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.      

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.      

On Constructing Parsimonious Type-2 Fuzzy Logic Systems via Influential Rule Selection

Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termed $R$-values, $c$-values, $omega _1 $-values, and $omega _2 $-values. The $R$-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. The $c$-values rank rules based on the effects of rule consequents, while the $omega _1 $-values and $omega _2 $-values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed “forward selection” and “backward elimination”) are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models.      

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.      

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.      

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.      

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]      

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.      

On the NP-Hardness of Checking Matrix Polytope Stability and Continuous-Time Switching Stability

Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of $k$ matrices in $R^{n times n}$ are stable. In particular, we are interested whether there exist algorithms which can solve this problem in time polynomial in $n$ and $k$. We show that if $k= lceil n^{d} rceil $ for any fixed real $d>0$, then the problem is NP-hard, meaning that no polynomial-time algorithm in $n$ exists provided that $P ne NP$, a widely believed conjecture in computer science. On the other hand, when $k$ is a constant independent of $n$ , then it is known that the problem may be solved in polynomial time in $n$. Using these results and the method of measurable switching rules, we prove our main statement: verifying the absolute asymptotic stability of a continuous-time switched linear system with more than $n^{d}$ matrices $A_{i} in R^{n times n}$ satisfying $0 succeq A_{i} + A_{i}^{T}$ is NP-hard.      

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.      

Analytical Model of Valveless Micropumps

The flow driven by a valveless micropump with a single cylindrical pump chamber and two diffuser/nozzle elements is studied theoretically using a 1-D model. The pump cavity is driven at an angular frequency $omega$ so that its volume oscillates with an amplitude $V_{rm m}$. The presence of diffuser/nozzle elements with pressure-drop coefficients $zeta_{+}$, $zeta_{-}( ≫ zeta_{+})$ and throat cross-sectional area $A_{1}$ creates a rectified mean flow. In the absence of frictional forces the maximum mean volume flux (with zero pressure head) is $Q_{0}$ where $Q_{0}/V_{rm m}omega = (zeta_{-} -break zeta_{+})pi/16(zeta_{-}+zeta_{+})$, while the maximum pressure that can be overcome is $Delta P_{max}$ where $ Delta P_{max}A_{1}^{2}/V_{rm m}^{2} omega^{2} !=! (zeta_{-} -break zeta_{+})/16$. These analytical results agree with numerical calculations for the coupled system of equations and compare well with the experimental results of Stemme and Stemme.$hfill$ [2008-0244]      

$H_{infty}$ Controller Synthesis via Switched PDC Scheme for Discrete-Time T--S Fuzzy Systems

This paper is concerned with the problem of designing switched state feedback $H_{infty}$ controllers for discrete-time Takagi--Sugeno (T--S) fuzzy systems. New types of state feedback controllers, namely, switched parallel distributed compensation (PDC) controllers, are proposed, which are switched based on the values of membership functions. Switched quadratic Lyapunov functions are exploited to derive a new method for designing switched PDC controllers to guarantee the stability and $H_{infty}$ performances of closed-loop nonlinear systems. The design conditions are given in terms of solvability of a set of linear matrix inequalities. It is shown that the new method provides better or at least the same results of the existing design methods via the pure PDC scheme with a quadratic Lyapunov function or switched constant controller gain scheme. Numerical examples are given to illustrate the effectiveness of the proposed method.      

Evanescent-Wave Spectroscopy Using an SU-8 Waveguide for Rapid Quantitative Detection of Biomolecules

A 30-mm-long multimode waveguide, 40 $muhbox{m}$ wide and 40 $muhbox{m}$ high, is fabricated on a silicon wafer using polymer SU-8 as the core and liquid buffer as the cladding. Antibodies are successfully immobilized on the SU-8 surface designated for binding target antigens dispersed in the buffer solution. Evanescent-wave spectroscopy is performed by exciting the fluorescently labeled antigens, bound to the waveguide surface within its evanescence field, and measuring the emission light intensity. This evanescent-wave biosensor detects specific molecular interaction. The optical output as a function of the antigen concentration can be described by Langmuir equation. Antigen concentration as low as 1.5 $muhbox{g}/hbox{mL}$ is detected; concentrations higher than 100 $muhbox{g}/hbox{mL}$ lead to sensor saturation. $hfill$[2008-0058]      

