Stability margins of nonlinear optimal regulators with nonquadratic performance criteria involving cross-weighting terms

In this paper we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal regulators that minimize a nonlinear-nonquadratic performance criterion involving cross-weighting terms. Specifically, sufficient conditions that guarantee gain, sector, and disk margins are given in terms of the state, control, and cross-weighting nonlinear-nonquadratic weighting functions. The proposed results provide a generalization of the “meaningful” inverse optimal nonlinear regulator stability margins as well as the classical linear-quadratic optimal regulator gain and phase margins.     

Stabilization of the inverted pendulum around its homoclinic orbit

The inverted pendulum has been used as a benchmark for motivating the study of nonlinear control techniques. We propose a simple controller for balancing the inverted pendulum and raise it to its upper equilibrium position while the cart displacement is brought to zero. The control strategy is based on an energy approach of the cart and pendulum system.     

Recursive algorithm and accurate computation of dyadic Green’s functions for stratified uniaxial anisotropic media

A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.     

现代密码学上的弹性函数综述

本文介绍了在容错分布、量子密码学中的密钥分配以及流密码中的随机序列产生等领域都有着广泛应用的一类多输出布尔函数——弹性函数。弹性函数和0,1上多维空间的正交分划(一个正交矩阵组)是一致的。在此基础上,介绍了弹性函数的正交分划的递归构造方法和简单计数。     

现代密码学上的弹性函数综述

本文介绍了在容错分布、量子密码学中的密钥分配以及流密码中的随机序列产生等领域都有着广泛应用的一类多输出布尔函数——弹性函数。弹性函数和0,1上多维空间的正交分划（一个正交矩阵组）是一致的。在此基础上,介绍了弹性函数的正交分划的递归构造方法和简单计数。     

On the complexity of binary samples

Consider a class of binary functions h: X→{ − 1, + 1} on an interval . Define the sample width of h on a finite subset (a sample) S ⊂ X as ω _S (h) =  min _x ∈ S |ω _h (x)| where ω _h (x) = h(x) max {a ≥ 0: h(z) = h(x), x − a ≤ z ≤ x + a}. Let be the space of all samples in X of cardinality ℓ and consider sets of wide samples, i.e., hypersets which are defined as Through an application of the Sauer-Shelah result on the density of sets an upper estimate is obtained on the growth function (or trace) of the class , β > 0, i.e., on the number of possible dichotomies obtained by intersecting all hypersets with a fixed collection of samples of cardinality m. The estimate is .      

Building ensemble classifiers using belief functions and OWA operators

A pervasive task in many forms of human activity is classification. Recent interest in the classification process has focused on ensemble classifier systems. These types of systems are based on a paradigm of combining the outputs of a number of individual classifiers. In this paper we propose a new approach for obtaining the final output of ensemble classifiers. The method presented here uses the Dempster–Shafer concept of belief functions to represent the confidence in the outputs of the individual classifiers. The combing of the outputs of the individual classifiers is based on an aggregation process which can be seen as a fusion of the Dempster rule of combination with a generalized form of OWA operator. The use of the OWA operator provides an added degree of flexibility in expressing the way the aggregation of the individual classifiers is performed.     

Towards the next generation of artificial neural networks for civil engineering

The purpose of this paper is to stimulate interest within the civil engineering research community for developing the next generation of applied artificial neural networks. In particular, it identifies what the next generation of these devices needs to achieve, and provides direction in terms of how their development may proceed. An analysis of the current situation indicates that progress in the development of artificial neural network applications has largely stagnated. Suggestions are made for advancing the field to the next level of sophistication and application, using genetic algorithms and related techniques. It is shown that this approach will require the design of some very sophisticated genetic coding mechanisms in order to develop the required higher-order network structures, and will utilize development mechanisms observed in nature such as growth, self-organization, and multi-stage objective functions. The capabilities of such an approach and the way in which they can be achieved are explored with reference to the problems of: (a) determining truck attributes from the strain envelopes they induce in structural members when crossing a bridge, and; (b) developing a decision support system for dynamic control of industrialized manufacturing of houses.     

Fuzzy functions with LSE

“Fuzzy Functions” are proposed to be determined by the least squares estimation (LSE) technique for the development of fuzzy system models. These functions, “Fuzzy Functions with LSE” are proposed as alternate representation and reasoning schemas to the fuzzy rule base approaches. These “Fuzzy Functions” can be more easily obtained and implemented by those who are not familiar with an in-depth knowledge of fuzzy theory. Working knowledge of a fuzzy clustering algorithm such as FCM or its variations would be sufficient to obtain membership values of input vectors. The membership values together with scalar input variables are then used by the LSE technique to determine “Fuzzy Functions” for each cluster identified by FCM. These functions are different from “Fuzzy Rule Base” approaches as well as “Fuzzy Regression” approaches. Various transformations of the membership values are included as new variables in addition to original selected scalar input variables; and at times, a logistic transformation of non-scalar original selected input variables may also be included as a new variable. A comparison of “Fuzzy Functions-LSE” with Ordinary Least Squares Estimation (OLSE)” approach show that “Fuzzy Function-LSE” provide better results in the order of 10% or better with respect to RMSE measure for both training and test cases of data sets.     

Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge

This paper presents an analysis of the performance of the (μ/μ,λ)-ES with isotropically distributed mutations and cumulative step length adaptation on the noisy parabolic ridge. Several forms of dependency of the noise strength on the distance from the ridge axis are considered. Closed form expressions are derived that describe the mutation strength and the progress rate of the strategy in high-dimensional search spaces. It is seen that as for the sphere model, larger levels of noise present lead to cumulative step length adaptation generating increasingly inadequate mutation strengths, and that the problem can be ameliorated to some degree by working with larger populations.