Saudi Cultural Missions Theses & Dissertations
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Item Restricted Stability Analysis and Boundary Control of Coupled ODE-PDE Systems with a Class of Nonlinearity(University of Sheffield, 2025-04-15) Almazmoumi, Eissa; Guo, LingzhongThe research effort focusses on formulating boundary control for systems that have coupled ordinary differential equations (ODEs) and partial differential equations (PDEs), incorporating nonlinearity as characterized by the Wiener and Hammerstein models. The system coupling is considered through either the states or via input-output cascade configurations. The main objectives of the project include studying the formation and representation of ODE-PDE systems with nonlinearities described by both the Wiener and Hammerstein models. Additionally, the project aims to develop controllers and conduct stability analysis for these systems. The key contributions of the project are the development of a backstepping controller for the Wiener ODE system coupled with a heat PDE system, along with performing stability analysis for the same. Furthermore, the research led to the design of a backstepping controller for a Hammerstein ODE system cascaded with a wave PDE system and the corresponding stability analysis. A similar contribution was made for the Hammerstein ODE system cascaded with a heat PDE system, where both the controller design and stability analysis were achieved. A significant future milestone is to extend the development to handle coupled ODE-PDE systems with different classes of nonlinearity, which is expected to enrich the real-world applications. In summary, this research makes valuable contributions to boundary control strategies for nonlinear coupled ODE-PDE systems, providing initial steps for further work on more complex systems.14 0Item Restricted LOW SENSITIVITY DESIGN OF NONLINEAR SYSTEMS USING LINEARIZED MODELS(Wichita State University, 2024-05-17) Alotaibi, Jameelah Saad; Delillo, ThomasLow sensitivity linearized models ensure that the predictability and stability of nonlinearized models are achieved in a very assertive manner. The stability, which characterizes the trajectory in terms of equilibrium point, is of utmost importance. It should be noted that an equilibrium is considered asymptotically stable when there is a Lyapunov function present. One must not overlook the fact that the linear optimal state feedback for quadratic criteria, which do not include sensitivity, has the remarkable ability to automatically reduce sensitivity. It is an undeniable fact that the maximization of performance measures or the minimization of cost functions plays a crucial role in ensuring optimization. The primary focus of the research conducted was to significantly reduce the adverse impact of uncertainty on low sensitivity nonlinear models. To achieve this, a single perturbation technique was employed to convert the high-order system into a reduced model. This approach not only simplifies implementation but also effectively mitigates the impact of uncertainty. Additionally, the application of the KF estimator further enhances the reliability of the methodology. In this particular case, the static output feedback gain emerges as a more static and reliable output feedback control method that eliminates the need for an observer to estimate the states of system.21 0Item Restricted Nonlinear Models for Mixture Experiments Including Process Variables(University Of Southampton, 2024) Alzahrani, Shroug; Biedermann, StefanieThis present work is concerned with finding and assessing a class of models that flexibly fits data from mixture experiments and mixture-process variables experiments, and with providing guidelines for how to design mixture experiments and mixture-process variables experiments when these models are fitted. Most models in the literature are either based on polynomials and are therefore not very flexible, or have a large number of parameters that make the response surface interpretation difficult to understand. The modified fractional polynomial models are a recent class of models from the literature that are flexible and parsimonious but quite restrictive. We contribute to mixture experiments by proposing a new class of nonlinear models, the complement mixture fractional polynomial (CMFP) models, by making an additional transformation of the fractional polynomial, which results in less restrictive models while retaining (and indeed exceeding) the advantages of this class. Moreover, we suggest an extended form for the modified fractional polynomial models to fit data from mixture-process variables experiments.13 0Item Metadata only LOW SENSITIVITY DESIGN OF NONLINEAR SYSTEMS USING LINEARIZED MODELS(Wichita State University, 2024-05-17) Alotaibi, Jameelah Saad; Delillo, ThomasLow sensitivity linearized models ensure that the predictability and stability of nonlinearized models are achieved in a very assertive manner. The stability, which characterizes the trajectory in terms of equilibrium point, is of utmost importance. It should be noted that an equilibrium is considered asymptotically stable when there is a Lyapunov function present. One must not overlook the fact that the linear optimal state feedback for quadratic criteria, which do not include sensitivity, has the remarkable ability to automatically reduce sensitivity. It is an undeniable fact that the maximization of performance measures or the minimization of cost functions plays a crucial role in ensuring optimization. The primary focus of the research conducted was to significantly reduce the adverse impact of uncertainty on low sensitivity nonlinear models. To achieve this, a single perturbation technique was employed to convert the high-order system into a reduced model. This approach not only simplifies implementation but also effectively mitigates the impact of uncertainty. Additionally, the application of the KF estimator further enhances the reliability of the methodology. In this particular case, the static output feedback gain emerges as a more static and reliable output feedback control method that eliminates the need for an observer to estimate the states of system.35 0