On a Connection between Procedural and Applicative Languages

This paper reports on the connection between procedural and applicative languages. It presents features, notions and methods derived from abstract data type theory that in our judgement are helpful and necessary for multi-level software engineering environments in general, and especially for the treatment of verification issues there. Reference is made to an existing software engineering system and exemplary languages of it. A denotational semantics based on algebraic structures is introduced and employed. Since object-orientedness is looked at as one of the most important properties of such environments the notion of correctness is applied to objects and object relations. Finally a realistic semi-automatic method for the check of correctness criteria is given, accompanied by remarks on our existing implementation

The Variable Gradient Method of Generating Liapunov Functions with Application to Automatic Control Systems

The contribution of this thesis is the introduction and development of the variable gradient method of generating Liapunov functions. A Liapunov function, V, is considered to be generated if the form of V is not known before the generating procedure is applied. Two previous attempts at the generation of Liapunov functions to prove global asymptotic stability for nonlinear autonomous systems have been made. These attempts are summarized and evaluated in some detail, as they form the basis for the variable gradient approach proposed in this thesis. It is assumed that the system whose stability is being investigated is represented by n first order, ordinary, nonlinear differential equations in state variable form The particular state variables used throughout the thesis are the phase variables. This was done for convenience. The problem of finding a scalar V(x) to satisfy a particular Liapunov theorem is recast into the problem of finding a vector function, \nabla V, having suitable properties. As the name implies, \nabla V is assumed to be a vector of n elements, \nabla Vi, each of which has n arbitrary coefficients. These coefficients, designated as α ij may be constants or functions of the state variables, In its most general form, the variable gradient is assumed to be V may be determined as a line integral of \nabla V if the following (n-l)n/2 partial differential equations are satisfied. Here \nabla V^ are the elements of the vector \nabla V. The equations (3) are referred to as generalized curl equations. dv/dt may also be determined from \nabla V. An outline of the procedure by which a suitable V and dY/dt may be determined for a particular problem, starting from the variable gradient of (2) is as follows, 1. Assume a gradient of the form (2), 2. From the variable gradient, determine dV/dt by equation (4). 3. In conjunction with and subject to the requirements of the generalized curl equations (3), constrain dV/dt to be at least negative semi- definite, 4. From the now known \nabla V, determine V, 5. Invoke the necessary theorem to establish stability, Numerous examples are worked to illustrate the procedure outlined above, V functions are generated that involve higher order terms in x, integrals, and terms involving three state variables as factors. The problem of determining Hurwitz like criteria for nonlinear systems is considered in some detail. The last chapter attempts to extend .the variable gradient approach to nonautonosnous systems. The results of this chapter, though somewhat marginal, are of interest from the point of view of further researc

An operational approach to semantics and translation for concurrent programming languages

The problems of semantics and translation for concurrent programming languages are studied in this thesis. A structural operational approach is introduced to specify the semantics of parallelism and communication. Using this approach, semantics for the concurrent programming languages CSP (Hoare's Communicating Sequential Processes), multitasking and exception handling in Ada, Brinch-Hansen's Edison and CCS (Milner's Calculus of Communicating Systems) are defined and some of their properties are studied. An operational translation theory for concurrent programming languages is given. The concept of the correctness of a translation is formalised, the problem of composing transitions is studied and a composition theorem is proved. A set of sufficient conditions for proving the correctness of a translation is given. A syntax-directed translation from CSP to CCS is given and proved correct. Through this example the proof techniques of this approach is demonstrated. Finally, as an application of operational semantics and translation, a proposal for implementing multitasking in Ada is given via a two-step syntax-directed translation

