Output regulation of periodic signals for DPS: an infinite-dimensional signal Generator

In this note, we consider output regulation and disturbance rejection of periodic signals via state feedback in the setting of exponentially stabilizable linear infinite-dimensional systems. We show that if an infinite-dimensional exogenous system is generating periodic reference signals, solvability of the state feedback regulation problem is equivalent to solvability of the so called equations. This result allows us to consider asymptotic tracking of periodic reference signals which only have absolutely summable Fourier coefficients, while in related existing work the reference signals are confined to be infinitely smooth. We also discuss solution of the regulator equations and construct the actual feedback law to achieve output regulation in the single-input-single-output (SISO) case: The output regulation problem is solvable if the transfer function of the stabilized plant does not have zeros at the frequencies i/spl omega//sub n/ of the periodic reference signals and if the sequence ([CR(i/spl omega//sub n/, A+BK)B]/sup -1/ /spl times/(Q/spl phi//sub n/-CR(i/spl omega//sub n/, A+BK)P/spl phi//sub n/)) /sub n/spl isin/z//spl isin/l/sup n2/. A one-dimensional heat equation is used as an illustrative example.     

Remarks on the L/sup p/-input converging-state property

Let X /spl sub/ /spl Ropf//sup N/ and consider a system x/spl dot/ = f(x,u), f : X /spl times/ /spl Ropf//sup M/ /spl rarr/ /spl Ropf//sup N/, with the property that the associated autonomous system x/spl dot/ = f (x,0) has an asymptotically stable compactum C with region of attraction A. Assume that x is a solution of the former, defined on [0,/spl infin/), corresponding to an input function u. Assume further that, for each compact K /spl sub/ X, there exists k > 0 such that |f(z,v) - f(z,0)| /spl les/ k|v| for all (z,v) /spl isin/ /spl times/ /spl Ropf//sup M/. A simple proof is given of the following L/sup p/-input converging-state property: if u /spl isin/ L/sup p/ for some p /spl isin/ [1,/spl infin/) and x has an /spl omega/-limit point in A, then x approaches C.     

Computation of the frequency response of multilinear affine systems

Deals with the problem of computing the frequency response of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form P(s, q) = l/sub o/ (q) + l/sub 1/ (q) s + /spl middot//spl middot//spl middot/ + l/sub n/, (q) s/sup n/ whose coefficients depend linearly on q = [q/sub 1/, q/sub 2/, ..., q/sub q/]/sup T/ and the uncertainty box is Q = {q: q/sub i/ /spl epsiv/ [q/sub i/, q/sub i/], i = 1, 2,..., q}. Using the geometric structure of the value set of P(s, q), a powerful edge elimination procedure is proposed for computing the Bode, Nyquist, and Nichols envelopes of these uncertain systems. A numerical example is included to illustrate the benefit of the method presented.     

IR uncooled bolometers based on amorphous Ge/sub x/Si/sub 1-x/O/sub y/ on silicon micromachined structures

In this work, we present the fabrication of bulk micromachined microbolometers made of amorphous germanium-silicon-oxygen compounds (Ge/sub x/Si/sub 1-x/O/sub y/) grown by reactive sputtering of a Ge/sub 0.85/Si/sub 0.15/ target. We describe the complete procedure for fabricating thermally isolated microbolometers consisting of Ge/sub x/Si/sub 1-x/O/sub y/ sensing films deposited on sputtered silicon dioxide membranes suspended over a silicon substrate. The electrical properties of the sensitive material are set by controlling the deposition parameters of the sputtering technique. Under optimum deposition conditions, Ge/sub x/Si/sub 1-x/O/sub y/ layers with moderate electrical resistivity and thermal coefficient at room temperature as high as -4.2% /spl middot/ K/sup -1/ can be obtained. Isolated structures measured at atmospheric pressure in air have a thermal conductance of 3 /spl times/ 10/sup -6/ W /spl middot/ K/sup -1/ and a thermal capacitance of 6/spl middot/10/sup -9/ W /spl middot/ s /spl middot/ K/sup -1/, yielding a response time of 1.8 ms. Bolometers with an IR responsivity of 380 V /spl middot/ W/sup -1/ and a NEDT of 3.85 K at 100 nA bias current are obtained. The use of sputtered films allows designing a fully low-temperature fabrication process, wholly compatible with silicon integrated circuit technologies.     