A Programmable Array for Contact-Free Manipulation of Floating Droplets on Featureless Substrates by the Modulation of Surface Tension

This paper presents a contactless droplet manipulation system that relies on thermally generated Marangoni flows. Programmable 2-D control of aqueous microdroplets suspended in an oil film on a plain featureless glass substrate is achieved using a 128-pixel heater array suspended 100–500 $mu hbox{m}$ above the oil layer. The heaters generate surface temperature perturbations $(≪ 25 ^{circ}hbox{C})$, resulting in local Marangoni flows that can move droplets in either a push or a pull mode. Programmed movement is achieved by the sequential activation of the heaters, with digital control circuitry and a graphical interface providing addressable control of each heater. Droplets with diameters of 300–1000 $muhbox{m}$ are manipulated and merged at speeds up to 140 $muhbox{m/s}$. Evaporation rates can be reduced by almost two orders of magnitude by using a two-layer-oil medium, and the choice of an optimum carrier fluid can achieve fluid velocities over 17 000 $mu hbox{m/s}$. The system provides a contactless platform for parallel droplet-based assays. As such, it circumvents the challenges of sample contamination and loss that occur when a droplet interacts with a solid surface.$hfill$[2008-0272]      

Discharge-Based Pressure Sensors for High-Temperature Applications Using Three-Dimensional and Planar Microstructures

Two versions of microdischarge-based pressure sensors, which operate by measuring the change, with pressure, in the spatial current distribution of pulsed dc microdischarges, are reported. The inherently high temperatures of the ions and electrons in the microdischarges make these devices amenable to high-temperature operation. The first sensor type uses 3-D arrays of horizontal bulk metal electrodes embedded in quartz substrates with electrode diameters of 1–2 mm and 50–100-$muhbox{m}$ interelectrode spacing. These devices were operated in nitrogen over a range of 10–2000 torr, at temperatures as high as 1000 $^{circ}hbox{C}$. The maximum measured sensitivity was 5420 ppm/torr at the low end of the dynamic range and 500 ppm/torr at the high end, while the temperature coefficient of sensitivity ranged from $-$925 to $-$550 ppm/K. Sensors of the second type use planar electrodes and have active areas as small as 0.13 $hbox{mm}^{2}$. These devices, when tested in a chemical sensing system flowing helium as a carrier gas, had a maximum sensitivity of 9800 ppm/torr, a dynamic range of 25–200 torr, and a temperature coefficient of sensitivity of approximately $-$1412 ppm/K.$hfill$ [2008-0262]      

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.      

A Low-Voltage Large-Displacement Large-Force Inchworm Actuator

Inchworm microactuators are popular in micropositioning applications for their long ranges. However, until now, they could not be considered for applications such as in vivo biomedical applications because of their high input voltages. This paper reports on the modeling, design, fabrication, and testing of a new family of pull-in-based electrostatic inchworm microactuators which provides a solution to this problem. Actuators with only 7-V operating voltage are achieved with a $pm 18hbox{-}muhbox{m}$ total range and a $pm 30hbox{-}muhbox{N}$ output force. Larger operating voltage (16 V) actuators show even better results in force ($pm 110 mu hbox{N}$) and range $(pm 35 muhbox{m})$. The actuator has an in-plane angular deflection conversion which provides a force-displacement tradeoff and allows us to set step sizes varying from few nanometers to few micrometers with a minor change in design. In this paper, we designed 1- and 4-$muhbox{m}$ step-size devices. The actuator step size may change during the operation because of the slipping of the shuttle and the beam bending; however, our model successfully explains the reasons. One of our actuator prototypes has survived more than 25 million cycles without performance deterioration. The device is fabricated using the silicon-on-insulator-based multiuser MEMS process.$hfill$[2007-0146]      

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.