Chain matrix decompositions,continued fractions and the optimal inhomogeneous ladder networks

Studies of two-element-kind ladder networks are well known in the classical literature, among them, the most celebrated ones are due to Cauer. Driving point immittance function synthesis by using continued fractions to obtain the series and shunt arm L-C element values is a standard and routine work. The idea of introducing a class of more general networks, the inhomogeneous ladder networks, was first developed by Lee and Brown, and subsequently the synthesis techniques of such a network were established.In this paper, new results are found such as: (1) the Iff. conditions of the existence of an inhomogeneous ladder network by a given chain matrix of the network satisfying: (a) determinant of the chain matrix is 1; (b) the zeros of A(s) and z^?1B(s) or A(s) and y^?1C(s) alternate with respect to [z(s)y(s), k] with an appropriate leading set of zeros of A(s); (c) the poles of A(s) and z^?1B(s) or A(s) and y^?1C(s) are the poles of z(s)y(s) of multiplicity of n and n?1, where n the number of sections of ladder networks; (2) the Iff. condition for the inhomogeneous ladder network to be optimal is that it be antimetrical, whereas for the extended class of inhomogeneous ladder networks it is symmetrical, where an optimal inhomogeneous ladder network is defined as the corresponding network with the minimum sum of immittance levels in the series and shunt arms; (3) algorithms of synthesis procedures were developed as the by-products of the Theorems.     

New approach to the optimal control of delay systems via Chebyshev series

Based on the Chebyshev series, a directly computational formulation in matrix form is established for evaluating the optimal control and trajectory of time-delay systems. In a comparison with the previous work (3, Int. J. Control, Vol. 41, pp. 1221-1234, 1985), the formulation is shown to be more straightforward and convenient for digital computation. Thus the difficulty in obtaining a solution of the two-point boundary-value problem with both delayed and advanced arguments is circumvented. An example compares the actual solution with the one obtained using the technique of this paper.     

On the computation of the transfer function matrix of singular systems

For singular systems, i.e. for systems of the form E[xdot] = Ax + Bu, with E singular, the problem of computing the transfer function matrix has been studied. An algorithm is developed which is similar to the corresponding algorithm proposed by Faddeev or Leverrier for regular systems. The present results involve the Drazin inverse and yield an expression for the transfer function matrix suitable for computer use.     

Hybrid Analysis of a Large-scale Network by Node-tearing

A new hybrid analysis technique for large-scale networks by node-tearing is presented. The interconnection function matrix is defined and the formulation for computing the transfer function matrix W, the general return difference matrix F_K(X) and the general null return difference matrix F̂_K(X) of a large-scale network is given. In the overall computational process, all the hybrid port parameters are derived from the indefinite-admittance matrix and/or the indefinite-impedance matrix of the component subnetworks.     

Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of $\text{∫}\text{0}\text{t}$s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.     

Some Properties of Matrices with 1, -1 and 0 Entries

A class of matrices with 1, -1 and 0 entries, called the H-matrices, is introduced and properties of such matrices are investigated. It is shown that for an H-matrix K the matrix G = KDK^T, where D is a diagonal matrix with nonnegative diagonal entries, has certain properties applicable to topological synthesis of networks. A technique for decomposing a particular symmetrical matrix G, called the Q-matrix, into KDK^T, where K is an H-matrix and D is a diagonal matrix with positive diagonal entries, is also developed.     

The inverse lure problem of optimal control

Given the linear system $\text{x}\text{}$ = Ax - bu, y = c^Tx, it is shown that, for a certain non-quadratic cost functional, the optimal control is given by u_opt(x) = h(c^Tx), where the function h(y) must satisfy the conditions ky²?h(y)y>0 for y≠0, h(0) = 0 and existence of h^-1 everywhere. The linear system considered must satisfy the Popov condition 1/k + (1 +?ωβ) G(?ω)>0 for all ω, G(s) being the y(s)/u(s) transfer function.     

Study on stability and stabilizability of discrete-time mean-field stochastic systems

This paper is to study the mean square stabilizability and regional stability of discrete-time mean-field stochastic systems. Firstly, a necessary and sufficient condition is presented via the spectrum of linear operator to illustrate the stabilizability of discrete-time mean-field stochastic systems. B(0, γ)-stabilizability is introduced and transformed into solving linear matrix inequalities (LMIs). Secondly, B_M-stability is characterized, especially, the stabilities of circular region, sector region and annulus regions are discussed extensively. Finally, as applications, it is shown that B(0, γ₁; γ₂)-stability has close relationship with the decay rate of the system state response and the Lyapunov exponent.     

