Robust Guaranteed Cost Control for Yaw Control of Helicopter

针对具有时变不确定性且不确定性界为椭球的线性系统提出了一种新的具有自适应机制的鲁棒保性能控制器设计方法。首先,引入一个具有可由自适应律在线调整的可调参数的目标模型,通过该参数来保证由目标模型与被控模型所获得的误差系统渐近稳定。结合保证目标模型稳定性的设计,最终形成保证闭环系统稳定且控制器增益仿射依赖于可调参数的鲁棒保性能跟踪控制器。应用于安装在试验平台上的小型直升机航向控制中,仿真试验表明了该方法的有效性。

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

复杂介质边界元法数值模拟研究

A major impetus to study the rough surface and complex structure in near surface model is because accuracy of seismic observation and geophysical prospecting can be improved. Wave theory study about fluid-satuated porous media has important significance for some scientific problems, such as explore underground resources, study of earth's internal structure, and structure response of multi-phase porous soil under dynamic and seismic effect. Seismic wave numerical modeling is one of the effective methods which understand seismic propagation rules in complex media. As a numerical simulation method, boundary element methods had been widely used in seismic wave field study. This paper mainly studies randomly rough surface scattering which used some approximation solutions based on boundary element method. In addition, I developed a boundary element solution for fluid saturated porous media. In this paper, we used boundary element methods which based on integral expression of wave equation to study the free rough surface scattering effects of Kirchhoff approximation method, Perturbation approximation method, Rytov approximation method and Born series approximation method. Gaussian spectrum model of randomly rough surfaces was chosen as the benchmark model. The approximation methods result were compared with exact results which obtained by boundary element methods, we study that the above approximation methods were applicable how rough surfaces and it is founded that this depends on and ( here is the wavenumber of the incident field, is the RMS height and is the surface correlation length ). In general, Kirchhoff approximation which ignores multiple scatterings between any two surface points has been considered valid for the large-scale roughness components. Perturbation theory based on Taylor series expansion is valid for the small-scale roughness components, as and are .Tests with the Gaussian topographies show that the Rytov approximation methods improves the Kirchhoff approximation in both amplitude and phase but at the cost of an extra treatment of transformation for the wave fields. The realistic methods for the multiscale surfaces come with the Born series approximation and the second-order Born series approximation might be sufficient to guarantee the accuracy of randomly rough surfaces. It could be an appropriate choice that a complex rough surface can be divided into large-, medium-, and small-scale roughness components with their scattering features be studied by the Kirchhoff or Rytov phase approximations, the Born series approximation, and the perturbation theory, respectively. For this purpose, it is important to select appropriate parameters that separate these different scale roughness components to guarantee the divided surfaces satisfy the physical assumptions of the used approximations, respectively. In addition, in this paper, the boundary element methods are used for solving the porous elastic wave propagation and carry out the numerical simulation. Based on the fluid-saturated porous model, this paper analyses and presents the dynamic equation of elastic wave propagation and boundary integral equation formulation of fluid saturated porous media in frequency domain. The fundamental solutions of the elastic wave equations are obtained according to the similarity between thermoelasticity and poroelasticity. At last, the numerical simulation of the elastic wave propagation in the two-phase isotropic media is carried out by using the boundary element method. The results show that a slow quasi P-wave can be seen in both solid and fluid wave-field synthetic seismograms. The boundary element method is effective and feasible.

地下水流动数值模拟的并行计算方法研究

Numerical modeling of groundwater is very important for understanding groundwater flow and solving hydrogeological problem. Today, groundwater studies require massive model cells and high calculation accuracy, which are beyond single-CPU computer’s capabilities. With the development of high performance parallel computing technologies, application of parallel computing method on numerical modeling of groundwater flow becomes necessary and important. Using parallel computing can improve the ability to resolve various hydro-geological and environmental problems. In this study, parallel computing method on two main types of modern parallel computer architecture, shared memory parallel systems and distributed shared memory parallel systems, are discussed. OpenMP and MPI (PETSc) are both used to parallelize the most widely used groundwater simulator, MODFLOW. Two parallel solvers, P-PCG and P-MODFLOW, were developed for MODFLOW. The parallelized MODFLOW was used to simulate regional groundwater flow in Beishan, Gansu Province, which is a potential high-level radioactive waste geological disposal area in China. 1. The OpenMP programming paradigm was used to parallelize the PCG (preconditioned conjugate-gradient method) solver, which is one of the main solver for MODFLOW. The parallel PCG solver, P-PCG, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. The largest test model has 1000 columns, 1000 rows and 1000 layers. Based on the timing results, execution times using the P-PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree. 2. P-MODFLOW, a domain decomposition–based model implemented in a parallel computing environment is developed, which allows efficient simulation of a regional-scale groundwater flow. The basic approach partitions a large model domain into any number of sub-domains. Parallel processors are used to solve the model equations within each sub-domain. The use of domain decomposition method to achieve the MODFLOW program distributed shared memory parallel computing system will process the application of MODFLOW be extended to the fleet of the most popular systems, so that a large-scale simulation could take full advantage of hundreds or even thousands parallel processors. P-MODFLOW has a good parallel performance, with the maximum speedup of 18.32 (14 processors). Super linear speedups have been achieved in the parallel tests, indicating the efficiency and scalability of the code. Parallel program design, load balancing and full use of the PETSc were considered to achieve a highly efficient parallel program. 3. The characterization of regional ground water flow system is very important for high-level radioactive waste geological disposal. The Beishan area, located in northwestern Gansu Province, China, is selected as a potential site for disposal repository. The area includes about 80000 km2 and has complicated hydrogeological conditions, which greatly increase the computational effort of regional ground water flow models. In order to reduce computing time, parallel computing scheme was applied to regional ground water flow modeling. Models with over 10 million cells were used to simulate how the faults and different recharge conditions impact regional ground water flow pattern. The results of this study provide regional ground water flow information for the site characterization of the potential high-level radioactive waste disposal.

Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.

Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

The effect of the product cost factor on error handling in industrial robots

N.W. Hardy and M.H. Lee. The effect of the product cost factor on error handling in industrial robots. In Maria Gini, editor, Detecting and Resolving Errors in Manufacturing Systems. Papers from the 1994 AAAI Spring Symposium Series, pages 59-64, Menlo Park, CA, March 1994. The AAAI Press. Technical Report SS-94-04, ISBN 0-929280-60-1.

Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Gough, John; Van Handel, R., (2007) 'Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode', Journal of Statistical Physics 127(3) pp.575-607 RAE2008

The cost of multiple large shareholders

Previous research argues that large non-controlling shareholders enhance firm value because they deter expropriation by the controlling shareholder. We propose that the conflicting incentives faced by large shareholders may induce a nonlinear relationship between the relative size of large shareholdings and firm value. Consistent with this prediction, we present evidence that there are costs of having a second (and third) largest shareholder, especially when the largest shareholdings are similar in size. Our results are robust to various relative size proxies, firm performance measures, model specifications, and potential endogeneity issues.

Cost and benefits of the Universal Basic Income implementation in Navarra

The Basic Income has been defined as a relatively small income that the public Administration unconditionally provides to all its members as a citizenship right. Its principal objective consists on guaranteeing the entire population with an income enough to satisfy living basic needs, but it could have other positive effects such as a more equally income redistribution or tax fraud fighting, as well as some drawbacks, like the labor supply disincentives. In this essay we present the argument in favor and against this policy and ultimately define how it could be financed according to the actual tax and social benefits’ system in Navarra. The research also approaches the main economic implications of the proposal, both in terms of static income redistribution and discusses other relevant dynamic uncertainties.

How Much Does It Cost to Provide Antiretroviral Therapy for HIV/AIDS in Africa?

Background: Many African countries are rapidly expanding HIV/AIDS treatment programs. Empirical information on the cost of delivering antiretroviral therapy (ART) for HIV/AIDS is needed for program planning and budgeting. Methods: We searched published and gray sources for estimates of the cost of providing ART in service delivery (non-research) settings in sub-Saharan Africa. Estimates were included if they were based on primary local data for input prices. Results: 17 eligible cost estimates were found. Of these, 10 were from South Africa. The cost per patient per year ranged from $396 to $2,761. It averaged approximately $850/patient/year in countries outside South Africa and $1,700/patient/year in South Africa. The most recent estimates for South Africa averaged $1,200/patient/year. Specific cost items included in the average cost per patient per year varied, making comparison across studies problematic. All estimates included the cost of antiretroviral drugs and laboratory tests, but many excluded the cost of inpatient care, treatment of opportunistic infections, and/or clinic infrastructure. Antiretroviral drugs comprised an average of one third of the cost of treatment in South Africa and one half to three quarters of the cost in other countries. Conclusions: There is very little empirical information available about the cost of providing antiretroviral therapy in non-research settings in Africa. Methods for estimating costs are inconsistent, and many estimates combine data drawn from disparate sources. Cost analysis should become a routine part of operational research on the treatment rollout in Africa.

Unicast Routing: Cost-Performance Tradeoffs

The objective of unicast routing is to find a path from a source to a destination. Conventional routing has been used mainly to provide connectivity. It lacks the ability to provide any kind of service guarantees and smart usage of network resources. Improving performance is possible by being aware of both traffic characteristics and current available resources. This paper surveys a range of routing solutions, which can be categorized depending on the degree of the awareness of the algorithm: (1) QoS/Constraint-based routing solutions are aware of traffic requirements of individual connection requests; (2) Traffic-aware routing solutions assume knowledge of the location of communicating ingress-egress pairs and possibly the traffic demands among them; (3) Routing solutions that are both QoS-aware as (1) and traffic-aware as (2); (4) Best-effort solutions are oblivious to both traffic and QoS requirements, but are adaptive only to current resource availability. The best performance can be achieved by having all possible knowledge so that while finding a path for an individual flow, one can make a smart choice among feasible paths to increase the chances of supporting future requests. However, this usually comes at the cost of increased complexity and decreased scalability. In this paper, we discuss such cost-performance tradeoffs by surveying proposed heuristic solutions and hybrid approaches.

On the Cost of Supporting Multihoming and Mobility

As the Internet has evolved and grown, an increasing number of nodes (hosts or autonomous systems) have become multihomed, i.e., a node is connected to more than one network. Mobility can be viewed as a special case of multihoming—as a node moves, it unsubscribes from one network and subscribes to another, which is akin to one interface becoming inactive and another active. The current Internet architecture has been facing significant challenges in effectively dealing with multihoming (and consequently mobility). The Recursive INternet Architecture (RINA) [1] was recently proposed as a clean-slate solution to the current problems of the Internet. In this paper, we perform an average-case cost analysis to compare the multihoming / mobility support of RINA, against that of other approaches such as LISP and MobileIP. We also validate our analysis using trace-driven simulation.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.