System analysis, modelling and control with polytopic linear models

This research investigates the suitability of Polytopic Linear Models (PLMs) for the analysis, modelling and control of a class of nonlinear dynamical systems. The PLM structure is introduced as an approximate and alternative description of nonlinear dynamical systems for the benefit of system analysis and controller design. The model structure possesses three properties that we would like to exploit. Firstly, a PLM is build upon a number of linear models, each one of which describes the system locally within a so-called operating regime. If these models are combined in an appropriate way, that is by taking operating point dependent convex combinations of parameter values that belong to the different linear models, then a PLM will result. Consequently, the parameter values of a PLM vary within a polytope, and the vertices of this polytope are the parameter values that belong to the different linear models. A PLM owes its name to this feature. Accordingly, a PLM can be interpreted on the basis of a regime decomposition. Secondly, since a PLM is based on several linear models, it is possible to describe the nonlinear system more globally compared to only a single linear model. Thirdly, it is demonstrated that, under the appropriate conditions, nonlinear systems can be approximated arbitrary close by a PLM, parametrized with a finite number of parameters. There will be given an upper bound for the number of required parameters, that is sufficient to achieve the prescribed desired accuracy of the approximation. An important motivation for considering PLMs rests on its structural similarities with linear models. Linear systems are well understood, and the accompanying system and control theory is well developed. Whether or not the control related system properties such as stability, controllability etcetera, are fulfilled, can be demonstrated by means of (often relatively simple) mathematical manipulations on the linear system’s parameterization. Controller design can often be automated and founded on the parameterization and the control objective. Think of control laws based on stability, optimality and so on. For nonlinear systems this is only partly the case, and therefore further development of system and control theory is of major importance. In view of the similarities between a linear model and a PLM, the expectation exists that one can benefit from (results and concepts of) the well developed linear system and control theory. This hypothesis is partly confirmed by the results of this study. Under the appropriate conditions, and through a simple analysis of the parametrization of a PLM, it is possible to establish from a control perspective relevant system properties. One of these properties is stability. Under the appropriate conditions stability of the PLM implies stability of the system. Moreover, a few easy to check conditions are derived concerning the notion of controllability and observability. It has to be noticed however, that these conditions apply to a class of PLMs of which the structure is further restricted. The determination of system properties from a PLM is done with the intention to derive a suitable model, and in particular to design a model based controller. This study describes several constructive methods that aim at building a PLM representation of the real system. On the basis of a PLM several control laws are formulated. The main objective of these control laws is to stabilize the system in a desired operating point. A few computerized stabilizing control designs, that additionally aim at optimality or robustness, are the outcome of this research. The entire route of representing a system with an approximate PLM, subsequently analyzing the PLM, and finally controlling the system by a PLM based control design is illustrated by means of several examples. These examples include experimental as well as simulation studies, and nonlinear dynamic (mechanical) systems are the subject of research

Parameterized macromodeling of passive and active dynamical systems

L'abstract è presente nell'allegato / the abstract is in the attachmen

Qualitative Properties of Stochastic Hybrid Systems and Applications

Hybrid systems with or without stochastic noise and with or without time delay are addressed and the qualitative properties of these systems are investigated. The main contribution of this thesis is distributed in three parts. In Part I, nonlinear stochastic impulsive systems with time delay (SISD) with variable impulses are formulated and some of the fundamental properties of the systems, such as existence of local and global solution, uniqueness, and forward continuation of the solution are established. After that, stability and input-to-state stability (ISS) properties of SISD with fixed impulses are developed, where Razumikhin methodology is used. These results are then carried over to discussed the same qualitative properties of large scale SISD. Applications to automated control systems and control systems with faulty actuators are used to justify the proposed approaches. Part II is devoted to address ISS of stochastic ordinary and delay switched systems. To achieve a variety stability-like results, multiple Lyapunov technique as a tool is applied. Moreover, to organize the switching among the system modes, a newly developed initial-state-dependent dwell-time switching law and Markovian switching are separately employed. Part III deals with systems of differential equations with piecewise constant arguments with and without random noise. These systems are viewed as a special type of hybrid systems. Existence and uniqueness results are first obtained. Then, comparison principles are established which are later applied to develop some stability results of the systems

