Proportional navigation with delayed line-of-sight rate

This brief discusses the convergence analysis of proportional navigation (PN) guidance law in the presence of delayed line-of-sight (LOS) rate information. The delay in the LOS rate is introduced by the missile guidance system that uses a low cost sensor to obtain LOS rate information by image processing techniques. A Lyapunov-like function is used to analyze the convergence of the delay differential equation (DDE) governing the evolution of the LOS rate. The time-to-go until which decreasing behaviour of the Lyapunov-like function can be guaranteed is obtained. Conditions on the delay for finite time convergence of the LOS rate are presented for the linearized engagement equation. It is observed that in the presence of line-of-sight rate delay, increasing the effective navigation constant of the PN guidance law deteriorates its performance. Numerical simulations are presented to validate the results.

Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Synchronization and balancing on the N-torus

In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space. © 2006 Elsevier B.V. All rights reserved.

强化学习算法中启发式回报函数的设计及其收敛性分析

回报函数设计的好与坏对学习系统性能有着重要作用,按回报值在状态-动作空间中的分布情况,将回报函数的构建分为两种形式:密集函数和稀疏函数,分析了密集函数和稀疏函数的特点.提出启发式回报函数的基本设计思路,利用基于保守势函数差分形式的附加回报函数,给学习系统提供更多的启发式信息,并对算法的最优策略不变性和迭代收敛性进行了证明.启发式回报函数能够引导学习,加快学习进程,从而可以实现强化学习在实际大型复杂系统应用中的实时控制和调度.

A randomized solution to BGP divergence

The Border Gateway Protocol (BGP) is an interdomain routing protocol that allows each Autonomous System (AS) to define its own routing policies independently and use them to select the best routes. By means of policies, ASes are able to prevent some traffic from accessing their resources, or direct their traffic to a preferred route. However, this flexibility comes at the expense of a possibility of divergence behavior because of mutually conflicting policies. Since BGP is not guaranteed to converge even in the absence of network topology changes, it is not safe. In this paper, we propose a randomized approach to providing safety in BGP. The proposed algorithm dynamically detects policy conflicts, and tries to eliminate the conflict by changing the local preference of the paths involved. Both the detection and elimination of policy conflicts are performed locally, i.e. by using only local information. Randomization is introduced to prevent synchronous updates of the local preferences of the paths involved in the same conflict.

An Adaptive Management Approach to Resolving Policy Conflicts

The Border Gateway Protocol (BGP) is the current inter-domain routing protocol used to exchange reachability information between Autonomous Systems (ASes) in the Internet. BGP supports policy-based routing which allows each AS to independently define a set of local policies on which routes it accepts and advertises from/to other networks, as well as on which route it prefers when more than one route becomes available. However, independently chosen local policies may cause global conflicts, which result in protocol divergence. In this paper, we propose a new algorithm, called Adaptive Policy Management Scheme(APMS), to resolve policy conflicts in a distributed manner. Akin to distributed feedback control systems, each AS independently classifies the state of the network as either conflict-free or potentially conflicting by observing its local history only (namely, route flaps). Based on the degree of measured conflicts, each AS dynamically adjusts its own path preferences---increasing its preference for observably stable paths over flapping paths. APMS also includes a mechanism to distinguish route flaps due to topology changes, so as not to confuse them with those due to policy conflicts. A correctness and convergence analysis of APMS based on the sub-stability property of chosen paths is presented. Implementation in the SSF network simulator is performed, and simulation results for different performance metrics are presented. The metrics capture the dynamic performance (in terms of instantaneous throughput, delay, etc.) of APMS and other competing solutions, thus exposing the often neglected aspects of performance.

An approximation method using approximate approximations

The aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Monetary integration and real estate markets: an investigation of the impact of the introduction of a single currency on real estate performance

This paper assesses the impact of the monetary integration on different types of stock returns in Europe. In order to isolate European factors, the impact of global equity integration and small cap factors are investigated. European countries are sub-divided according to the process of monetary convergence. Analysis shows that national equity indices are strongly influenced by global market movements, with a European stock factor providing additional explanatory power. The global and European factors explain small cap and real estate stocks much less well –suggesting an increased importance of ‘local’ drivers. For real estate, there are notable differences between core and non-core countries. Core European countries exhibit convergence – a convergence to a European rather than a global factor. The non-core countries do not seem to exhibit common trends or movements. For the non-core countries, monetary integration has been associated with increased dispersion of returns, lower correlation and lower explanatory power of a European factor. It is concluded that this may be explained by divergence in underlying macro-economic drivers between core and non-core countries in the post-Euro period.

Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Caracterização de estruturas planares com substratos Iso/Anisotrópicos truncados através da técnica da ressonância transversa modificada

This work presents a theoretical and numerical analysis using the transverse resonance technique (TRT) and a proposed MTRT applied in the analysis of the dispersive characteristics of microstrip lines built on truncated isotropic and anisotropic dielectric substrates. The TRT uses the transmission lines model in the transversal section of the structure, allowing to analyze its dispersive behavior. The difference between TRT and MTRT consists basically of the resonance direction. While in the TRT the resonance is calculated in the same direction of the metallic strip normal axis, the MTRT considers the resonance in the metallic strip parallel plane. Although the application of the MTRT results in a more complex equivalent circuit, its use allows some added characterization, like longitudinal section electric mode (LSE) and longitudinal section magnetic mode (LSM), microstrips with truncated substrate, or structures with different dielectric regions. A computer program using TRT and MTRT proposed in this work is implemented for the characterization of microstrips on truncated isotropic and anisotropic substrates. In this analysis, propagating and evanescent modes are considered. Thus, it is possible to characterize both the dominant and higher order modes of the structure. Numerical results are presented for the effective permittivity, characteristic impedance and relative phase velocity for microstrip lines with different parameters and dimensions of the dielectric substrate. Agreement with the results obtained in the literature are shown, as well as experimental results. In some cases, the convergence analysis is also performed by considering the limiting conditions, like particular cases of isotropic materials or structures with dielectric of infinite size found in the literature. The numerical convergence of the formulation is also analyzed. Finally, conclusions and suggestions for the continuity of this work are presented

Algoritmos genéticos: uso de lógica nebulosa e análise de convergência por cadeia de Markov

In this work, the Markov chain will be the tool used in the modeling and analysis of convergence of the genetic algorithm, both the standard version as for the other versions that allows the genetic algorithm. In addition, we intend to compare the performance of the standard version with the fuzzy version, believing that this version gives the genetic algorithm a great ability to find a global optimum, own the global optimization algorithms. The choice of this algorithm is due to the fact that it has become, over the past thirty yares, one of the more importan tool used to find a solution of de optimization problem. This choice is due to its effectiveness in finding a good quality solution to the problem, considering that the knowledge of a good quality solution becomes acceptable given that there may not be another algorithm able to get the optimal solution for many of these problems. However, this algorithm can be set, taking into account, that it is not only dependent on how the problem is represented as but also some of the operators are defined, to the standard version of this, when the parameters are kept fixed, to their versions with variables parameters. Therefore to achieve good performance with the aforementioned algorithm is necessary that it has an adequate criterion in the choice of its parameters, especially the rate of mutation and crossover rate or even the size of the population. It is important to remember that those implementations in which parameters are kept fixed throughout the execution, the modeling algorithm by Markov chain results in a homogeneous chain and when it allows the variation of parameters during the execution, the Markov chain that models becomes be non - homogeneous. Therefore, in an attempt to improve the algorithm performance, few studies have tried to make the setting of the parameters through strategies that capture the intrinsic characteristics of the problem. These characteristics are extracted from the present state of execution, in order to identify and preserve a pattern related to a solution of good quality and at the same time that standard discarding of low quality. Strategies for feature extraction can either use precise techniques as fuzzy techniques, in the latter case being made through a fuzzy controller. A Markov chain is used for modeling and convergence analysis of the algorithm, both in its standard version as for the other. In order to evaluate the performance of a non-homogeneous algorithm tests will be applied to compare the standard fuzzy algorithm with the genetic algorithm, and the rate of change adjusted by a fuzzy controller. To do so, pick up optimization problems whose number of solutions varies exponentially with the number of variables