Comments on “The Extreme Learning Machine”

This comment letter points out that the essence of the “extreme learning machine (ELM)” recently appeared has been proposed earlier by Broomhead and Lowe and Pao , and discussed by other authors. Hence, it is not necessary to introduce a new name “ELM.”      

A comment on “L∞ optimal control of SISO continuous-time systems”

The paper “L_∞ optimal control of SISO continuous-time systems” by Wang and Sznaier (Wang & Sznaier (1997). Automatica, 33 (1), 85–90) studies the problem of designing a controller that optimally minimizes the peak absolute value of system output, due to a fixed input signal. With a newly defined function space A_∞, it was claimed that the set of all L_∞-bounded outputs could be parameterized and that the problem could be transformed to a minimal distance problem on L_∞ space. We believe, however, their formulation has essential flaws.     

Report on test matrices for generalized inverses

This paper is a comprehensive report on test matrices for the generalized inversion of matrices. Two principles are described how to construct singular square or arbitrary rectangular test matrices and their Moore-Penrose inverses. By prescribing the singular values of the matrices or by suitably choosing the free parameters test matrices with condition numbers of any size can be obtained. We also deal with test matrices which are equal to their Moore-Penrose inverse. In addition to many advices how to construct test matrices the paper presents many test matrices explicitly, in particular singular square matrices of ordern, sets of 7×6 and 7×5 matrices of different rank, a set of 5×5 matrices which are equal to their Moore-Penrose inverse and some special test matrices known from literature. For the set of 7×6 parameter matrices also the singular values corresponding to six values of the parameter are listed. For three simple parameter matrices of order 5×4 and 6×5 even test results obtained by eight different algorithms are quoted. As “by-products” the paper contains inequalities between condition numbers of different norms, representations for unitary, orthogonal, column-orthogonal and row-orthogonal matrices, a generalization of Hadamard matrices and representations of matrices which are equal to their Moore-Penrose inverse (or their inverse). All test matrices given in this paper may also be used for testing algorithms solving linear least squares problems.     

Comments on “Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/ Detectability Criterion”

This note gives a correct proof for the first part of Theorem 3.2 in the above paper, which is an important theorem of the above paper.      

A modification of the Nevanlinna algorithm on the solution of theH∞m×n-optimization problem

A modification of the Nevanlinna algorithm is presented for the solution of the H^∞_m×m-optimization problem. This is an essential modification when the Nevanlinna algorithm is applied to find the extremal function of the matrix H^∞ interpolation problem which deals with the case that the interpolation points have multiplicities. For the computation of the minimal H^∞-norm, a pure matrices computational algorithm is used where the formulation is solely in terms of the coefficients of the inner function     

Comment and Further Result on “Fault Detection and Isolation Method Based on H−/H∞ Unknown Input Observer Design in Finite Frequency Domain”

This paper considers the work entitled “Fault detection and isolation method based on H_?/H_∞ unknown input observer design in finite frequency domain”, published previously in the Asian Journal of Control. We point out that some design matrices in the above mentioned article have no effect on the design result. Furthermore, we show that the conditions proposed therein for H_∞ design are conservative and propose an improved design method.     

一个反求Bezier曲面控制点的算法

本文将反求m×n次Bezier曲面控制点问题,转化为求解m+1个n+1阶线性方程组和n+1个m+1阶线性方程组问题。这些线性方程组的系数矩阵是著名的Vandermonde矩阵。通过求解Vandermonde矩阵的逆矩阵,使CAD/CAM曲面造型中常常遇到的反求Bezier曲面控制点问题得到有效的解决。同时本文给出了一种求解Vandermonde矩阵的逆矩阵的方法。     

Comments on “Backpropagation Algorithms for a Broad Class of Dynamic Networks”

In a recent paper, De JesÚs proposed a general framework for describing dynamic neural networks. Gradient and Jacobian calculations were discussed based on backpropagation-through-time (BPTT) algorithm and real-time recurrent learning (RTRL). Some errors in the paper of De JesÚs bring difficulties for other researchers who want to implement the algorithms. This comments paper shows the critical parts of the publication and gives errata to facilitate understanding and implementation.      

