Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency-domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single-input-single-output equations are presented.     

一种检测动力系统振动频率的新方法

为了检测动力系统的振动频率,建立了动力系统的拓扑空间u和非平稳正弦函数空间M,采用拓扑反变理论把空间u映射到已知的空间M中,通过拓扑反变算子f：u→M检测未知的空间u振动频率,求出这个反变算子后,通过Poincare映射给出该反变算子稳定的存在条件,通过此方法即能够检测出动力系统振动特征频率的瞬变性,同时该方法具有较强的抗干扰能力,实验测试结果表明该方法是可行的。     

Sensitivity of the characteristic gain loci

In the generalized Nyquist stability criterion for linear, time-invariant, multivariable, feedback systems, stability is determined from the characteristic gain loci. This paper examines the sensitivity of the latter, and introduces sets of indices, called sensitivity indices, which characterize the sensitivity of the loci to small system perturbations.     

The asymptotic behaviour of a distributive sorting method

In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned inton/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions.     

Remarks on the asymptotic behaviour of Koiter shells

We review some results about the behaviour of a general Koiter shell, in the framework of linear elasticity. In particular, we investigate the asymptotics (for the thickness tending to zero) of the energy functional and of the percentage of the energy which is stored in the bending term. Such an analysis is motivated by the need to better understand how to numerically treat an arbitrary thin shell, when the discretization is performed using a finite element strategy. We present some instances to which our theory can be applied. Some numerical tests confirming our theoretical predictions are also provided.     

The asymptotic optimal frequency domain filter for edge detection

In an earlier paper by Shanmugam, Dickey, and Green, an edge detection filter was derived which maximized the energy within a specified interval about an edge feature. The initial expression of this filter involved a prolate spheroidal wave function. However, a careful analysis of the application of an asymptotic approximation to this function uncovered a major dimensional error. The corrected derivation of the asymptotic optimal filter forms the subject of this paper. To verify the results, the filter found is compared to a similar filter developed independently by Marr and Hildreth.     

The asymptotic local approach to change detection and model validation

We present a systematic approach for the design of change detection and model validation algorithms for dynamical systems. We show how to associate to any identification algorithm a change detection and a model validation procedure, which are optimal in some asymptotic sense. The foundations of our method go back to the asymptotic local approach in statistics, and our method generalizes this approach.     

Tracking algorithm designed by the local asymptotic approach

The problem of sequential detection of parameter jumps in linear systems with constant noise level is discussed. The detection problem is analyzed by the asymptotic local approach, using the normalized output error sequence as the detection signal. For linear regression, ARMAX, and state-space models, a central limit theorem is proved, transforming the original problem into the problem of detecting an increase in the man of an asymptotically Gaussian distributed scalar process. The performance of the tracking algorithm, which consists of a parameter estimator with decreasing gain and a single Hinkley's detector, has been studied by simulations and compared to the performance of constant- and adaptive-gain parameter estimators. The proposed algorithm seems to be superior in performance, requiring only a little, generally negligible, additional computational effort. The algorithm provides the information about the jump times, and the time delay of jump detection seems to be unaffected by the measurement noise level, provided that this level is not affected by the change     

The parametric characteristic of frequency response functions for nonlinear systems

The characteristic of the frequency response functions of nonlinear systems can be revealed and analyzed by analyzing of the parametric characteristics of these functions. To achieve these objectives, a new operator is defined, and several fundamental and important results about the parametric characteristics of the frequency response functions of nonlinear systems are developed. These theoretical results provide a significant and novel insight into the frequency domain characteristics of nonlinear systems and circumvent a large amount of complicated integral and symbolic calculations which have previously been required to perform nonlinear system frequency domain analysis. Several new results for the analysis and synthesis of nonlinear systems are also developed. Examples are included to illustrate potential applications of the new results.     

Dynamic performance,interaction, and the characteristic locus method: a quantitative approach

The characteristic locus method, in addition to its role in the assessment of system stability, is also an effective approach for evaluating tracking accuracy, interaction and dynamic/static loop performance. However, with regard to the evaluation of the latter three, there exists a degree of ambiguity and personal judgement, in addition to a requirement for a priori assumptions about proper problem conditioning. This paper stipulates quantitative bounds/measures of accuracy, interaction and loop assessment that identify the pertinent open-loop system factors affecting the particular performance aspect, and thus provide unambiguous measures to aid system design. Additionally, eigenvector scaling is introduced in order to tighten the bounds.     

On the asymptotic behaviour of solutions of differential equations in a banach space

The purpose of this paper is to consider the asymptotic behaviour of solutions of the initial value problemdu/dt = Au + F(t, u) u(t ₀) =u ₀ t t ₀ in a Banach spaceX with an unbounded, nonlinear operatorA. Conditions are given which guarantee that for sufficiently smallu ₀ the solutions converge to zero. The problem of asymptotic stability is also treated. In the last section there are applications to partial differential equations.     

