B. Boulkroune, H. Rafaralahy, M. Zasadzinski. Circle Criterion-Based Observer Design
for Lipschitz and Monotonic Nonlinear Systems - Enhanced LMI Conditions and Constructive Discussions. Automatica, vol. 85, n°11: 412-
425, 2017.
[3] R. Rajamani, Y. Wang, G. Nelson, R. Madson, A. Zemouche. Observers with Dual Spatially Separated Sensors for Enhanced
Estimation - Industrial, Automotive and Biomedical Applications. IEEE Control Systems Magazine, vol. 37, n°3: 42-58, 2017.
[4] W. Jeon, A. Zemouche, R. Rajamani. Tracking of Vehicle Motion on Highways and Urban Roads Using A Nonlinear Observer.
IEEE/ASME Transactions on Mechatronics, regular paper, vol. 24, n°2, pp. 644-655, April 2019.
[5] K. Chaib-Draa, A. Zemouche, R. Rajamani, T.M. Laleg-Kirati. Finite-Time State Estimation of Discrete-Time Linear Systems with Some
Extensions. Application to Steering Lateral Vehicle Model. 2019 IEEE Conference on Decision and Control, CDC'19, Nice, France,
December 2019.
[6] H. Movahedi, A. Zemouche, R. Rajamani. Linear Position Estimation on Smart Actuators Using a Nonlinear Observer. 2019 American
Control Conference, ACC'19, Philadelphia, Pennsylvania, USA, July 2019.
[7] Y. Shoukry, P. Tabuada. Event-triggered projected Luenberger observer for linear systems under sparse sensor attacks. 2014 IEEE
Conference on Decision and Control, CDC'14, Los Angeles, CA, USA, December 2014.
[8] V. Andrieu, M. Nadri, U. Serres, J.-C. Vivalda, Self-triggered Continuous Discrete Observer with Updated Sampling Period.
Automatica, Volume 62, Pages 106-113, 2015.
[9] T. Ngoc Dinh, V. Andrieu, M. Nadri, U. Serres, Continuous-discrete time observer design for Lipschitz systems with sampled
measurements, IEEE Transactions on Automatic Control, Vol.60, Issue 3, Pages 787-792, 2015.
Keywords:
Estimation, observers, nonlinear, sampled outputs, event triggering conditions, Lyapunov theory
Conditions:
- Cotutelle between Université de Tizi-Ouzou and Université de Lorraine.
- Funding: Application to ProfasB+ algerian-french program.
Department(s): 
Control Identification Diagnosis
Funds:
Application to ProfasB+ algeiran-french program