Tubular reactors cover a large class of processes in chemical and biochemical engineering. They are typically reactors in which the medium is not homogeneous (like fixed-bed reactors, packed-bed reactors, fluidized-bed reactors,...) and possibly involve diferent phases (liquid/solid/gas). The dynamics of nonisothermal axial dispersion or plug flow tubular reactors are described by semilinear partial differential equations (PDE's) derived from mass and energy balances. The main source of nonlinearities in such dynamics is concentrated in the kinetics terms of the model equations. Like tubular reactors many physical phenomena are modelled by partial differential equations (PDE's). Such systems are called distributed parameter systems. Control problems of these systems can be formulated in state-space form in a way analogous to those of lumped parameter systems (those described by ordinary differential equations) if one introduces a suitable infinite-dimensional state-space and suitable operators instead of the usual matrices. This thesis deals with the synthesis of optimal control laws with a view to regulate the temperature and the reactant concentration of a nonisothermal plug flow reactor model. Several tools of linear and semilinear infinite-dimensional system theory are extended and/or developed, and applied to this model. On the one hand, the concept of asymptotic stability is studied for a class of infinite-dimensional semilinear Banach state- space systems. Asymptotic stability criteria are established, which are based on the concept of strictly m-dissipative operator. This theory is applied to a nonisothermal plug flow reactor. On the other hand, the concept of optimal Linear-Quadratic (LQ) feedback is studied for class of infinite-dimensional linear systems. This theory is applied to a linearized plug flow reactor model in order to design an LQ optimal feedback controller. Then the resulting nonlinear closed-loop system performances are analyzed. Finally this control design strategy is extended to a large class of first-order hyperbolic PDE's systems.

We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter.

In this work we are concerned with the characterization of certain classes of stochastic processes via duality formulae. First, we introduce a new formulation of a characterization of processes with independent increments, which is based on an integration by parts formula satisfied by infinitely divisible random vectors. Then we focus on the study of the reciprocal classes of Markov processes. These classes contain all stochastic processes having the same bridges, and thus similar dynamics, as a reference Markov process. We start with a resume of some existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. In the context of pure jump processes we derive the following new results. We will analyze the reciprocal classes of Markov counting processes and characterize them as a group of stochastic processes satisfying a duality formula. This result is applied to time-reversal of counting processes. We are able to extend some of these results to pure jump processes with different jump-sizes, in particular we are able to compare the reciprocal classes of Markov pure jump processes through a functional equation between the jump-intensities.

Esta tesis se propone el estudio de la relación entre propiedades de un anillo R y propiedades de algunos de sus anillos de matrices infinitas. Así, un resultado "modelo" sobre este problema será de la forma: "Sean P y Q dos propiedades. El anillo R cumple la propiedad P si y sólo cierto anillo de matrices infinitas, S, sobre R, cumple la propiedad Q.Los tipos principales de anillos de matrices infinitas sobre algún anillo R consideradas en este trabajo son, primero, aquellas que tienen un número finito de entradas no nulas en cada fila, conocidas como "matrices de filas finitas" y, segundo, aquellas que tienen en cada fila y cada columna un número finito de entradas no nulas, conocidas como "matrices de filas y columnas finitas. / The purpose of this thesis is the study of the relationship between properties of a ring R and properties of some of its infinite matrix rings.A standard result in this topics may be stated as: "Let P and Q two properties. The ring R satisfies property P if and only if certain infinite matrix ring, S, over R, satisfies property Q.The principal infinite matrix types considered in this thesis are, first, those matrices that have a finite number of nonzero entries in each row, known as "row finite matrices", and second, those matrices that have a finite number of nonzero elements in each row and each column, known as "row and column finite matrices".

Many important software systems, including communication protocols and concurrent and distributed algorithms generate infinite state-spaces. Model-checking which is the most prominent algorithmic technique for the verification of concurrent systems is restricted to the analysis of finite-state models. Algorithmic analysis of infinite-state models is complicated--most interesting properties are undecidable for sufficiently expressive classes of infinite-state models. In this thesis, we focus on the development of algorithmic analysis techniques for two important classes of infinite-state models: FIFO Systems and Parameterized Systems. FIFO systems consisting of a set of finite-state machines that communicate via unbounded, perfect, FIFO channels arise naturally in the analysis of distributed protocols. We study the problem of computing the set of reachable states of a FIFO system composed of piecewise components. This problem is closely related to calculating the set of all possible channel contents, i.e. the limit language. We present new algorithms for calculating the limit language of a system with a single communication channel and important subclasses of multi-channel systems. We also discuss the complexity of these algorithms. Furthermore, we present a procedure that translates a piecewise FIFO system to an abridged structure, representing an expressive abstraction of the system. We show that we can analyze the infinite computations of the more concrete model by analyzing the computations of the finite, abridged model. Parameterized systems are a common model of computation for concurrent systems consisting of an arbitrary number of homogenous processes. We study the reachability problem in parameterized systems of infinite-state processes. We describe a framework that combines Abstract Interpretation with a backward-reachability algorithm. Our key idea is to create an abstract domain in which each element (a) represents the lower bound on the number of processes at a control location and (b) employs a numeric abstract domain to capture arithmetic relations among variables of the processes. We also provide an extrapolation operator for the domain to guarantee sound termination of the backward-reachability algorithm.