HCA: Hierarchical Compare Aggregate model for question retrieval in community question answering

We address the problem of finding similar historical questions that are semantically equivalent or relevant to an input query question in community question-answering (CQA) sites. One of the main challenges for this task is that questions are usually too long and often contain peripheral information in addition to the main goals of the question. To address this problem, we propose an end-to-end Hierarchical Compare Aggregate (HCA) model that can handle this problem without using any task-specific features. We first split questions into sentences and compare every sentence pair of the two questions using a proposed Word-Level-Compare-Aggregate model called WLCA-model and then the comparison results are aggregated with a proposed Sentence-Level-Compare-Aggregate model to make the final decision. To handle the insufficient training data problem, we propose a sequential transfer learning approach to pre-train the WLCA-model on a large paraphrase detection dataset. Our experiments on two editions of the Semeval benchmark datasets and the domain-specific AskUbuntu dataset show that our model outperforms the state-of-the-art models.     

Least squares Hermitian solution of the complex matrix equation AXB+CXD=E with the least norm

In this paper, a new method is presented to solve the least squares Hermitian problem of the complex matrix equation AXB+CXD=E. The explicit expression of least squares Hermitian solution with the least norm is given. The least squares Hermitian solution with the least norm of complex matrix equation AXB=E is also derived. Numerical algorithms and numerical examples show the feasibility of our method.     

The solution to matrix equation AX+XC=B

In this note, the problem of solution to the matrix equation AX+X^TC=B is considered by the Moore-Penrose generalized inverse matrix. A general solution to this equation is obtained. At the same time, some useful conclusions are made, which play important roles in the linear system theories and applications.     

Asynchronous consensus of multi-agent systems via variable period intermittent control with heterogeneous pulse-modulated function

Most existing consensus control in multi-agent systems (MASs) require agents to update their state synchronously, which means that some agents need to wait for all individuals to complete the iteration before starting the next iteration. To overcome this bottleneck, this paper studied asynchronous consensus problems of second-order MASs (SOMASs) with aperiodic communication. An asynchronous pulse-modulated intermittent control (APIMC) with heterogeneous pulse-modulated function and time-varying control period, which can unify impulsive control and sampled-data control, is proposed for the consensus of SOMASs. A time-varying discrete system is constructed to describe the evolution of the sample values of position and velocity of the SOMAS. Then, by the analysis tools from the stochastic matrix and the properties of the Laplace matrix of graph, some effective conditions are obtained to show the relationship between the convergence of the controlled SOMASs and the control parameters. Finally, a 300-node SOMAS whose topology is a random geographic network is included to verify the feasibility of the proposed control and the correctness of the theoretical analysis.     

Optimal residual generation for fault detection in linear discrete time-varying systems with uncertain observations

This work deals with the problem of optimal residual generation for fault detection (FD) in linear discrete time-varying (LDTV) systems subject to uncertain observations. By introducing a generalized fault detection filter (FDF) with four parameter matrices as the residual generator, a novel FDF design scheme is formulated as two bi-objective optimization problems such that the sensitivity of residual to fault is enhanced and the robustness of residual to unknown input is simultaneously strengthened. A generalized operator based optimization approach is proposed to deduce solutions to the corresponding optimization problems in operator forms, where the related H_∞/H_∞ or $H_{?}/H_{\infty }$ FD performance index is maximized. With the aid of the addressed methods, the connections among the derived solutions are explicitly announced. The parameter matrices of the FDF are analytically derived via solving simple matrix equations recursively. It is revealed that our proposed results establish an operator-based framework of optimal residual generation for some kinds of linear discrete-time systems. Illustrative examples are given to show the applicability and effectiveness of the proposed methods.     

Leader–follower decentralized optimal control for large population hexarotors with tilted propellers: A Stackelberg game approach

In this paper, we consider leader–follower decentralized optimal control for a hexarotor group with one leader and large population followers. Our hexarotor is modeled based on the quaternion framework to resolve singularity of the rotation matrix represented by Euler angles, and has 6-DoF due to six tilted propellers, which allows to control its translation and attitude simultaneously. In our problem setup, the leader hexarotor is coupled with the follower hexarotors through the followers’ average behavior (mean field), and the followers are coupled with each other through their average behavior and the leader’s arbitrary control. By using the mean field Stackelberg game framework, we obtain a set of decentralized optimal controls for the leader and N follower hexarotors when N is arbitrarily large, where each control is a function of its local information. We show that the corresponding decentralized optimal controls constitute an ϵ-Stackelberg equilibrium for the leader and N followers, where ϵ → 0 as N → ∞. Through simulations with two different operating scenarios, we show that the leader–follower hexarotors follow their desired position and attitude references, and the followers are controlled by the leader while effectively tracking their approximated average behavior. Furthermore, we show the nonsingularity and 6-DoF control performance of the leader–follower hexarotor group due to the novel modeling technique of the hexarotor presented in the paper.     