L/sup p/ approximation of Sigma-Pi neural networks

A feedforward Sigma-Pi neural network with a single hidden layer of m neurons is given by /sup m//spl Sigma//sub j=1/c/sub j/g(n/spl Pi//sub k=1/x/sub k/-/spl theta//sub k//sup j///spl lambda//sub k//sup j/) where c/sub j/, /spl theta//sub k//sup j/, /spl lambda//sub k//spl isin/R. We investigate the approximation of arbitrary functions f: R/sup n//spl rarr/R by a Sigma-Pi neural network in the L/sup p/ norm. An L/sup p/ locally integrable function g(t) can approximate any given function, if and only if g(t) can not be written in the form /spl Sigma//sub j=1//sup n//spl Sigma//sub k=0//sup m//spl alpha//sub jk/(ln|t|)/sup j-1/t/sub k/.     

Adaptive optimization of least-squares tracking algorithms: with applications to adaptive antenna arrays for randomly time-varying mobile communications systems

Adaptive antenna arrays are used for reducing the effects of interference and increasing capacity in mobile communications systems. Typical algorithms recursively compute the antenna weights that minimize the weighted error function (at discrete times kh, k=1,2,..., for a sampling interval h) /spl sigma//sub l=1//sup k//spl alpha//sup k-l/[e/sub l/(W)]/sup 2/, where e/sub l/(W) is a measure of the reception error at time lh with antenna weight vector W, and /spl alpha/<1. The forgetting factor /spl alpha/<1 allows tracking as conditions change and the minimization is used only to get the weights. The average detection error rate depends heavily on the chosen value of /spl alpha/, whose optimal value can change rapidly in time, perhaps significantly in seconds. We add another adaptive loop that tracks the optimal value of /spl alpha/ and greatly improves the operation when the environment is randomly time-varying. The additional adaptive loop is based on an approximation to a natural "gradient descent" method. The algorithm is practical and can improve the performance considerably. In terms of average detection error rates and for all of the scenarios tested, the new system tracks the optimal value of /spl alpha/ well, and always performs better (sometimes much better) than the original algorithm that uses any fixed value of /spl alpha/. Although the initial motivation arises in adaptive antennas, the method can be used to improve algorithms for tracking parameters of time-varying nonlinear systems, where similar issues are involved.     

Uncooled multimirror broad-band infrared microbolometers

A new generation of microbolometers were designed, fabricated and tested for the NASA CERES (Clouds and the Earth's Radiant Energy System) instrument to measure the radiation flux at the Earth's surface and the radiant energy now within the atmosphere. These detectors are designed to measure the earth radiances in three spectral channels consisting of a short wave channel of 0.3 to 5 /spl mu/m, a wide-band channel of 0.3 to 100 /spl mu/m and a window channel from 8 to 12 /spl mu/m each housing a 1.5 mm x 1.5 mm microbolometers or alternatively 400 /spl mu/m x 400 mm microbolometers in a 1 /spl times/ 4 array of detectors in each of the three wavelength bands, thus yielding a total of 12 channels. The microbolometers were fabricated by radio frequency (RF) magnetron sputtering at ambient temperature, using polyimide sacrificial layers and standard micromachining techniques. A semiconducting YBaCuO thermometer was employed. A double micromirror structure with multiple resonance cavities was designed to achieve a relatively uniform absorption from 0.3 to 100 /spl mu/m wavelength. Surface micromachining techniques in conjunction with a polyimide sacrificial layer were utilized to create a gap underneath the detector and the Si/sub 3/N/sub 4/ bridge layer. The temperature coefficient of resistance was measured to be -2.8%/K. The voltage responsivities were over 10/sup 3/ V/W, detectivities above 10/sup 8/ cm Hz/sup 1/2//W, noise equivalent power less than 4 /spl times/ 10/sup -10/W/Hz/sup 1/2/ and thermal time constant less than 15 ms.     