New approaches to higher-dimensional general relativity

This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the future. Unfortunately, many calculations using the Newman-Penrose formalism can be unnecessarily complicated. To address this, I describe new work introducing a higher-dimensional generalization of the so-called Geroch-Held-Penrose formalism, which allows for a partially covariant reformulation of general relativity. This approach provides great simplifications for many calculations involving spacetimes which admit one or two preferred null directions. The next chapter describes the proof of an important result regarding algebraic classification in higher dimensions. The classification is based upon the existence of a particular null direction that is aligned with the Weyl tensor of the geometry in some appropriate sense. In four dimensions, it is known that a null vector field is such a multiple Weyl aligned null direction (WAND) if and only if it is tangent to a shearfree null geodesic congruence. This is not the case in higher dimensions. However, I have formulated and proved a partial generalization of the result to arbitrary dimension, namely that a spacetime admits a multiple WAND if and only if it admits a geodesic multiple WAND. Moving onto more physical applications, I describe how the formalism that we have developed can be applied to study certain aspects of the stability of extremal black holes in arbitrary dimension. The final chapter of the thesis has a rather different flavour. I give a detailed analysis of the properties of a particular solution to the Einstein equations in five dimensions: the Pomeransky-Sen'kov doubly spinning black ring. I study geodesic motion around this black ring and demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics. I show that this unexpected separability can be understood in terms of a symmetry described by a conformal Killing tensor on a four dimensional spacetime obtained by a Kaluza-Klein reduction of the original black ring spacetime.This work was supported by the Science and Technology Facilities Council (student number ST/F003978/1

A comparative study of the maximum principle and the multi-level system theory and their application

LD2668 .T4 1966 C52Master of Scienc

BRAND PROTECTION FOR STEEL PACKAGING PRODUCTS

In recent years, the underground market of counterfeit products has grown into a global network, causing the raised concern of the general public and initiating a series of reforms in governmental regulations and policies worldwide. As the largest independent metal decorating business in the UK, Tinmasters is at the centre of these developments. The overall aim of this project was the development of a novel anti-counterfeiting technology that is compatible with Tinmasters’ manufacturing process, food contact/safe, and preferably overt, with a special focus on aesthetic appeal. A review of pre-existing technologies revealed a trend toward systems relying on the fast-growing capacity of wireless internet and smartphone devices. The latest anti-counterfeiting systems are track-and-trace enabled and offer user-based product authentication. The review narrowed the scope of the project to the development of a scheme for the creation of printable 2D codes,capable to store information that can be retrieved using a smartphone device. The core element of the feature is a trajectory of a 3D nonlinear dynamical system operating within its chaotic region, which is captured by the system’s “strange” attractor. These types of trajectories are known for their high complexity and thought, by many, to possess beauty. More importantly, they can be retrieved via a mechanism known as chaotic synchronisation. In order to create a printable code, a 3D chaotic trajectory is projected to two dimensions. The printed feature is captured by a smartphone camera and is subsequently processed in order to retrieve the trajectory. An almost equally important element of the feature is a frame, especially designed to address matters of alignment, perspective correction, and coordinate transformations. Aside form the main field of nonlinear dynamics, the proposed scheme makes use of concepts and methods from the fields of image processing, digital photography, and numerical analysis

Stability Analysis of Magnetised Neutron Stars - a Semi-Analytic Approach

The stability problem of magnetised neutron stars is addressed by applying a new semi-analytic method for stability analysis which is based on the energy variational principle. It is shown that the semi-analytic method represents a valuable tool for stability investigations, aiming at explaining the durability and long-lasting stability of magnetised neutron stars. The method provides the opportunity to constrain the interior neutron star magnetic field structure which is still widely unknown but highly interesting for all kinds of neutron star studies. This work describes the analytical and numerical setup of the method and shows applications on neutron star models with polytropic as well as non-barotropic equations of state, purely toroidally and purely poloidally magnetised stars as well as mixed magnetic fields. The validity of the Cowling approximation is tested and new physical insights are presented.Diese Arbeit befasst sich mit dem Stabilitätsproblem magnetisierter Neutronensterne, unter Verwendung einer neuen semi-analytischen Untersuchungsmethode zur Stabilitätsanalyse, welche auf dem Energievariationsprinzip basiert. Es wird gezeigt, dass die semi-analytische Methode ein nützliches Hilfsmittel darstellt, um die Ursachen von hoher Lebensdauer und anhaltender Stabilität magnetisierter Neutronensterne zu untersuchen. Die Methode ermöglicht es die bislang weitgehend unbekannte, aber für alle Arten von Neutronensternuntersuchungen hochinteressante, innere Magnetfeldstruktur von Neutronensternen einzugrenzen. In dieser Arbeit werden der analytische und numerische Aufbau der Methode sowie Anwendungen auf Neutronensternmodelle mit polytroper und nicht-barotroper Zustandsgleichung, rein toroidalem, rein poloidalem und gemischtem Magnetfeld gezeigt. Die Gültigkeit der Cowling-Näherung wird untersucht und neue physikalische Erkenntnisse werden präsentiert