Application of a fast simulation method to the estimation of the number of some <Emphasis Type="Italic">k</Emphasis>-dimensional subspaces over a finite space

A fast simulation method is proposed for estimation of the number of k-dimensional subspaces of weight w in an n-dimensional vector space over the Galois field containing q components. Unbiased estimates are constructed for the cases when w = 1 and w = 2, and lower and upper estimates are proposed for the case when w = 3. It is proved that the relative error remains bounded as q → ∞. A high accuracy of the method proposed is illustrated by numerical examples.     

Tight Approximation Ratio of a General Greedy Splitting Algorithm for the Minimum <Emphasis Type="Italic">k</Emphasis>-Way Cut Problem

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter.     

Efficient Algorithms for Integer Programs with Two Variables per Constraint<Superscript><Emphasis Type="Italic">1</Emphasis></Superscript>

Given a bounded integer program with n variables and m constraints, each with two variables, we present an O(mU) time and O(m) space feasibility algorithm, where U is the maximal variable range size. We show that with the same complexity we can find an optimal solution for the positively weighted minimization problem for monotone systems. Using the local-ratio technique we develop an O(nmU) time and O(m) space 2 -approximation algorithm for the positively weighted minimization problem for the general case. We further generalize all results to nonlinear constraints (called axis-convex constraints ) and to nonlinear (but monotone) weight functions. Our algorithms are not only better in complexity than other known algorithms, but also considerably simpler, and they contribute to the understanding of these very fundamental problems. Received June 21, 1996; revised December 5, 1997.     

The free‐weight matrix approach to event‐driven output H∞ control of networked control systems

This paper puts forward a new free‐weight matrix method used to analyse Network control systems (NCSs) with the H∞ performance index level based on event‐driven control. Firstly, design a relative triggering mechanism contain the measured output for a linear system with external disturbances. Secondly, in order to reduce the conservativeness an appropriate Lyapunov‐Krasovskii function is constructed. For the integral term generated after the above functional derivation, the free‐weight matrix inequality is selected for scaling. Finally,the sufficient condition that the closed‐loop system represented by the linear matrix inequality (LMI) satisfies the H∞ performance index and the solution of the controller are obtained.The validity of the scheme is confirmed by a given numerical case.     

Poisson‐Based Weight Reduction of Animated Meshes

While animation using barycentric coordinates or other automatic weight assignment methods has become a popular method for shape deformation, the global nature of the weights limits their use for real‐time applications. We present a method that reduces the number of control points influencing a vertex to a user‐specified number such that the deformations created by the reduced weight set resemble that of the original deformation. To do so we show how to set up a Poisson minimization problem to solve for a reduced weight set and illustrate its advantages over other weight reduction methods. Not only does weight reduction lower the amount of storage space necessary to deform these models but also allows GPU acceleration of the resulting deformations. Our experiments show that we can achieve a factor of 100 increase in speed over CPU deformations using the full weight set, which makes real‐time deformations of large models possible.     

Generalized <Emphasis Type="Italic">H</Emphasis>∞-optimal control as a trade-off between the <Emphasis Type="Italic">H</Emphasis>∞-optimal and γ-optimal controls

for the linear dynamic plant that is subjected to exogenous action and uncertainty generated by the unknown initial plant conditions, the level of perturbation suppression was determined as the greatest value of the ratio of the L2-norm of the objective output to the quadratic root of the sum of the squared L2-norm of the exogenous disturbance and norm of the initial state taken with a weight coefficient. Determination of the worst exogenous disturbance and the initial state maximizing this index was demonstrated. The role of the weight coefficient in the trade-off between the H∞-norm, that is, the level of suppression of the exogenous disturbance under the zero initial conditions, and the level γ0 of suppression of the initial uncertainties, was clarified in the absence of exogenous disturbance. The generalized H∞-optimal laws of state and output control minimizing the chosen criterion were designed in terms of the linear matrix inequalities. The advantage of the generalized controller over the ordinary H∞-optimal controller was demonstrated by way of an example of the linear oscillator with unknown initial conditions.     

Parametric optimal control problems with weighted <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>-norm in the cost function

In the paper, an optimal control problem with weighted L ₁-norm in the cost function is studied. The problem is considered as a parametric problem where L ₁-norm weight ratio is treated as a parameter. We analyze the dependence of solution to the mentioned optimization problem on values of the parameter. A theorem that describes properties of the solution under small parameter perturbations is proved. Differential properties of the solution are investigated. Under assumption that a solution to unperturbed problem is known, rules for construction of solutions to perturbed optimization problems are given.     

