How to Make $T$-Transitive a Proximity Relation

Three ways to approximate a proximity relation $R$ (i.e., a reflexive and symmetric fuzzy relation) by a $T$ -transitive one where $T$ is a continuous Archimedean $t$-norm are given. The first one aggregates the transitive closure $overline{R}$ of $R$ with a (maximal) $T$-transitive relation $B$ contained in $R$ . The second one computes the closest homotecy of $overline{R}$ or $B$ to better fit their entries with the ones of $R$. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for $T$ the $Lstrok$ukasiewicz or the product $t$-norm. The previous methods do not apply for the minimum $t$-norm. An algorithm to approximate a given proximity relation by a ${rm Min}$-transitive relation (a similarity) is given in the last section of the paper.      

On $Delta$-Transforms

Any set of two legs in a Gough–Stewart platform sharing an attachment is defined as a $Delta$component. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a $Delta$ component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Gough–Stewart platform remains the same, provided that no architectural singularities are introduced. Such leg rearrangements are defined as $Delta$-transforms, and they can be applied sequentially and simultaneously. Although it may seem counterintuitive at first glance, the rearrangement of legs using simultaneous $Delta$-transforms does not necessarily lead to leg configurations containing a $Delta$component. As a consequence, the application of $Delta$-transforms reveals itself as a simple, yet powerful, technique for the kinematic analysis of large families of Gough–Stewart platforms. It is also shown that these transforms shed new light on the characterization of architectural singularities and their associated self-motions.      

Performance Analysis for Overlay Multimedia Multicast on $r$-ary Tree and $m$-D Mesh Topologies

Without requiring multicast support from the underlying networks, overlay multicast has the advantage of implementing inter-domain multimedia multicast communications. Usually, overlay multicast protocols employ two different topologies: $r$-ary tree and $m$-D mesh. In this paper, we study the influence of topology selection on multimedia multicast performance. We present a set of theoretical results on the worst performance, the average performance, and the performance difference along the link stress, the number of overlay hops, and the number of shortest paths for $r$-ary tree-based and $m$ -D mesh-based multicast, respectively. Furthermore, through simulations in NS2, we observe and compare tree and mesh topologies along the metrics analyzed theoretically. Simulation results match our theoretical analyses. Finally we give our evaluations of and insights into these two kinds of multicast when used to transmit multimedia streams. The selection of overlay topology is application dependent. To the best of our knowledge, this is the first evaluation of multimedia multicast performances in different overlay topologies. We believe that this study is useful for protocol design of target multimedia applications and for investigating multicast functions.      

Simultaneous $H^{infty}$ Control for Nonlinear Systems

This note develops a novel method for designing simultaneous $H^{infty}$ state feedback controllers for a collection of single-input nonlinear systems. Based on the Kalman—Yakubovich—Popov Lemma, necessary and sufficient conditions for the existence of simultaneous $H^{infty}$ controllers are derived by the control storage function approach. A universal formula for constructing continuous, time-invariant, simultaneous $H^{infty}$ state feedback controllers is presented.      

Decentralized $H_{infty }$ Filter Design for Discrete-Time Interconnected Fuzzy Systems

This paper describes a decentralized $H_{infty }$ filter design for discrete-time interconnected fuzzy systems based on piecewise-quadratic Lyapunov functions. The systems consist of $J$discrete-time interconnected Takagi–Sugeno (T–S) fuzzy subsystems, and a decentralized $H_infty$ filter is designed for each subsystem. It is shown that the stability of the overall filtering-error system with $H_{infty }$ performance can be established if a piecewise-quadratic Lyapunov function can be constructed. Moreover, the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Two simulation examples are given to show the effectiveness of the proposed approach.      

