1. Exponential stabilization of a wide class of affine nonlinear systems

Most physical systems, such as robot manipulators, motor drives, can be appropriately modeled as affine systems. I proposed for the first time a robust exponential stabilization of nonlinear affine systems using state feedback and static output feedback control laws in which the nonlinear systems cannot be necessary Lipschitz. Hence, I developed a new generalized Gronwall-Bellman lemma for nonlinear integer-order systems (nonlinear ordinary differential equations) to derive sufficient conditions for:

• the static state feedback exponential stabilization

• the static output feedback exponential stabilization

• the robust exponential stabilization with regards to parameter uncertainties

• the observer-based control.

2. Stabilization and observation of fractional-order systems

Fractional calculus extends derivatives and integrals to non-integer orders and has been widely used to model scientific and engineering problems. Many natural systems are better described with fractional-order differential equations. Fractional order can be a well-suited tool to analyze issues of fractal dimension with long-term memory and chaotic behavior. Although fractional differential equations have attracted significant attention in recent years, few studies have explored the stabilization and estimation problems.

• For the first time, I proposed sufficient conditions for the asymptotic stabilization of a class of nonlinear fractional-order systems based on the generalization of Gronwall-Bellman lemma. I extended the results for the asymptotic stability of nonlinear fractional-order systems and nonlinear singular fractional-order systems. Furthermore, I proposed sufficient conditions for the robust asymptotic stabilization of linear fractional-order systems and uncertain descriptor fractional-order systems.

• On the other side, I proposed observers' design for the nonlinear fractional-order systems and singular fractional-order systems. The approach is based on a parameterization of the solutions of generalized Sylvester equations.  I derived the conditions for the existence of these observers and proposed sufficient conditions for their stability using linear matrix inequality (LMI) formulation and the generalization of Gronwall-Bellman lemma. The advantage of the proposed method is that, firstly, the observation error does not depend explicitly on the state and control system. Secondly, this method unifies the design of fully reduced and minimal order observers.

• Furthermore, I studied the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Then, I proposed an adaptive observer to jointly estimate the states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method. Finally, the proposed H-infinity adaptive observer is robust against Lipschitz additive nonlinear uncertainties. 

3. Observers design in nonlinear systems  (with D. Zhang, A. Adil, A. Zemouche, R. Rajamani and T.-M. Laleg-Kirati)

The problem of observer design naturally arises in a system approach, as soon as one needs some internal information from external (directly available) measurements. Different purposes can motivate the need for this information: modeling (identification), monitoring (fault detection), or driving (control) the system. All those purposes are jointly required when aiming to keep a system under control and make the observer problem the heart of a general control problem. Unlike linear time-invariant systems where the state estimation problem is analogous to the control design problem, the design of a stable observer is a significant and separate challenge in nonlinear systems. 

• We developed a novel switched-gain discrete-time nonlinear observer for a light-emitting-diode (LED) based optical communication model to estimate the angle between the receiver aperture and the line-of-sight beam sent by the transmitter. The proposed switched-gain observer relies on the non-monotonicity feature of the nonlinear LED output functions composed of nonlinear vector functions of multi-scalar combinations of the states.

• Optical wireless communication system is hampered by noise jamming on the optical communication channel that reduces the system capacity of the wireless optical mobile networks. Additionally, actuator failures can occur due to malfunctions or high instantaneous torques of the actuator-mechanism flexible on the receiver orientation. To address this problem, we developed a novel extended state switched-gain, discrete-time nonlinear observer to simultaneously estimate the actuator fault and the optical communication system's state variables subject to noise jamming attack on the optical communication link.

•  We extended a numerical method for constructing the mapping, which drives the discrete-time nonlinear optical communication system into a stable linear system. We then design an observer to estimate the optical communication system's angular position and angular velocity to maintain a controlled line-of-sight link between transmitter and receiver.

• January 2024: Mohammed Salem Alharbi, (Committee member − Ph.D. proposal defense), King Abdullah University of Science and Technology, KAUST, Saudi Arabia
  Title: Advancements in Data-driven estimation for dynamical systems: wastewater treatment and pedestrian localization

• November 2022: Ania Adil, (Invited (student mentoring) − Ph.D. Thesis defense), Mouloud Mammeri University, Tizi-Ouzou, Algeria
  Title: On estimation and observer design for nonlinear systems: theory and application

• October 2022: Fahad Aljehani, (Co-supervisor − Ph.D proposal defense), King Abdullah University of Science and Technology, KAUST, Saudi Arabia
  Title: Bridging model-based and model-free approaches for control and estimation problems in smart aquaculture systems

Xiao Chen, (Master student) King Abdullah University of Science and Technology, September 2023 – December 2023.
Research project: Fish weight prediction using empirical and data-driven models in aquaculture systems.