Classification of optimal (<Emphasis Type="Italic">v</Emphasis>, 4, 1) binary cyclically permutable constant-weight codes and cyclic 2-(<Emphasis Type="Italic">v</Emphasis>, 4, 1) designs with <Emphasis Type="Italic">v</Emphasis> ≤ 76

We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constantweight (CPCW) codes with v ≤ 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence between optimal (v, 4, 1) CPCW codes, optimal cyclic binary constant-weight codes with weight 4 and minimum distance 6, (v, 4; ⌎(v − 1)/12⌏) difference packings, and optimal (v, 4, 1) optical orthogonal codes. Therefore, the classification of CPCW codes holds for them too. Perfect (v, 4, 1) CPCWcodes are equivalent to (v, 4, 1) cyclic difference families, and thus (73, 4, 1) cyclic difference families are classified too.     

Design of Digital State <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-Controllers of the MIMO Systems with Prescribed Precision

For the linear MIMO plants subject to polyharmonic perturbations, a method of designing digital state controllers was developed with regard for the requirements on limitedness of the control actions in the stable state as well as on limitedness of the controlled variables. A notion of radius of the stable state of a closed-loop system was introduced, and the problem of using the full state vector to design a discrete controller providing the desired radius was formulated. Its necessary and sufficient solvability conditions were obtained using the procedure of H _∞-optimization by selecting the weight matrices of the discrete Lur’e-Riccati equation.__________Translated from Avtomatika i Telemekhanika, No. 8, 2005, pp. 46–51.Original Russian Text Copyright © 2005 by Chestnov.     

Design of prescribed-precision controllers of multivariable systems by root-mean-square criterion on the basis of <Emphasis Type="Italic">LQ</Emphasis>-optimization procedures

A problem of designing the continuous controllers of multivariable linear systems ensuring in the root-mean-square their desired precision in the controlled variables under the action of nonmeasurable, power-bounded polyharmonic determinate exogenous disturbances having unknown amplitudes, frequencies, and number of frequencies was formulated. Conditions were established for solvability of the problem with state controllers (in this case, the disturbances and controls must be applied to the same point) and measurable output controllers (the plant must be minimum phase with the same number of controls and controlled variables) on the basis of the LQ-optimization procedures by selecting the weight coefficients of the quadratic optimization functional.     

Bipartite Linear χ‐Consensus of Double‐Integrator Multi‐Agent Systems With Measurement Noise

The bipartite consensus problem is investigated for double‐integrator multi‐agent systems in the presence of measurement noise. A distributed protocol with time‐varying consensus gain is proposed. By using tools of state transition matrix and algebraic graph theory, necessary and sufficient conditions for the designed protocol to be a mean square bipartite linear χ‐consensus protocol are given. It is shown that the signed digraph being structurally balanced and having a spanning tree are not only sufficient, but also necessary for bipartite consensus. Furthermore, the protocol is proved to be a mean square bipartite average consensus protocol if the signed graph is weight balanced.     

Normal forms for multi‐input flat systems of minimal differential weight

We present normal forms for nonlinear control systems that are the closest to static feedback linearizable ones, that is, for systems that become feedback linearizable via the simplest dynamic feedback, which is the one‐fold prolongation of a suitably chosen control. They form a particular class of flat systems, namely those of differential weight n + m + 1, where n is the number of states and m is the number of controls. We also show that the dynamic feedback may create singularities in the control space depending on the state and we discuss them. We also address the issue of the normalization of the system only versus that of the system together with a flat output. Finally, we illustrate our results by several examples.     

Inverting and noninverting H∞ controllers

It is well known that two-block S/KS/T H_∞ problems in which the plant is weighted at the output tend to invert the plant in the controller. This paper shows that even four-block S/KS/T problems in which the plant is weighted at the input result in controllers which invert the plant. However, if a GS/T weighting scheme is used where the weight for the sensitivity includes the plant, the inversion is avoided. This GS/T scheme therefore is especially suited for ill-conditioned plants. An example confirms these results.     

Optimal‐switched extended H∞ filter for nonlinear systems with stochastic uncertainties

The extended H_∞ filter (EH_∞F) is a conservative solution with infinite‐horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH_∞F design, we developed an optimal‐switched (OS) filtering mechanism based on the standard EH_∞F to obtain an optimal‐switched extended H_∞ filter (OS‐EH_∞F). The OS mechanism has an error‐tolerant switched (ETS) structure, which switches the filtering mode between optimal and H_∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS‐EH_∞F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS‐EH_∞F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.     