Adaptive asymptotic tracking of repetitive signals-a frequencydomain approach

The problem of designing an adaptive tracking controller for repetitive signals is considered. It is assumed that the controlled plant is linear time-invariant (LTI) and that its steady-state behavior can be described by its frequency response. The proposed controller, being able to identify the gain and phase of a plant at selected frequencies, adjusts the input/output (I/O) map at frequencies contained in the reference signal so as to achieve zero steady-state errors. Hence, no structural knowledge of the plant is needed. However, the proposed controller does not alter the transient property of the plant, e.g., locations of poles. The transient property can be improved by adding feedback control action. A combination of the adaptive controller and a feedback LTI controller is studied     

On the generative–discriminative tradeoff approach: Interpretation, asymptotic efficiency and classification performance

The interpretation of generative, discriminative and hybrid approaches to classification is discussed, in particular for the generative–discriminative tradeoff (GDT), a hybrid approach. The asymptotic efficiency of the GDT, relative to that of its generative or discriminative counterpart, is presented theoretically and, by using linear normal discrimination as an example, numerically. On real and simulated datasets, the classification performance of the GDT is compared with those of normal-based linear discriminant analysis (LDA) and linear logistic regression (LLR). Four arguments are made as follows. First, the GDT is a generative model integrating both discriminative and generative learning. It is therefore subject to model misspecification of the data-generating process and hindered by complex optimisation. Secondly, among the three approaches being compared, the asymptotic efficiency of the GDT is higher than that of the discriminative approach but lower than that of the generative approach, when no model misspecification occurs. Thirdly, without model misspecification, LDA performs the best; with model misspecification, LLR or the GDT with an optimal, large weight on its discriminative component may perform the best. Finally, LLR is affected by the imbalance between groups of data.     

Global existence and asymptotic behaviour of the solution of a generalized burger's equation with viscosity

We obtain the global existence and uniqueness for a generalized Burger's equation with viscosity and the initial value being in L^∞ by successive method. Moreover, under certain condition on the initial value the solution tends to the solution of a linear heat equation in H¹.     

The response behaviour of a submerged cylindrical shell using the doubly asymptotic approximation method (DAA)

This paper presents experimentally measured and theoretically calculated responses of a flexible cylindrical shell subjected to an impulsive excitation in air and in water. The flat-ended, thin cylindrical shell of overall length 1284 mm, external radius 180 mm, thickness 3 mm is made of mild steel. The predicted responses are derived from a method using the doubly asymptotic approximation (DAA) models in order to uncouple the motion of the fluid from that of the structure. The DAAs enable the radiated pressure to be specified in terms of surface motion of the structure. The method, which employs the DAAs, is applied to determine the responses, i.e. acceleration, velocity and displacement, of the finite length cylindrical shell excited by an impulsive mechanical force. The calculated acceleration responses are compared with the experimental measurements.     

Sufficient conditions for the existence and asymptotic behaviour of solution to a quasi-linear elliptic problem

In this article, we combine the existing regularity theory, perturbation method and the lower and upper solutions method to study the existence and asymptotic behaviour of positive solution to a boundary value problem for the p-Laplacian operator. More exactly, we study the existence and asymptotic behaviour of the positive solution to a quasi-linear elliptic problem of the form?Δ _p u=λ a(x)g(u) in D′(Ω), u>0 in Ω, lim _{x→? Ω} u(x)=0. Under some conditions on a and g, we show that there is a non-negative number Λ₀ such that for all λ∈(0, Λ₀], the problem has a solution u _λ in the sense of distribution, which is bounded from above by some positive numbers μ(λ). Such estimates and the asymptotic behaviour are important in computer programs when we know an algorithm for determining the solution.     

Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve strong convergence, one usually needs to impose more restrictive properties for the involved operators, like strong monotonicity (respectively, strong convexity for optimization problems). In this paper, we propose a modified Krasnosel'ski?–Mann algorithm in connection with the determination of a fixed point of a nonexpansive mapping and show strong convergence of the iteratively generated sequence to the minimal norm solution of the problem. Relying on this, we derive a forward–backward and a Douglas–Rachford algorithm, both endowed with Tikhonov regularization terms, which generate iterates that strongly converge to the minimal norm solution of the set of zeros of the sum of two maximally monotone operators. Furthermore, we formulate strong convergent primal–dual algorithms of forward–backward and Douglas–Rachford-type for highly structured monotone inclusion problems involving parallel-sums and compositions with linear operators. The resulting iterative schemes are particularized to the solving of convex minimization problems. The theoretical results are illustrated by numerical experiments on the split feasibility problem in infinite dimensional spaces.     

A new approach to computing the Euler characteristic

In this paper we describe a new approach to computing the Euler characteristic of a three dimensional digital image. Our approach is based on computing the change in numbers of black components, tunnels and cavities in 3 × 3 × 3 neighborhood of an object (black) point due to its deletion. The existing algorithms to computing the Euler characteristic of a 3D digital image are based on counting the numbers of all k-dimensional elements (0 ≤ k ≤ 3) in a polyhedral representation of the image. Our approach can be modified for (6,26), (18,6), (6,18) and other connectivity relations of grid points. A parallel implementation of the algorithm is described using the concept of sub-fields.