Effects of a magnetic field on the free convective flow through a porous medium bounded by an infinite vertical porous plate with constant heat flux

This paper investigates the effects of a magnetic field on the free convective flow of a viscous, incompressible, dissipative fluid through a porous medium, occupying a semi-infinite region of the space bounded by an infinite vertical and porous plate. The plate is subjected to a normal suction velocity and the heat flux at the plate is constant. The magnetic field is of uniform strength and is applied perpendicular to the plate. An analytical solution to the problem is obtained. The influence of the magnetic parameter (M) and permeability parameter (K) is discussed for the case of air (P = 0.71) when the plate is subjected to a constant suction velocity and is being cooled by free convection currents.     

Synthesis of β(1 → 3) and β(1 → 6) galactooligosaccharides from lactose and whey using a recombinant β-galactosidase from Pantoea anthophila

BackgroundMilk whey, a byproduct of the dairy industry has a negative environmental impact, can be used as a raw material for added-value compounds such as galactooligosaccharides (GOS) synthesis by β-galactosidases.ResultsB-gal42 from Pantoea anthophila strain isolated from tejuino belonging to the glycosyl hydrolase family GH42, was overexpressed in Escherichia coli and used for GOS synthesis from lactose or milk whey. Crude cell-free enzyme extracts exhibited high stability; they were employed for GOS synthesis reactions. In reactions with 400 g/L lactose, the maximum GOS yield was 40% (w/w) measured by HPAEC-PAD, corresponding to 86% of conversion. This enzyme had a strong predilection to form GOS with β(1 → 6) and β(1 → 3) galactosyl linkages. Comparing GOS synthesis between milk whey and pure lactose, both of them at 300 g/L, these two substrates gave rise to a yield of 38% (60% of lactose conversion) with the same product profile determined by HPAEC-PAD.ConclusionsB-gal42 can be used on whey (a cheap lactose source) to produce added value products such as galactooligosaccharides.How to cite: Yañez-Ñeco CV, Cervantes FV, Amaya-Delgado L, et al. Synthesis of β(1→3) and β(1→6) galactooligosaccharides from lactose and whey using a recombinant β-galactosidase from Pantoea anthophila. Electron J Biotechnol 2021;49. https://dx.doi.org/10.1016/j.ejbt.2020.10.004     

Generalization of all stabilizing compensators for finite-dimensional linear systems

For finite-dimensional linear systems, the Youla-Kucera parameterization (YKP) with a Q parameter over RH_∞ is assumed to satisfy the Diophantine identity. However, the stability is guaranteed if the Diophantine equation is the “U(RH_∞)“ equality, but not if it is the “identity” equality. However, Vidyasagar's structure with an H parameter over U(RH_∞) is an observer-controller configuration that satisfies the Diophantine equation. This study discusses the deficiency of the Diophantine identity; expands the YKP using an H parameter over U(RH_∞), and expands the Vidyasagar's structure using a Q_v parameter over RH_∞ so that both of the expanded parameterizations satisfy the Diophantine equation and are equivalent for all stabilizing compensators. Moreover, an equation that relates to Q, Q_v, and H will be introduced to establish relationships among the YKP, Vidyasagar's structure and both expanded parameterizations.     

Mixed H∞ and passivity control for a class of stochastic nonlinear sampled-data systems

In this paper, we consider the problem of mixed H_∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H_∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.     

An application of homomorphic deconvolution to the tomographic restoration of radiographs

This paper derives an optimal homomorphic tomographic filter, to restore tomographic images of blurred radiographs, by taking into account the noise contributed by the other layers. The method is based on the homomorphic deconvolution technique, which is well-known for its performance in image restoration. A computer simulation of the procedure is presented. The results are compared with those obtained by using inverse filtering (3, IEEE Trans on Medical Imaging, Vol. 2, pp. 89–102, 1983) and Wiener filtering (4, Proc. Digitech '84). The paper shows that homomorphic filtering is a suitable and often preferable technique for the tomographic filtering of radiographs.     

Orthogonal nonnegative matrix tri-factorization for co-clustering: Multiplicative updates on Stiefel manifolds

Matrix factorization-based methods become popular in dyadic data analysis, where a fundamental problem, for example, is to perform document clustering or co-clustering words and documents given a term-document matrix. Nonnegative matrix tri-factorization (NMTF) emerges as a promising tool for co-clustering, seeking a 3-factor decomposition X≈USV^?$\mathit{X}\approx {\mathit{USV}}^{?}$ with all factor matrices restricted to be nonnegative, i.e., U?0,S?0,V?0.$\mathit{U}?0\text{,}\mathit{S}?0\text{,}\mathit{V}?0\text{.}$ In this paper we develop multiplicative updates for orthogonal NMTF where X≈USV^?$\mathit{X}\approx {\mathit{USV}}^{?}$ is pursued with orthogonality constraints, U^?U=I,${\mathit{U}}^{?}\mathit{U}=\mathit{I}\text{,}$ and V^?V=I${\mathit{V}}^{?}\mathit{V}=\mathit{I}$, exploiting true gradients on Stiefel manifolds. Experiments on various document data sets demonstrate that our method works well for document clustering and is useful in revealing polysemous words via co-clustering words and documents.