The accuracy, ease of use, and execution time of the finite element method based software Maxwell coupled to the system simulation software Simplorer was evaluated for simulation of hydropower generator - power grid interaction. A generator test rig were modelled in Maxwell and coupled to Simplorer with a strong circuit coupling as a single machine infinite bus system. The accuracy of the model was measured by comparing the simulated output power oscillation frequency and damping characteristics to the measured ones after a torque step. The result shows that the difference in output power oscillation frequency between the model and the generator test rig was small, and that the difference in damping characteristics was significant. The usability of the software package was found to be fair, as were the execution times.

Many important software systems, including communication protocols and concurrent and distributed algorithms generate infinite state-spaces. Model-checking which is the most prominent algorithmic technique for the verification of concurrent systems is restricted to the analysis of finite-state models. Algorithmic analysis of infinite-state models is complicated--most interesting properties are undecidable for sufficiently expressive classes of infinite-state models. In this thesis, we focus on the development of algorithmic analysis techniques for two important classes of infinite-state models: FIFO Systems and Parameterized Systems. FIFO systems consisting of a set of finite-state machines that communicate via unbounded, perfect, FIFO channels arise naturally in the analysis of distributed protocols. We study the problem of computing the set of reachable states of a FIFO system composed of piecewise components. This problem is closely related to calculating the set of all possible channel contents, i.e. the limit language. We present new algorithms for calculating the limit language of a system with a single communication channel and important subclasses of multi-channel systems. We also discuss the complexity of these algorithms. Furthermore, we present a procedure that translates a piecewise FIFO system to an abridged structure, representing an expressive abstraction of the system. We show that we can analyze the infinite computations of the more concrete model by analyzing the computations of the finite, abridged model. Parameterized systems are a common model of computation for concurrent systems consisting of an arbitrary number of homogenous processes. We study the reachability problem in parameterized systems of infinite-state processes. We describe a framework that combines Abstract Interpretation with a backward-reachability algorithm. Our key idea is to create an abstract domain in which each element (a) represents the lower bound on the number of processes at a control location and (b) employs a numeric abstract domain to capture arithmetic relations among variables of the processes. We also provide an extrapolation operator for the domain to guarantee sound termination of the backward-reachability algorithm.

Based on the Lyapunov stability theorem, a sliding mode control design methodology is proposed in this thesis for a class of perturbed switched systems. The control of the systems is rest restricted to switching between two different constant values. New sliding mode reaching conditions are proposed for the controllers so that the controlled systems can enter the sliding mode in finite time. Once the switched control system is in the sliding mode, the stability of the system is guaranteed by choosing a suitable sliding surface. In addition, a method for alleviating the infinite switching phenomenon is also provided in this thesis. Finally, a numerical and a practical example with computer simulation results are given for demonstrating the feasibility of the proposed control scheme.

The inverse nodal problem is the problem of understanding the potential function of the Sturm-Liouville operator from the set of the nodal data ( zeros of eigenfunction ). This problem was first defined by McLaughlin[12]. Up till now, the problem on finite intervals has been studied rather thoroughly. Uniqueness, reconstruction and stability problems are all solved. In this thesis, I investigate the inverse nodal problem on semi-infinite intervals q(x) is real and continuous on [0,1) and q(x)!1, as x!1. we have the following proposition. L is in the limit-point case. The spectral function of the differential operator in (1) is a step function which has discontinuities at { k} , k = 0, 1, 2, .... And the corresponding solutions (eigenfunction) k(x) = (x, k) has exactly k zeros on [0,1). Furthermore { k} forms an orthogonal set. Finally we also discuss that density of nodal points and a reconstruction formula on semiinfinite intervals.

The Finite-Difference Time-Domain Method (FDTD) is a very powerful numerical method for the full wave analysis electromagnetic phenomena. Due to its flexibility, it can be used to solve numerous electromagnetic scattering problems on microwave circuits, dielectrics, and electromagnetic absorption in biological tissue at microwave frequencies. However, it needs so much computation time to simulate microwave integral circuits by applying the FDTD method. If the structure we simulated is complicated and we want to obtain accurate frequency domain scattering parameters, the simulation time will be so much longer that the efficiency of simulation will be bad as well. Therefore, in the thesis, we introduce an artificial neural networks (ANN) method called ¡§Infinite Impulse Response Neural Networks (IIRNN)¡¨ can speed up the FDTD simulation time. In order to boost the efficiency of the FDTD simulation time by stopping the simulation after a sufficient number of time steps and using FIRNN as a predictor to predict time series signal.