The wonham filter with random parameters: rate of convergence and error bounds

Let /spl alpha/(t) be a finite-state continuous-time Markov chain with generator Q=(q/sup ij/)/spl isin/R/sup m/spl times/m/ and state space M={z/sup i/,...,z/sup m/}, where z/sup 1/ for i/sub /spl middot//spl middot//spl middot//spl middot//m are distinct real numbers. When the state-space and the generator are known a priori, the best estimator of /spl alpha/(t) (in terms of mean square error) under noisy observation is the classical Wonham filter. This note addresses the estimation issue when values of the state-space or values of the generator are unknown a priori. In each case, we propose a (suboptimal) filter and prove its convergence to the desired Wonham filter under simple conditions. Moreover, we obtain the rate of convergence using both the mean square and the higher moment error bounds.     

Effect of trimethylsilane flow rate on the growth of SiC thin-films for fiber-optic temperature sensors

We have investigated the effect of trimethylsilane ([(CH/sub 3/)/sub 3/SiH] or 3MS) flow rate on the growth of SiC thin-film on single-crystal sapphire substrate for fiber-optic temperature sensor. The SiC film thickness was in the range of 2-3 /spl mu/m. The variation of the 3MS flow rate affected the structural properties of the SiC films. This, in turn, changed the optical properties and temperature sensing performance of the sensors. Optical reflection from the SiC thin-film Fabry-Pe/spl acute/rot interferometers showed one-way phase shifts in resonant minima on all measured samples. Linear fits to the resonant minima (at 660 to 710 nm) versus temperature provide the corresponding thermal expansion coefficient, /spl kappa//sub /spl phi//, of 1.7-1.9/spl times/10/sup -5///spl deg/C. With the optimized 3MS flow rate, the SiC temperature sensor exhibits a temperature accuracy of /spl plusmn/2.8/spl deg/C from 22 to 540/spl deg/C. The short-term SiC sensor stability at 532/spl deg/C for two weeks shows a very small standard deviation of 0.97/spl deg/C.     

An exact stability analysis test for single-parameter polynomially-dependent linear systems

We provide a new condition for testing the stability of a single-parameter, polynomially-dependent linear system of polynomial degree N of the form x/spl dot/=A(/spl rho/)x, A(/spl rho/)=/spl Sigma//sub i=0//sup N//spl rho//sup i/ A/sub i/ (1) over a compact interval. The test is nonconservative and can be cast as a convex feasibility problem in terms of a pair of linear matrix inequalities (LMIs).     

Fabrication and measured performance of a first-generation microthermoelectric cooler

The measured performance of a column-type microthermoelectric cooler, fabricated using vapor-deposited thermoelectric films and patterned using photolithography processes, is reported. The columns, made of p-type Sb/sub 2/Te/sub 3/ and n-type Bi/sub 2/Te/sub 3/ with an average thickness of 4.5 /spl mu/m, are connected using Cr/Au/Ti/Pt layers at the hot junctions, and Cr/Au layers at the cold junctions. The measured Seebeck coefficient and electrical resistivity of the thermoelectric films, which were deposited with a substrate temperature of 130/spl deg/C, are -74 /spl mu/V/K and 3.6/spl times/10/sup -5/ /spl Omega/-m (n-type, power factor of 0.15 mW/K/sup 2/-m), and 97 /spl mu/V/K and 3.1/spl times/10/sup -5/ /spl Omega/-m (p-type, power factor of 0.30 mW/K/sup 2/-m). The cooling performance of devices with 60 thermoelectric pairs and a column width of 40 /spl mu/m is evaluated under a minimal cooling load (thermobuoyant surface convection and surface radiation). The average cooling achieved is about 1 K. Fabrication challenges include the reduction of the column width, implementation of higher substrate temperatures for optimum thermoelectric properties, and improvements of the top connector patterning and deposition.     