Modular configuration of service elements based on the improved K‐means algorithm

To reduce the vagueness and subjectivity of customer demand in the process of product–service system design, a fuzzy semantic calculation method is proposed to obtain the importance of service demand. In addition, according to the demand of the clustering of service modules, a new clustering method is proposed to analyse discrete data based on the improved K‐means algorithm that is based on the Kruskal algorithm. According to the criterion of the service module division and its weight, the correlation coefficient between any two service activities is judged to form the comprehensive correlation coefficient matrix, and the comprehensive dissimilarity matrix can be obtained by the additive model. Then, this method calculates the minimum cost spanning tree (MCST) using the Kruskal algorithm. The different clusters of service activities with different centres can be found based on the MCST, and the edge values can be calculated by the improved K‐means algorithm. This paper uses 28 service activities of excavators. These activities can be divided into K (K = 4, 5, 6, and 7) clusters by the improved K‐means algorithm. Finally, the service element configuration model is established based on the demand weight, which is optimized by using the maximum customer satisfaction of competition.     

A lightweight multi‐beam cylindrical Luneberg lens antenna loaded with multiple dielectric posts

A multi‐beam cylindrical Luneberg lens antenna loaded with multiple light dielectric posts for the purpose of light weight is presented. The antenna is based on a parallel‐plate waveguide and specifically composed of 10 E‐shaped patch antennas feeds, 2 parallel plates, and 491 epoxy posts. The equivalent gradient index of the Luneberg lens antenna is realized via the positions of the epoxy posts between the parallel plates. The features of low‐profile height (0.55λ) and large radiating area (4.4 × 0.55λ²) of the cylindrical Luneberg lens result in wide beamwidth in elevation plane and high gain while operating at 4 GHz. Consequently, the 3 dB beamwidth in the elevation plane is >65°. Furthermore, the multi‐beams cover a wide scan angle of 120° in the azimuth plane. The measured aperture efficiency of the fabricated lens antenna is above 50% from 3.9 to 4.3 GHz. In addition to the good radiation performance, features of light weight and ease of fabrication have also been demonstrated for the proposed lens antenna.     

Modeling of maximum endurance time for one‐handed carrying tasks

The objective of this study was to establish models to predict maximum endurance time (MET) for one‐handed carrying tasks. A one‐handed carrying experiment, under three loads and two walking speeds, was performed. The participant carried a dumbbell on the side using either dominant or nondominant hand. His or her arm was straight‐down. The MET values were collected. Both power and exponential functions were adopted in establishing simplified MET models considering the relative force (f_MVC) applied. The simplified models were further expanded to full models where body weight and walking speed were also included. It was found that the power models provided better estimates than the exponential models when the f_MVC was lower than approximately 0.17 for both the simplified and full models. Considering the effects of the walking speed, the full models are recommended when the f_MVC is 0.3 or lower.     

Weighted‐average ℓ1 filtering for switched positive systems

In this paper, the filtering problem for a class of switched positive systems with dwell time is investigated. A novel weighted‐average technique is proposed for filter design such that the final estimate of the unmeasurable outputs of the considered system is more accurate than that of traditional approaches. The main contributions of this paper are summarized as follows: By exploiting the positivity and characteristics of switched positive systems with dwell time, a candidate linear copositive Lyapunov function, which is both quasi‐time‐dependent and mode‐dependent, is presented to establish the closed‐loop stability of the considered systems. Upon the established closed‐loop stability, less conservative bounded positive filters (both upper‐bound and lower‐bound filter) with ? ₁ disturbance attenuation performance are designed for the considered system. By introducing a proper weight, a weighted‐average approach, which is more general than the bounded filter design method, is proposed for filter design. The worst ? ₁ disturbance attenuation performance of the novel developed filter is evaluated. Both the bounded filters and the weighted‐average filter are designed by solving standard linear programming problems. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

A biased random‐key genetic algorithm for OSPF and DEFT routing to minimize network congestion

Interior gateway routing protocols like Open Shortest Path First (OSPF) and Distributed Exponentially Weighted Flow Splitting (DEFT) send flow through forward links toward the destination node. OSPF routes only on shortest‐weight paths, whereas DEFT sends flow on all forward links, but with an exponential penalty on longer paths. Finding suitable weights for these protocols is known as the weight setting problem (WSP). In this paper, we present a biased random‐key genetic algorithm for WSP using both protocols. The algorithm uses dynamic flow and dynamic shortest path computations. We report computational experiments that show that DEFT achieves less network congestion when compared with OSPF, while, however, yielding larger delays.     

The expected additive weight of trees

Summary We consider a general additive weight of random trees which depends on the structure of the subtrees, on weight functions defined on the number of internal and external nodes and on the degrees of the nodes appearing in the tree and its subtrees. Choosing particular weight functions, the corresponding weight is an important parameter appearing in the analysis of sorting and searching algorithms. For a simply generated family of rooted planar trees , we shall derive a general approach to the computation of the average weight of a tree T with n nodes and m leaves for arbitrary weight functions. This general result implies exact and asymptotic expressions for many types of average weights of a tree T with n nodes if the weight functions are arbitrary polynomials in the number of nodes and leaves with coefficients depending on the node degrees.