Fahad Aljehani, (PhD student) King Abdullah University of Science and Technology, September 2019 - present.                                                                                      Research project: Smart aquaculture project.

Abdullah Al-Hashim, (visiting student) King Abdullah University of Science and Technology, February 2019 - August 2019.                                                                   Research project: Free-space optical communication and trajectory tracking.

Mohammad Mohammad, (visiting student) King Saud University, Riyad, June 2019 - August 2019.                                                                                                             Research project: Observer design and input observer design for blood arterial systems.

Ania Adil, (visiting student) University Mouloud Mammeri and University of Lorraine, November 2019 - April 2020.                                                                               Research project: High-gain observer design for nonlinear systems with delayed outputs.

Ding Zhang, (visiting student) The Hong Kong University of Science and Technology, China, May 2019 - August 2019.                                                                             Research project: LED-based optical communication, underwater optical communication, trajectory tracking and localization.

Lukas Staab, (visiting student) Ilmenau University of Technology, Germany, May 2019 - November 2019.                                                                                                Research project: Non-asymptotic estimation approach using Chebyshev polynomials.

Asayil Al-Shaikh, Effat University, Jeddah, Saudi Arabia, October 2018 - April 2019.                                                                                                                                        Capstone final report: Design and real-time implementation of PID and fractional-order PID controllers on the solar collector system.

Hadeel Al-Maghrabi, Effat University, Jeddah, Saudi Arabia, October 2018 - April 2019.                                                                                                                                 Capstone final report: Design and real-time implementation of PID and fractional-order PID controllers on the solar collector system.

Sarah Toonsi, King Abdullah University of Science and Technology (KAUST), March 2019 - June 2019 and  May 2016 - August 2016.                                                   Research project: Design and real-time implementation of PID and fractional-order PID controllers in a coupled tanks system.

Xingang Guo, Northeastern University at Qinhuangdao, China, December 2016 - June 2017.                                                                                                                         Research project: Real-time Implementation of fractional-order PID controller in laser beam setup.

Nouha Rouis, National School of Engineers of Tunis, University of Tunis El Manar, April - October 2017.                                                                                                              MS thesis: Intelligent LQR based PID controller for trajectory tracking of 2-DoF helicopter: comparison and experimental results.

Adil Aloufi, Jubail University, Kingdom of Saudi Arabia, June 2017 - December 2017.                                                                                                                                      Research project: Laser beam control and model-free control.

Wenqi Cai, Northeastern University, China,  November 2017 - May 2017.                                                                                                                                                          Research project: Free-space optical communication, pointing error control.

Asem Al-Awan, KFUPM, Kingdom of Saudi Arabia, April - October 2017.                                                                                                                                                            Research project: Free-space optical communication, pointing error control.

Abderrazak Chahid, King Abdullah University of Science and Technology (KAUST), September 2019 - October 2020.                                                                              Research project: Smart aquaculture systems, feeding control, reinforcement learning.

Yingquan Li and Zhenwen Zhang, King Abdullah University of Science and Technology (KAUST), Kingdom of Saudi Arabia, March 2021 -  December 2021.            Research project: Deep learning observer design.

Spring 2021: Observer designs: theory and applications (online course), by Ali Zemouche, KAUST, Saudi Arabia.

Spring 2020: Dynamic programming, by Jeff Shamma, KAUST, Saudi Arabia.

Spring 2019: Robust control, by Jeff Shamma, KAUST, Saudi Arabia.

Fall 2019: Advanced estimation methods, by Taous-Meriem Laleg-Kirati, KAUST, Saudi Arabia.

Fall 2017: Dynamic programming, by Jeff Shamma, KAUST, Saudi Arabia.

April 2010: LMI, optimization and polynomial methods, by Didier Henrion, HYCON-EECI, Graduate School on Control, SUPELEC, Paris - France.

March 2010: Nonlinear output regulation, by Alberto Isidori, HYCON-EECI, Graduate School on Control, SUPELEC, Paris - France.