Design, fabrication, and measurement of high-sensitivity piezoelectric microelectromechanical systems accelerometers

Microelectromechanical systems (MEMS) accelerometers based on piezoelectric lead zirconate titanate (PZT) thick films with trampoline or annular diaphragm structures were designed, fabricated by bulk micromachining, and tested. The designs provide good sensitivity along one axis, with low transverse sensitivity and good temperature stability. The thick PZT films (1.5-7 /spl mu/m) were deposited from an acetylacetonate modified sol-gel solution, using multiple spin coating, pyrolysis, and crystallization steps. The resulting films show good dielectric and piezoelectric properties, with P/sub r/ values >20 /spl mu/C/cm/sup 2/, /spl epsiv//sub r/>800, tan/spl delta/<3%, and |e/sub 31,f/| values >6.5 C/m/sup 2/. The proof mass fabrication, as well as the accelerometer beam definition step, was accomplished via deep reactive ion etching (DRIE) of the Si substrate. Measured sensitivities range from 0.77 to 7.6 pC/g for resonant frequencies ranging from 35.3 to 3.7 kHz. These accelerometers are being incorporated into packages including application specific integration circuit (ASIC) electronics and an RF telemetry system to facilitate wireless monitoring of industrial equipment.     

Optimal algorithms for the channel-assignment problem on a reconfigurable array of processors with wider bus networks

The computation model on which the algorithms are developed is the reconfigurable array of processors with wider bus networks (abbreviated to RAPWBN). The main difference between the RAPWBN model and other existing reconfigurable parallel processing systems is that the bus width of each network is bounded within the range [2,[/spl radic/(N)]]. Such a strategy not only saves the silicon area of the chip as well as increases the computational power enormously, but the strategy also allows the execution speed of the proposed algorithms to be tuned by the bus bandwidth. To demonstrate the computational power of the RAPWBN, the channel-assignment problem is derived in this paper. For the channel-assignment problem with N pairs of components, we first design an O(T + [N//spl omega/]) time parallel algorithm using 2N processors with a 2N-row by 2N-column bus network, where the bus width of each bus network is /spl omega/-bit for 2 /spl les/ /spl omega/ /spl les/ [/spl radic/N] and T = [log/sub /spl omega//N] + 1. By tuning the bus bandwidth to the natural log N-bit and the extended N/sup 1/c/-bit (N/sup 1/c/ > log N) for any constant c and c /spl ges/ 1, two more results which run in O(log N/log log N) and O(1) time, respectively, are also derived. When compared to the algorithms proposed by Olariu et al. [17] and Lin [14], it is shown that our algorithm runs in the equivalent time complexity while significantly reducing the number of processors to O(N).     

An O(1) time algorithm for the 3D Euclidean distance transform on the CRCW PRAM model

We develop a parallel algorithm for the 2D Euclidean distance transform (2D/spl I.bar/EDT, for short) of a binary image of size N /spl times/ N in O(1) time using N/sup 2+/spl delta/+/spl epsi// CRCW processors and a parallel algorithm for the 3D Euclidean distance transform (3D/spl I.bar/EDT, for short) of a binary image of size N /spl times/ N /spl times/ N in O(1) time using N/sup 3+/spl delta/+/spl epsi// CRCW processors, where /spl delta/=1/, /spl epsi/=1/(2/sup c+1/-1), h, and are constants and positive integers. Our 2D/spl I.bar/EDT (3D/spl I.bar/EDT) parallel algorithm can be used to build up Voronoi diagram and Voronoi polygons (polyhedra) in a 2D (3D) binary image also. All of these parallel algorithms can be performed in O(1) time using N/sup 2+/spl delta/+/spl epsi// (N/sup 3+/spl delta/+/spl epsi//) CRCW processors. To the best of our knowledge, all results derived above are the best O(1) time algorithms known.     

