サイテキ セイギョ モンダイ ノ ケイサン ホウホウ ニ カンスル キソテキ ケンキュウ

京都大学0048新制・論文博士工学博士乙第2141号論工博第552号新制||工||234(附属図書館)UT51-47-K111(主査)教授 得丸 英勝, 教授 椹木 義一, 教授 三根 久学位規則第5条第2項該当Kyoto UniversityDFA

Constrained optimization using a conjugate gradient technique, with control applications

Imperial Users onl

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Computational and numerical aspects of full waveform seismic inversion

Full-waveform inversion (FWI) is a nonlinear optimisation procedure, seeking to match synthetically-generated seismograms with those observed in field data by iteratively updating a model of the subsurface seismic parameters, typically compressional wave (P-wave) velocity. Advances in high-performance computing have made FWI of 3-dimensional models feasible, but the low sensitivity of the objective function to deeper, low-wavenumber components of velocity makes these difficult to recover using FWI relative to more traditional, less automated, techniques. While the use of inadequate physics during the synthetic modelling stage is a contributing factor, I propose that this weakness is substantially one of ill-conditioning, and that efforts to remedy it should focus on the development of both more efficient seismic modelling techniques, and more sophisticated preconditioners for the optimisation iterations. I demonstrate that the problem of poor low-wavenumber velocity recovery can be reproduced in an analogous one-dimensional inversion problem, and that in this case it can be remedied by making full use of the available curvature information, in the form of the Hessian matrix. In two or three dimensions, this curvature information is prohibitively expensive to obtain and store as part of an inversion procedure. I obtain the complete Hessian matrices for a realistically-sized, two-dimensional, towed-streamer inversion problem at several stages during the inversion and link properties of these matrices to the behaviour of the inversion. Based on these observations, I propose a method for approximating the action of the Hessian and suggest it as a path forward for more sophisticated preconditioning of the inversion process.Open Acces

On-line monitoring of water distribution networks

This thesis is concerned with the development of a computer-based, real-time monitoring scheme which is a prerequisite of any form of on-line control. A new concept, in the field of water distribution systems, of water system state estimation is introduced. Its function is to process redundant, noise-corrupted telemeasurements in order to supply a real-time data base with reliable estimates of the current state and structure of the network. The information provided by the estimator can then be used in a number of on-line programs. In view of the strong nonlinearity of the network equations, two methods of state estimation, which have enhanced numerical stability, are examined in this thesis. The first method uses an augmented matrix formulation of a classical least-squares problem, and the second is based on a least absolute value solution of an over determined set of equations. Two water systems, one of which is a realistic 34-node network, are used to evaluate the performance of the proposed methods .The problem of bad data processing and its extension to the validation of network topology and leakage detection is also examined. It is shown that the method based on least absolute values estimation provides a more immediate indication of erroneous measurements. In addition, this method demonstrates the useful feature of eliminating the effects of gross errors on the final state estimate. The important question of water system observability is then studied. Two original combinatorial methods are proposed to check topological observability. The first one is an indirect technique which searches for a maximum measurement-to-branch matching and then attempts to build a spanning tree of the network graph using only the branches with measurement assignment. The second method is a direct search for an observable spanning tree. A number of systems are used to test both techniques, including a 34-node water supply network and an IEEE 118-bus power system. The problem of minimisation of distributed leakages is solved efficiently using a state estimation technique. Comparison of the head profile achieved for the calculated optimal valve controls with the standard operating conditions for a 25-node network indicates a major reduction of the volume of leakages. In the final part of this thesis a software package, which simulates the real-time operation of a water distribution system, is described. The programs are designed in such a way that by replacing simulated measurements with live telemetry data they can be directly used for. water network monitoring and control

Optimization Theory and Dynamical Systems: Invariant Sets and Invariance Preserving Discretization Methods

Invariant set is an important concept in the theory of dynamical systems and it has a wide range of applications in control and engineering. This thesis has four parts, each of which studies a fundamental problem arising in this field. In the first part, we propose a novel, simple, and unified approach to derive sufficient and necessary conditions, which are referred to as invariance conditions for simplicity, under which four classic families of convex sets, namely, polyhedral, polyhedral cones, ellipsoids, and Lorenz cones, are invariant sets for linear discrete or continuous dynamical systems. This novel method establishes a solid connection between optimization theory and dynamical systems. In the second part, we propose novel methods to compute valid or largest uniform steplength thresholds for invariance preserving of three classic types of discretization methods, i.e., forward Euler method, Taylor type approximation, and rational function type discretization methods. These methods enable us to find a pre-specified steplength threshold which preserves invariance of a set. The identification of such steplength threshold has a significant impact in practice. In the third part, we present a novel approach to ensure positive local and uniform steplength threshold for invariance preserving on a set when a discretization method is applied to a linear or nonlinear dynamical system. Our methodology not only applies to classic sets, discretization methods, and dynamical systems, but also extends to more general sets, discretization methods, and dynamical systems. In the fourth part, we derive invariance conditions for some classic sets for nonlinear dynamical systems. This part can be considered as an extension of the first part to a more general case

NASA/Howard University Large Space Structures Institute

Basic research on the engineering behavior of large space structures is presented. Methods of structural analysis, control, and optimization of large flexible systems are examined. Topics of investigation include the Load Correction Method (LCM) modeling technique, stabilization of flexible bodies by feedback control, mathematical refinement of analysis equations, optimization of the design of structural components, deployment dynamics, and the use of microprocessors in attitude and shape control of large space structures. Information on key personnel, budgeting, support plans and conferences is included