$ {cal L}_{2}$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior

We investigate the $ {cal L}_{2}$ gain of periodic linear switched systems under fast switching. For systems that possess a suitable notion of a time-average system, we characterize the relationship between the ${cal L}_{2}$ gain of the switched system and the ${cal L}_{2}$ gain of its induced time-average system when the switching rate is sufficiently fast. We show that the switched system ${cal L}_{2}$ gain is in general different from the average system ${cal L}_{2}$ gain if the input or output coefficient matrix switches. If only the state coefficient matrix switches, the input-output energy gain for a fixed ${cal L}_{2}$ input signal is bounded by the ${cal L}_{2}$ gain of the average system as the switching rate grows large. Additionally, for a fixed ${cal L}_{2}$ input, the maximum pointwise in time difference between the switched and average system outputs approaches zero as the switching rate grows.      

The Global Kernel $k$-Means Algorithm for Clustering in Feature Space

Kernel $k$-means is an extension of the standard $k$ -means clustering algorithm that identifies nonlinearly separable clusters. In order to overcome the cluster initialization problem associated with this method, we propose the global kernel $k$-means algorithm, a deterministic and incremental approach to kernel-based clustering. Our method adds one cluster at each stage, through a global search procedure consisting of several executions of kernel $k$-means from suitable initializations. This algorithm does not depend on cluster initialization, identifies nonlinearly separable clusters, and, due to its incremental nature and search procedure, locates near-optimal solutions avoiding poor local minima. Furthermore, two modifications are developed to reduce the computational cost that do not significantly affect the solution quality. The proposed methods are extended to handle weighted data points, which enables their application to graph partitioning. We experiment with several data sets and the proposed approach compares favorably to kernel $k$ -means with random restarts.      

A ${bm lambda}$-Cut and Goal-Programming-Based Algorithm for Fuzzy-Linear Multiple-Objective Bilevel Optimization

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a ${lambda}$-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using ${lambda}$-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a ${lambda}$-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a ${lambda}$-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm.      

6H-SiC JFETs for 450 $^{circ}hbox{C}$ Differential Sensing Applications

N-channel 6H-SiC depletion-mode junction field-effect transistors (JFETs) have been fabricated, and characterized for use in high-temperature differential sensing. Electrical characteristics of the JFETs have been measured and are in good agreement with predictions of an abrupt-junction long-channel JFET model. The electrical characteristics were measured across a 2-in wafer for temperatures from 25 $^{ circ}hbox{C}$ to 450 $^{circ}hbox{C}$, and the extracted pinchoff voltage has a mean of 11.3 V and a standard deviation of about 1.0 V at room temperature, whereas pinchoff current has a mean of 0.41 mA with standard deviation of about 0.1 mA. The change in pinchoff voltage is minimal across the measured temperature range, whereas pinchoff current at 450 $^{circ}hbox{C}$ is about half its value at room temperature, consistent with the expected change in the $nmu_{n}$ product. The characterization of differential pairs and hybrid amplifiers constructed using these differential pairs is also reported. A three-stage amplifier with passive loads has a differential voltage gain of 50 dB, and a unity-gain frequency of 200 kHz at 450 $^{circ}hbox{C}$, limited by test parasitics. A two-stage amplifier with active loads has reduced sensitivity to off-chip parasitics and exhibits a differential voltage gain of 69 dB with a unity-gain frequency of 1.3 MHz at 450 $^{circ}hbox{C}$.$hfill$[2009-0029]      

Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type- ${n}$

In this paper, we use Zadeh's extension principle to extend Kosko's definition of the fuzzy subsethood measure $S(G,H)$ to type-2 fuzzy sets defined on any set $X$ equipped with a measure. Subsethood is itself a fuzzy set that is a crisp interval when $G$ and $H$ are interval type-2 sets. We show how to compute this interval and then use the result to compute subsethood for general type-2 fuzzy sets. A definition of subsethood for arbitrary fuzzy sets of type- $n ≫ 2$ is then developed. This subsethood is a type-( $n-1$) fuzzy set, and we provide a procedure to compute subsethood of interval type-3 fuzzy sets.      

