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Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 150-154).

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In this thesis, a class of control and identification methods on a typical laboratory process - a ball and beam system - are discussed. The ball and beam is a common laboratory process which contains nonlinearity, a double integrator and time-delay. In our project, the hardware made by Wincon (Quanser SRV02 +BB01) is used. The main contribution of this work is the development of a variety of controller design methods, which together with suitable parameter identification techniques provide tools for rapid prototyping for real time control of processes within the laboratory, in preparation for industrial implementation of more complex schemes. The novelty of this work lies in the use of model predictive control (MPC) methods based on a non-minimal state space formulation, which permits the inclusion of process measurements and actuations in the state vector, leading to controller designs which are immediately ready for on-line implementation. A linear MPC controller based on a non-minimal state space model is based on an approximate linear model. The results from simulation and online experiment show that the linear MPC controller realizes a satisfying reference tracking in the face of nonlinearity and time-delay. In the following chapter, a nonlinear Hammerstein model is identified, which is a type of reliable structure for describing nonlinear plants. A nonlinear MPC scheme is developed based on the Hammerstein model. An inversion block is created to cancel the effect of the nonlinearity. The performance IS also tested in both simulation and experiment. Finally, MPC is combined with sliding mode control. The non-minimal state space model is also used here. In the first part of this chapter, the idea underlying sliding mode control contributes a method of modifying the definition of the cost function in MPC. In the second half, MPC is used to design the switching surface in sliding mode control. The performance of tests on the example (ball and beam system) illustrates that these are both valid methods for dealing with complex processes.

The thesis is concerned with the inversion of matrices and the solution of linear systems and eigensystems in a parallel environment. Following an introductory chapter of concepts and definitions in the field of linear algebra, a general survey of parallel machines and algorithms is presented in Chapters 2 and 3, including a detailed description of the Distributed Array Processor (DAP) and the Neptune multiprocessing system. In Chapter 4, a new technique, the double-bordering algorithm, for the solution of linear systems is derived, and its application to the parallel solution of difference systems described. A modified form of the method for the inversion of matrices is derived, implemented on the Neptune multiprocessing system, and its performance compared with that of the Gauss-Jordan and (single) bordering algorithms. The results of the implementation of several other parallel algorithms are also presented. Chapter 5 deals with the class of matrices known as Toeplitz matrices, which arise in the field of signal processing. Trench's algorithm for the inversion of such matrices is implemented on the Neptune multiprocessing system, and, for the solution of banded symmetric Toeplitz systems, the relative efficiencies of three sequential strategies are compared: Levinson's algorithm, the double-bordering algorithm, and a method based on a novel factorisation scheme. Chapter 6 is concerned with the implementation of various iterative methods on the DAP. The solution of several difference systems by the Jacobi, Gauss-Seidel and successive over-relaxation (SOR) algorithms is compared with their solution by a variation (c. 1943) of the algorithms proposed by Hotelling, in which matrix-vector products are replaced by successive matrix squarings. The technique is also applied to the power method for the solution of the eigenvalue problem. The thesis concludes with a summary and recommendations for future work.

This thesis is concerned with various problems associated with the factorisation and feedback stabilisation of multidimensional linear discrete systems, which may be represented by rational matrices in several variables. Some factorisation techniques for polynomial and rational matrices in several variables have been explored and applied to the study of feedback stabilisation of multidimensional linear systems. The work presented here may be divided into two parts. The first part (Chapters 2 and 3) is concerned with two-dimensional systems, while the second part (Chapters 4 and 5) deals with three- and higher-dimensional systems. The emphasis of the first part is placed on the development of constructive algorithms for several kinds of factorisation of polynomial and rational matrices in two variables. In Chapter 2, an algorithm for obtaining primitive factorisation of polynomial matrices in two variables is developed, which is then followed by an algorithm for the decomposition of a rational matrix in two variables into factor coprime matrix fraction descriptions. Chapter 3 presents a procedure for the analysis and compensator design of two-dimensional feedback systems. A constructive algorithm for solving a Diophantine-type equation in two variables is derived. A necessary and sufficient condition for the feedback stabilisability of two-dimensional systems is obtained. The complete set of stabilising compensators for a given two-dimensional plant is then characterised. The role played by the matrix fraction description approach in the study of three- and higher dimensional systems, particularly with respect to the feedback stabilisation of these systems, is then investigated in detail in the second part. Chapter 4 deals with various kinds of factorisations for polynomial and rational matrices in three or more variables. For example, a criterion for the existence of primitive factorisation of a class of polynomial matrices in three or more variables is derived. By introducing a new concept: <i>generating polynomials</i>, it is shown that a direct generalisation of several existing results in two-dimensional systems theory to their higher-dimensional counterparts is not possible. In chapter 5, applying the generating polynomials, we obtain a stability test and a necessary and sufficient condition for feedback stabilisability of three- and higher-dimensional systems.

