I am a multidisciplinary researcher with engineering, mathematics, computer, and physics background. My research interests lie in the areas of applied mathematics, control theory, dynamical systems, and game theory, with specific interests in mechatronic applications, robotics, and human-machine systems. I worked on a broad range of projects including robust design, human-in-the-loop systems, control design for quantum systems, evolutionary game theory and evolutionary dynamics and fixable robotic arm manipulator. My main research interests currently include:
- Robotics and Intelligent Systems;
- Control Theory and Automation;
- Quantum Physics and Quantum Control;
- Population Games and Evolutionary Dynamics.
I began my career with a four years bachelor's degree in the field of applied mathematics and computer science in 2004. In 2009, I received my master’s degree (by research) in applied mathematics that focused on molding quantum systems. My master’s thesis was titled \textit{Studying the quantum properties of a system of atoms interacting with some fields}. During my master’s studies, I developed a mathematical model that describes multi-level atoms and their interaction with a two-mode quantized radiation field using a Jaynes-Cummings model. This work included exploring the entanglement between multi-level atoms interacting with a two-mode quantized radiation field. Furthermore, I investigated the evolution of a pair of coherent states in the context of two-qubit entanglement and cat-state generation. These research topics lead to the examination of the effect that the environment has on open quantum systems, as well as the master equation for multi-level atoms interacting with a two-mode quantized radiation field.
PhD Studies
In July 2013, I reserved my Ph.D. in Electrical Engineering from the University of New South Wales in Canberra (UNSW Canberra). During my Ph.D., my field of research was in Robust Control Theory, where I developed a new theory for a class of dissipative systems known as Negative Imaginary Systems Theory with applications in experimental quantum systems and flexible structure systems.
Figure 1: A negative-imaginary feedback control system. If the plant transfer function matrix G(s) is NI and the controller transfer function matrix G(s) is SNI, then the positive-feedback interconnection is internally stable if and only if the DC gain condition, max(G(0) G(0)) < 1; is satis ed.
The focus of my doctoral research was orientated towards utilizing my background in mathematics and physics to solve real-world engineering problems. In particular, I worked on robust control theory and its applications to flexible structures and nano-positioning systems. These flexible structure systems arise in many important engineering applications, such as ground and aerospace vehicles, atomic force microscopes, rotating flexible spacecraft, robotics and flexible link manipulators, hard disk drives, and other nano-positioning systems. These systems are often modeled as distributed parameter systems. It is important to consider the effect of highly resonant modes in the control system design for such flexible systems. These resonant modes are known to adversely affect the stability and performance of flexible structure control systems and are often very sensitive to changes in environmental variables. This can lead to vibrational effects that limit the ability of control systems to achieve desired levels of performance. During my Ph.D., I worked on developing and generalizing a control theory that can be applied to these flexible structure systems are known as negative imaginary (NI) systems. This theory has provided natural and useful syntheses methods in control system design for distributed parameter systems (infinite-dimensional systems), see Fig. 1. During my Ph.D. studies, I applied the NI theory to the practical applications of control system design such as a three-mirror optical cavity locking system and a robotic arm manipulator.
As a measure of my academic capability in the field of control theory, I have published more than thirty-one research papers in this area in international journals and conferences. Please see the list of publications in my CV. The majority of these research papers are in the field of the control system, quantum control, and model-based system design.
Past Postdoctoral Experience
After finishing my Ph.D., I joined UNSW Canberra as a post-doctoral fellow for one year. During this time, I developed a robust control design for quantum systems based on the numerical methodology of sampling-based learning control (SLC) for the control design of quantum systems with uncertainties. The SLC method includes two steps of training and testing. In the training step, an augmented system is constructed using artificial samples generated by sampling uncertainty parameters according to a given distribution. A gradient flow-based learning algorithm is developed to find the control for the augmented system. In the process of testing, a number of additional samples are tested to evaluate the control performance, where these samples are obtained through sampling the uncertainty parameters according to a possible distribution.