Piecewise $H_{infty}$ Controller Design of Uncertain Discrete-Time Fuzzy Systems With Time Delays

This paper considers the robust $H_{infty}$ control of uncertain discrete-time fuzzy systems with time delays based on piecewise Lyapunov--Krasovskii functionals. It is shown that the stability with $H_{infty}$ disturbance attenuation performance can be established for the closed-loop fuzzy control systems if there exists a piecewise Lyapunov--Krasovskii functional, and moreover, the functional and the corresponding controller can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A numerical example is given to demonstrate the efficiency and the advantage of the proposed method.      

Divide and Conquer: EKF SLAM in $O(n)$

In this paper, we show that all processes associated with the move-sense-update cycle of extended Kalman filter (EKF) Simultaneous Localization and Mapping (SLAM) can be carried out in time linear with the number of map features. We describe Divide and Conquer SLAM, which is an EKF SLAM algorithm in which the computational complexity per step is reduced from $O(n^2)$ to $O(n)$, and the total cost of SLAM is reduced from $O(n^3)$ to $O(n^2)$. Unlike many current large-scale EKF SLAM techniques, this algorithm computes a solution without relying on approximations or simplifications (other than linearizations) to reduce computational complexity. Also, estimates and covariances are available when needed by data association without any further computation. Furthermore, as the method works most of the time in local maps, where angular errors remain small, the effect of linearization errors is limited. The resulting vehicle and map estimates are more precise than those obtained with standard EKF SLAM. The errors with respect to the true value are smaller, and the computed state covariance is consistent with the real error in the estimation. Both simulated experiments and the Victoria Park dataset are used to provide evidence of the advantages of this algorithm.      

Factor Analysis Latent Subspace Modeling and Robust Fuzzy Clustering Using $t$-Distributions

Factor analysis is a latent subspace model commonly used for local dimensionality reduction tasks. Fuzzy $c$-means (FCM) type fuzzy clustering approaches are closely related to Gaussian mixture models (GMMs), and expectation--maximization (EM) like algorithms have been employed in fuzzy clustering with regularized objective functions. Student's $t$ -mixture models (SMMs) have been proposed recently as an alternative to GMMs, resolving their outlier vulnerability problems. In this paper, we propose a novel FCM-type fuzzy clustering scheme providing two significant benefits when compared with the existing approaches. First, it provides a well-established observation space dimensionality reduction framework for fuzzy clustering algorithms based on factor analysis, allowing concurrent performance of fuzzy clustering and, within each cluster, local dimensionality reduction. Second, it exploits the outlier tolerance advantages of SMMs to provide a novel, soundly founded, nonheuristic, robust fuzzy clustering framework by introducing the effective means to incorporate the explicit assumption about Student's $t$ -distributed data into the fuzzy clustering procedure. This way, the proposed model yields a significant performance increase for the fuzzy clustering algorithm, as we experimentally demonstrate.      

Moving Polymer Waveguides and Latching Actuator for 2 $ times$ 2 MEMS Optical Switch

We describe a novel type of MEMS optical switch based on moving waveguide which has merits inherited from both MEMS and integrated optics technologies. It provides an expandable 2 $times$ 2 switching capability, a first in this category of switches. The switch is built by assembling independently optimized latching silicon actuator and soft polymer waveguides. The actuator is based on two new structures: a microhinge, dubbed the fork hinge, and a latching structure using a precompressed microspring. The mechanical switching speed was measured below 0.5 ms. The complex polymer waveguide structure was thoroughly characterized to obtain all the components of the optical loss. This analysis allowed us to estimate robustly the insertion loss of the assembled optical switch below 3 dB and to identify the possibilities to improve this figure. $hfill$[2008-0142]      

A Parameter-Dependent Approach to Robust $H_{infty }$ Filtering for Time-Delay Systems

This paper is concerned with the problem of robust $H_{infty }$ filtering for linear continuous-time systems with polytopic parameter uncertainties and time-varying delay in the state. We utilize the polynomially parameter-dependent idea to solve the robust $H_{infty }$ filtering problem, with new linear matrix inequality conditions obtained for the existence of admissible filters. These conditions are developed based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The delay-dependence and polynomial parameter-dependence guarantee the proposed approach to be potentially less conservative, which is shown via a numerical example.      