There is an increasing amount of evidence in scientific research and industrial engineering indicating that the graphic processing unit (GPU) has a higher efficiency and a stronger ability over CPUs to process certain computations. The heat equation is one of the most well-known partial differential equations with well-developed theories, and application in engineering. Thus, we chose in this report to use the heat equation to numerically solve for the heat distributions at different time points using both GPU and CPU programs. The heat equation with three different boundary conditions (Dirichlet, Neumann and Periodic) were calculated on the given domain and discretized by finite difference approximations. The programs solving the linear system from the heat equation with different boundary conditions were implemented on GPU and CPU. A convergence analysis and stability analysis for the finite difference method was performed to guarantee the success of the program. Iterative methods and direct methods to solve the linear system are also discussed for the GPU. The results show that the GPU has a huge advantage in terms of time spent compared with CPU in large size problems.

Chang, Kwong Wa = 一般量子系統非馬可夫領域的主方程 / 張光華. / "October 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 89-92). / Abstracts in English and Chinese. / Chang, Kwong Wa = Yi ban liang zi xi tong fei Makefu ling yu de zhu fang cheng / Zhang Guanghua. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Born-Markov Master Equations --- p.4 / Chapter 2.1 --- Master Equations from von Neumann equation --- p.4 / Chapter 2.2 --- Born Approximation --- p.6 / Chapter 2.3 --- Markov Approximation --- p.8 / Chapter 2.4 --- Born-Markov Approximation --- p.10 / Chapter 2.5 --- Lindblad Equation --- p.12 / Chapter 2.6 --- The Limitations of the Born-Markov Approximation --- p.16 / Chapter 2.7 --- Beyond Born and Markov Approximations --- p.20 / Chapter 2.7.1 --- General projection operator approach --- p.20 / Chapter 2.7.2 --- Time-local form of the master equation --- p.21 / Chapter 3 --- TCL non-Markovian Master Equation for Linear Systems --- p.24 / Chapter 3.1 --- Model --- p.24 / Chapter 3.2 --- The General Structure of the TCL non-Markovian Master Equation for Initially Factorizable States --- p.27 / Chapter 3.3 --- Determination of Unknown Coefficients --- p.32 / Chapter 3.4 --- Weak-Coupling Approximation --- p.46 / Chapter 3.5 --- Steady State Solutions --- p.51 / Chapter 4 --- An Application: Coherence Protection by Parity Kicks --- p.54 / Chapter 4.1 --- Review on Parity Kicks --- p.54 / Chapter 4.2 --- Parity Kicks oil Damped Harmonic Oscillators --- p.58 / Chapter 4.3 --- Numerical Results for Soft Pulses --- p.61 / Chapter 5 --- Other Initial States --- p.67 / Chapter 5.1 --- Factorizable States --- p.67 / Chapter 5.2 --- Non-Factorizable States --- p.73 / Chapter 6 --- Non-Markovianity --- p.75 / Chapter 6.1 --- The Concept of non-Markovianity --- p.75 / Chapter 6.2 --- A Recent Measure --- p.76 / Chapter 6.3 --- A Prospective Measure --- p.79 / Chapter 7 --- Conclusion --- p.87 / Bibliography --- p.89 / Chapter A --- Evolution of Factorizable Coherent State for Linear Damped Harmonic Oscillator with RWA --- p.93 / Chapter B --- "Derivation of G, L and F" --- p.95 / Chapter C --- Comparison of Equations of Motion for Master Equation Coefficients --- p.98