I then joined the Capability Systems Centre at the University of New South Wales at the Australian Defence Force Academy, Canberra as a post-doctoral fellow for one year. My research was focused on systems engineering and systems design. During this time, I was working on integrating nonfunctional requirements into axiomatic design methodology. Also, I developed a mathematical framework for recursive model-based system design.
Current Postdoctoral Experience
Currently, I am working with intelligent systems and control (RISC) lab as a post-doctoral fellow at Kaust. One of my research interests at the moment is a central question in population games, as well as the related topic of learning in games, is understanding the long-run behavior of player strategies. In particular, under what conditions do population strategies converge to a solution concept such as Nash equilibrium? The outcome depends on both the underlying game and the particular evolutionary dynamics, and behaviors can range from convergence for classes of game/dynamics pairings to chaos in seemingly simple settings. Furthermore, a specific game can exhibit inherent obstacles to convergence for broad classes of evolutionary dynamics. Contrary to Nash equilibrium, there are relaxed solution concepts, such as coarse correlated equilibria, that are universally (i.e., for all games) induced by various forms of evolutionary dynamics. Of specific interest herein is the class of population games called stable games. These games exhibit a property called “self-defeating externalities”. Whenever a segment of the population revises its strategies, the payoff gains in the adopted strategy are less than the payoff gains of the abandoned strategy. It was shown that the class of stable games results in convergence to Nash equilibrium when paired with a variety of evolutionary dynamics. The Strong connection between passivity theory as a control concept and games theory was established in recent years. Generally speaking, it was shown that stable games exhibit a property related to passivity. Furthermore, various evolutionary dynamics also exhibit a form of passivity. Accordingly, since interconnections of passive dynamical systems exhibit stable behavior, one can conclude that passive evolutionary dynamics coupled with stable games exhibit stable behavior. The connection to passivity enables the opportunity to analyze in a similar way the broader class of both games and evolutionary dynamics. Of particular interest here are higher-order games and higher-order dynamics. In the canonical models of population games, the fitness of various population strategies is a static function of the population composition. Another research area that I am currently working on is human-machine systems. Modeling human behavior has been approached from several domains and theories such as optimal control theory, general control theory, expert systems, and cognitive science. The resulting models in most cases are not realistic, simplified not robust, and do not support the full man-machine systems modeling requirements for analysis and design of complex human-in-the-loop systems. In particular, the current engineering models of the human operator considers the human as a black box with constrained input processing and simple types of dynamics. We are interested in combining ideas from dynamical system theory, control theory, machine learning techniques, and data-driven models to develop a more realistic model for human behavior.
Future Interest
The variety of research topics I have worked on during my early research career has led to a solid theoretical background on control systems design with a focus on flexible structure systems. My future research plan is to extend my knowledge and contribution in the field of modern control and intelligent systems using modern techniques such as game-theoretic approaches and machine learning approaches.
The following are areas of research in which my background will provide sufficient expertise to carry out competitive and rigorous research. Furthermore, I anticipate starting immediately with the items listed below:
- Cyber-physical systems: Cyber-physical systems integrate computation, networking, human factors, and physical processes in order to build and synthesize systems that are distributed, reliable and efficient at the same time. The societal and economic potential of these systems is much greater than what has been realized, and huge investments are being made worldwide to develop such combinations of subsystems in composition synthesis methodologies
- Distributed Control and multi-agent systems: Distributed control and multi-agent systems are becoming increasingly important topics in systems theory. Distributed control and multi-agent systems extend well-established concepts in system’s theory to large-scale systems in a decentralized fashion.
- Quantum control theory: I am interested in the innovative field of quantum control theory. I believe that my applied mathematics background, coupled with my knowledge of theoretical quantum physics and control theory, provides the necessary skills to articulate and pursue innovative research in the field of quantum control theory.