Delay-Dependent $hbox{H}_{infty }$ Filter Design for Discrete-Time Fuzzy Systems With Time-Varying Delays

This paper investigates delay-dependent $hbox{H}_{bminfty }$ filter design problems for discrete-time fuzzy systems with time-varying delays. First, a novel delay-dependent piecewise Lyapunov–Krasovskii functional (DDPLKF) is proposed in which both the upper bound of delays and the delay interval are considered. Based on this DDPLKF, the delay-dependent stability criteria for discrete-time systems with constant or time-varying delays are obtained, respectively. Then, delay-dependent full-order and reduced-order $hbox{H}_{bminfty }$ filter design approaches are proposed. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Simulation examples are also given to illustrate the performance of the proposed approaches. It is shown that our approaches are less conservative and that the corresponding $hbox{H}_{bminfty }$ filters can achieve better performance than the existing approaches.      

${cal H}_{infty}$ State-Feedback Control Design for Fuzzy Systems Using Lyapunov Functions With Quadratic Dependence on Fuzzy Weighting Functions

This paper proposes a method for designing an ${cal H}_{infty}$ state-feedback fuzzy controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems. To derive less conservative ${cal H}_{infty}$ stabilization conditions, this paper enhances the interactions among the fuzzy subsystems using a multiple Lyapunov function with quadratic dependence on fuzzy weighting functions. Besides, for more allocation of the nonlinearity to the fuzzy control system, this paper introduces a slack variable that is quadratically dependent on the one-step-past fuzzy weighting functions as well as the current ones. In the derivation, the ${cal H}_{infty}$ stabilization conditions are formulated in terms of parameterized linear matrix inequalities (PLMIs), which are reconverted into LMI conditions with the help of an efficient relaxation technique.      

A $Q$ -Learning Approach to Derive Optimal Consumption and Investment Strategies

In this paper, we consider optimal consumption and strategic asset allocation decisions of an investor with a finite planning horizon. A $Q$-learning approach is used to maximize the expected utility of consumption. The first part of the paper presents conceptually the implementation of $Q$ -learning in a discrete state-action space and illustrates the relation of the technique to the dynamic programming method for a simplified setting. In the second part of the paper, different generalization methods are explored and, compared to other implementations using neural networks, a combination with self-organizing maps (SOMs) is proposed. The resulting policy is compared to alternative strategies.      

Firing Sequences Estimation in Vector Space Over $Z_{3}$ for Ordinary Petri Nets

Event sequences estimation is an important issue for fault diagnosis of Discrete event systems, so far as fault events cannot directly be measured. This paper is about event sequences estimation with Petri net models. Events are assumed to be represented with transitions, and firing sequences are estimated from measurements of the marking variation. Estimation with and without measurement errors are discussed in $n$-dimensional vector space over alphabet $Z_{3} = {-1, 0, 1}$. Sufficient conditions and estimation algorithms are provided. Performance is evaluated, and the efficiency of the approach is illustrated on two examples from manufacturing engineering.      

Relaxed ${cal H}_{infty }$ Stabilization Conditions for Discrete-Time Fuzzy Systems With Interval Time-Varying Delays

To derive less-conservative delay- and range-dependent ${cal H}_{infty }$ stabilization conditions for discrete-time Takagi–Sugeno (T–S) fuzzy systems with interval time-varying delays, the use of a fuzzy-weighting-dependent Lyapunov–Krasovskii functional (FWLKF), in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions, is proposed. Subsequently, parameterized linear matrix inequality (PLMI)-based ${cal H}_infty$ stabilization conditions are derived by following the free-weighting matrix approach. To fully exploit the convexity of fuzzy weighting functions, the derived PLMIs are sequentially replaced by a finite set of LMIs by considering all possible conditions associated with fuzzy weighting functions.