Browsing by Author "Alharthi, Mohammed"

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Optimal and Adaptive Control for Volterra Difference Equations
(Saudi Digital Library, 2023-11-06) Alharthi, Mohammed; Markus, Mueller
This thesis seeks to fill a knowledge gap in the area of dynamical systems and control theory concerning so-called Volterra Difference Equations (VDEs). A particular focus lies on controlled VDEs and related concepts, including characterizations of controllability and observability, and optimal and adaptive control designs for VDEs. Two different system classes of Volterra Difference Equations are being con- sidered: systems of convolution and non-convolution type. The concept of the resolvent or fundamental matrix for both types is introduced. The fundamental mat- rix allows derivation of solutions for VDEs, and in this thesis it is utilized to establish novel necessary and sufficient conditions for the controllability and observability of VDEs for both convolution and non-convolution types, and for VDEs of the first and second kind. The results develop respective controllability and Gramian matrices, for which invertibility or rank conditions are established respectively. The control- lability and observability characterization results are complementary. Examples are presented to illustrate the theory. Furthermore, this thesis investigates several approaches to the control designs for Volterra Difference Equations. First optimal control problems for VDEs of convolution type of the first kind are considered. The first results establish a solution for a finite horizon optimal control problem. The solution of this problem can be developed by solving a difference Riccati equation, or alternatively, and a novel contribution of this thesis, by derivation of a system of linear equations as an analogy for the optimal control problem. Solving this system of linear equations allows then for a direct approach to obtain the optimal control input. While this direct method is mathematically very convenient, a drawback is that constraints are not easily integrated in this optimal control approach. For this purpose, alternative approaches based on linear quadratic regulator design and a differential dynamic programming approach are developed. Second feedback and adaptive control designs are developed for VDEs of the convolution type of the first kind. Two adaptive control designs are explored, a simple adaptive controller and a direct adaptive controller. To illustrate the results of this thesis an epidemiological model and respective management of the epidemic is considered. We employ the various control strategies and designs to the respective Volterra Difference Equation and explore the efficacy of the designs with respect to different model parameters.
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Optimising the design of passive optical networks-based data centres
(University of Leeds, 2024) Alharthi, Mohammed; Elmirghani, Jaafar
The recent growth in cloud-based applications has motivated researchers to focus on improving the scalability, power efficiency, and cost-effectiveness of data centre architectures. State-of-the-art data centres consists of numerous access and aggregation switches which can be costly and can lead to inefficiencies such as unbalanced traffic and high-power consumption. Passive Optical Network (PON) technology, known for its high performance in access networks, can offer energy-efficient, cost-effective, and scalable solutions for modern and future data centres. This thesis aims to propose and enhance a PON-based data centre architecture to enable multi-path routing, load balancing and scalability, enhance resilience and energy efficiency, and reduce latency. The proposed design is based on a two-tier cascaded Arrayed Waveguide Grating Routers (AWGRs) fabric. We develop a Mixed Integer Linear Programming (MILP) model to optimise the wavelength assignment and multipath routing in the proposed architecture. Additionally, we investigate the resilience of the proposed architecture by evaluating its power consumption and delay under several failure scenarios. We also optimise virtual Machine (VM) placement in the proposed architecture to minimise power consumption. A MILP model and a heuristic are developed for VM placement in the proposed architecture and the results show significant power consumption reductions, up to 66% compared to VM placement in the state-of-the-art architecture, the spine and leaf architecture. Furthermore, we consider the use of WDM/TDM multiple access technique with multipath routing in the proposed architecture. A MILP model is developed to jointly optimise time slots allocation and routing and wavelength assignment.
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