Static output feedback controllers: stability and convexity

The main objective of this paper is to solve the following stabilizing output feedback control problem: given matrices (A; B₂ ; C₂) with appropriate dimensions, find (if one exists) a static output feedback gain L such that the closed-loop matrix A-B₂LC₂ is asymptotically stable. It is known that the existence of L is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set. Conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the above stabilizing output feedback control problem. As a natural extension, we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index. Some examples borrowed from the literature are solved to illustrate the theoretical results     

A note on “schedule of n jobs on two identical machines to minimize weighted mean flor time”

In a recent paper, Alidaee [Computers ind. Engng 24, 53–55 (1993)] notes the similarity between the scheduling problems of minimizing weighted mean flow time (WMFT) on two parallel machines and minimmizing weighted earliness/tardiness (WET) about a common due date on a single machine. Based on this similarity, Alidaee descirbes how a dynamic programming algorithm proposed by Hall and Posner [Opns Res. 39, 836–846 (1991)] for the WET problem can be modified and applied to the WMFT problem. The work is an important extension of earlier results on an equivalence relationship between the WMFT and WET problems. This Note helps consolidate the literature by recognizing Rothkopf [Mgmt Sci. 12, 437–447 (1966)] as the originator of algorithm described in [Computers ind. Engng 24 53–55 (1993)].     

Theories of contact specified by connection matrices

We begin by characterizing notions of geometric continuity represented by connection matrices. Next we present a set of geometric properties that must be satisfied by all reasonable notions of geometric continuity. These geometric requirements are then reinterpreted as an equivalent collection of algebraic constraints on corresponding sets of connection matrices. We provide a general technique for constructing sets of connection matrices satisfying these criteria and apply this technique to generate many examples of novel notions of geometric continuity. Using these constraints and construction techniques, we show that there is no notion of geometric continuity between reparametrization continuity of order 3, (G³), and Frenet frame continuity of order 3, (F³); that there are several notions of geometric continuity between G⁴ and F⁴; and that the number of different notions of geometric continuity between Gⁿ and Fⁿ grows at least exponentially with n.     

Analysis of “Salary man” motivation and the will to work (YARUKI)

The Inner Graphic Formula Method (IGF) which was originally conceived by Professor Ishiketa and further developed by him and his associates was used to investigate the motivation of new company employees.

Japanese companies traditionally recruit new employees from senior classes and notify successful candidates of their intention to employ them around the first of January. Since graduation is in March, April first is, then, the first day of work for almost all of these graduates in their new companies.

The investigation period for this study covers the eleven months from January until the middle of November, and therefore includes the three month period after notification but prior to actual work, from January first until March thirty-first, and the first eight month of actual work, from April first to the middle of November. The subjects fell, naturally, into two groups; a “Blue Collar” group and a “White Collar” group.

This paper deals with the motivation of these newly employed workers in general and, specifically, with the difference in motivational tendencies between “Blue Collar” and “White Collar” workers. As expected analysis showed that clear motivational differences appeared.

Motivation in the white collar workers tended to raise after an initial downturn, while a general downward trend was detected for the blue collar workers. White collar worker's attitudes toward themselves and toward their work seemed to change for the better as a result of having the chance to become introspective while plotting the graph and writing the anecdotal responses needed to complete the investigative sheet for this study.     

“Vague-to-Crisp” Neural Mechanism of Perception

This brief describes neural modeling fields (NMFs) for object perception, a bio-inspired paradigm. We discuss previous difficulties in object perception algorithms encountered since the 1950s, and describe how NMF overcomes these difficulties. NMF mechanisms are compared to recent experimental neuroimaging observations, which have demonstrated that initial top-down signals are vague and during perception they evolve into crisp representations matching the bottom-up signals from observed objects. Neural and mathematical mechanisms are described and future research directions outlined.      

