Distributed formation tracking control of multiple car-like robots

In this thesis, distributed formation tracking control of multiple car-like robots is studied. Each vehicle can communicate and send or receive states information to or from a portion of other vehicles. The communication topology is characterized by a graph. Each vehicle is considered as a vertex in the graph and each communication link is considered as an edge in the graph. The unicycles are modeled firstly by both kinematic systems. Distributed controllers for vehicle kinematics are designed with the aid of graph theory. Two control algorithms are designed based on the chained-form system and its transformation respectively. Both algorithms achieve exponential convergence to the desired reference states. Then vehicle dynamics is considered and dynamic controllers are designed with the aid of two types of kinematic-based controllers proposed in the first section. Finally, a special case of switching graph is addressed considering the probability of vehicle disability and links breakage

Effect of Temperature on the Corrosion Behaviours of L360QCS in the Environments Containing Elemental Sulphur and H₂S/CO₂

The effect of temperature on the corrosion behaviours of L360QCS in H₂S, CO₂ and elemental sulphur environments are investigated. The corrosion weight-loss rate, microscopy, chemical compositions and phase compositions of corrosion products are studied by means of the weight-loss analysis, SEM and XRD techniques. As shown, the corrosion rate increased greatly with an increase of the temperature, and the corrosion scale is dropped off easily because of the weak adhesion force between the matrix and the corrosion products. The composition and structure analysed by energy-dispersive x-ray spectroscopy (EDS) and XRD show that the corrosion product scales are composed of cubic FeS and little tetragonal FeS.Исследовано влияние температуры на режимы коррозии L360QCS в атмосферах H₂S, CO₂ и атомарной серы. Скорость коррозии, измеряемая по потере веса, микроскопия, химический и фазовый состав продуктов коррозии определялись анализом потери веса, СЭМ и рентгеноструктурным анализом (РСА). Показано, что скорость коррозии сильно возрастает с температурой, и коррозионная окалина легко отпадает благодаря слабой силе адгезии между матрицей и продуктами коррозии. Исследования состава и структуры методами рентгеноспектрального электронно-зондового микроанализа и РСА показали, что окалины продуктов реакции состоят из кубического FeS и небольшой части тетрагонального FeS.Досліджено вплив температури на режими корозії L360QCS в атмосфері H₂S, CO₂ та атомарної сірки. Швидкість корозії, яка вимірюється за втратами ваги, мікроскопія, хемічний та фазовий склад продуктів корозії визначалися аналізою втрати ваги, СЕМ та рентґеноструктурною аналізою (РСА). Показано, що швидкість корозії сильно збільшується з температурою, і корозійна жужелиця легко відпадає через слабку силу адгезії між матрицею та продуктами корозії. Дослідження складу та структури методами рентґеноспектральної електронно-зондової мікроаналізи та РСА показали, що жужелиці продуктів реакції складаються з кубічного FeS та незначної частки тетрагонального FeS

Virtual Element Methods Without Extrinsic Stabilization

Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension under the mesh assumption that all the faces of each polytope are simplices. The key is to construct local $H({\rm div})$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization.Comment: 25 pages, 8 figure

Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements

This paper delves into the world of high-order curl and div elements within finite element methods, providing valuable insights into their geometric properties, indexing management, and practical implementation considerations. It first explores the decomposition of Lagrange finite elements. The discussion then extends to H(div)-conforming finite elements and H(curl)-conforming finite element spaces by choosing different frames at different sub-simplex. The required tangential continuity or normal continuity will be imposed by appropriate choices of the tangential and normal basis. The paper concludes with a focus on efficient indexing management strategies for degrees of freedom, offering practical guidance to researchers and engineers. It serves as a comprehensive resource that bridges the gap between theory and practice in the realm of high-order curl and div elements in finite element methods, which are vital for solving vector field problems and understanding electromagnetic phenomena.Comment: 25 pages, 8 figure

Anisotropic analysis of VEM for time-harmonic Maxwell equations in inhomogeneous media with low regularity

It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal convergence for low-regularity solutions heavily relies on conforming spaces and highly-regular simplicial meshes. This can be a significant limitation for many popular methods based on polytopal meshes in the case of inhomogeneous media, as the discontinuity of electromagnetic parameters can lead to quite low regularity of solutions near media interfaces, and potentially worsened by geometric singularities, making many popular methods based on broken spaces, non-conforming or polytopal meshes particularly challenging to apply. In this article, we present a virtual element method for solving an indefinite time-harmonic Maxwell equation in 2D inhomogeneous media with quite arbitrary polytopal meshes, and the media interface is allowed to have geometric singularity to cause low regularity. There are two key novelties: (i) the proposed method is theoretically guaranteed to achieve robust optimal convergence for solutions with merely $\mathbf{H}^{\theta}$ regularity, $\theta\in(1/2,1]$; (ii) the polytopal element shape can be highly anisotropic and shrinking, and an explicit formula is established to describe the relationship between the shape regularity and solution regularity. Extensive numerical experiments will be given to demonstrate the effectiveness of the proposed method