The extreme eigenvalues and stability of real symmetric intervalmatrices

A novel Khoritonov-like algorithm for computing the minimal and maximal eigenvalues of n×n dimensional symmetric interval matrices is presented. It is proved that the maximal eigenvalue of a given set of interval matrices coincides with the maximal eigenvalue of a special set of 2^n-1 symmetric vertex matrices, whereas its minimal eigenvalue coincides with the minimal of another special set of 2^n-1 symmetric vertex matrices. As immediate corollaries of this algorithm, weak necessary and sufficient conditions for testing the Hurwitz and Schur stability of symmetric interval matrices, where one has to test the stability of 2^n-1 and 2ⁿ symmetric vertex matrices, respectively, are obtained     

Generalization of Cayley–Hamilton Theorem for Multivariate Rational Matrices

The two equivalent generalizations of the famous Cayley–Hamilton theorem for multivariate rational matrices over any number field are proposed, which are also generalizations of the nine known generalized Cayley–Hamilton theorems. Restricting our results to a smaller range leads to the two equivalent generalized Cayley–Hamilton theorems for multivariate polynomial matrices over any number field, one of which is more efficient in some cases than a known result.      

Comment on “On Siphon Computation for Deadlock Control in a Class of Petri Nets”

It was claimed recently in the paper by Li and Zhou that ldquoa polynomial time algorithm for finding the set of elementary siphons in S³PRs is proposed, which avoids complete siphon enumerationrdquo. However, this is incorrect because Proposition 1 and Corollary 6 of the aforementioned paper, which lead to the claim, are both incorrect. In this correspondence paper, Proposition 1 and Corollary 6 are disproved. As a consequence, some claims of the aforesaid paper are denied. Two examples are presented to disprove some claims of the previously mentioned paper.     

Inversion of Linear Systems on the Basis of State Space Realization

This paper considers the problem of constructing an inverse system for a given linear timeinvariant dynamical discrete-time system. We suggest a method to obtain the matrices of the inverse system based on calculating a finite-dimensional state space realization of the input-output map represented by a sequence of matrices.     

Optimal solution and approximation to thel1/H∞ control problem

This paper addresses the l₁/H_∞ optimal control problem for a system described by linear time-invariant finite dimensional discrete-time equations. It is shown that a solution to this problem exists and can be approximated arbitrarily by real-rational transfer matrices. Perhaps more interesting from a computational point of view, a bound on the order of a δ-suboptimal solution is also given     

6R关节型机器人运动学建模

为满足新开发的多机器人实验系统编程需要,研究了6R机器人运动学逆解问题.推导了代数逆解结果,并研究了将其用于实际控制系统时,逆解的漏解、增根和多解问题.与传统方法比较,采用了便于程序模块化的坐标系设置方式,在需要经常更换作业工具的多机器人系统中更为适用.推导过程只需2次矩阵逆乘,步骤简单.基于VC++和OpenGL技术编制了系统程序,检验了方法的有效性.以其中一个位姿为例,对比几何方法得出的结果,验证了算法的正确性.研究的结果适用于MOTOMAN-UP6和PUMA560等相似构型的所有机器人.     

Controller approximation: approaches for preserving H∞ performance

Investigates the design of reduced-order controllers using an H _∞ framework. Given a stabilizing controller which satisfies a prespecified level of closed-loop H_∞ performance, sufficient conditions are derived for another controller to be stabilizing and satisfy the same level of H_∞, performance. Such controllers are said to be (P,γ)-admissible, where P is the model of the plant under consideration and γ is the required level of prespecified H_∞ performance. The conditions are expressed as norm bounds on particular frequency-weighted errors, where the weights are selected to make a specific transfer function a contraction. The design of reduced-order (P,γ)-admissible controllers is then formulated as a frequency-weighted model reduction problem. It is advantageous for the required weights to be large in some sense. Solutions which minimize either the trace, or the determinant, of the inverse weights are characterized. We show that the procedure for minimizing the determinant of the inverse weights always gives a direction where the weights are the best possible. To conclude, we demonstrate by way of a numerical example, that when used in conjunction with a combined model reduction/convex optimization scheme, the proposed design procedures are effective in substantially reducing controller complexity