Effect of electrode geometry on performance of an EHD thin-film evaporator

This paper presents details of an optimization process of electrode geometry for an electrohydrodynamically (EHD) driven thin-film evaporator. The operation principle of the device is based on the action of the EHD force on the molecules of a dielectric liquid in a highly convergent electric field. The force starts at the end of a pair of electrodes, where the electric field changes from zero far from the electrodes to a finite value in between the electrodes. This force drives the liquid up into the spacing between the electrodes. The electrodes in this study were deposited thinly on a SiO/sub 2//Si wafer, so the liquid could be held within micrometers of thickness over the surface. Since the performance of the device in removing heat from the surface is a function of its pumping head and consequently its electrode geometry, the performances of different electrodes were evaluated by testing twelve sets of electrode pairs with different geometries. Then the optimum electrode design was incorporated into the design of a large size (32/spl times/32 mm/sup 2/) EHD thin-film evaporator. The device was fabricated, and its pumping and heat transfer performances were tested. A pumping head equal to the full height of the electrodes and a heat transfer coefficient of 1.9 W/cm/sup 2/./spl deg/C was achieved using HFE-7100 liquid.     

A min-max approach to fuzzy clustering, estimation, and identification

This study, for any unknown physical process y=f(x/sub 1/,...,x/sub n/), is concerned with the: 1) fuzzy partition of n-dimensional input space X=X/sub 1//spl times//spl middot//spl middot//spl middot//spl times/X/sub n/ into K different clusters, 2) estimating the process behavior y/spl circ/=f(x/spl circ/) for a given input x/spl circ/=(x/spl circ//sub 1/,/spl middot//spl middot//spl middot/,x/spl circ//sub n/)/spl isin/X, and 3) fuzzy approximation of the process, with uncertain input-output identification data {(x(k)/spl plusmn//spl delta/x/sub k/),(y(k)/spl plusmn/v/sub k/)}/sub k=1,.../, using a Sugeno type fuzzy inference system. A unified min-max approach (that attempts to minimize the worst-case effect of data uncertainties and modeling errors on estimation performance), is suggested to provide robustness against data uncertainties and modeling errors. The proposed method of min-max fuzzy parameters estimation does not make any assumption and does not require a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. To show the feasibility of the approach, simulation studies and a real-world application of physical fitness classification based on the fuzzy interpretation of physiological parameters, have been provided.     

Sparse component analysis and blind source separation of underdetermined mixtures

In this letter, we solve the problem of identifying matrices S /spl isin/ /spl Ropf//sup n/spl times/N/ and A /spl isin/ /spl Ropf//sup m/spl times/n/ knowing only their multiplication X = AS, under some conditions, expressed either in terms of A and sparsity of S (identifiability conditions), or in terms of X (sparse component analysis (SCA) conditions). We present algorithms for such identification and illustrate them by examples.     

l/sup /spl infin//-bounded robustness for nonlinear systems: analysis and synthesis

The purpose of this paper is to describe systematic analysis and design tools for robust control problems with l/sup /spl infin// criteria. We first generalize the Hill-Moylan-Willems framework for dissipative systems to accommodate l/sup /spl infin// criteria, and then derive state feedback and measurement feedback synthesis procedures for l/sup /spl infin// robust control problems. The information state framework is used for the measurement feedback robust control problem. Necessary and sufficient conditions are proved, and new synthesis procedures using dynamic programming are presented.     

Constructing edge-disjoint spanning trees in product networks

A Cartesian product network is obtained by applying the cross operation on two graphs. We study the problem of constructing the maximum number of edge-disjoint spanning trees (abbreviated to EDSTs) in Cartesian product networks. Let G=(V/sub G/, E/sub G/) be a graph having n/sub 1/ EDSTs and F=(V/sub F/, E/sub F/) be a graph having n/sub 2/ EDSTs. Two methods are proposed for constructing EDSTs in the Cartesian product of G and F, denoted by G/spl times/F. The graph G has t/sub 1/=|E/sub G/|/spl middot/n/sub 1/(|V/sub G/|-1) more edges than that are necessary for constructing n/sub 1/ EDSTs in it, and the graph F has t2=|E/sub F/'-n/sub 2/(|V/sub F/|-1) more edges than that are necessary for constructing n/sub 2/ EDSTs in it. By assuming that t/sub 1//spl ges/n/sub 1/ and t/sub 2//spl ges/n/sub 2/, our first construction shows that n/sub 1/+n/sub 2/ EDSTS can be constructed in G/spl times/F. Our second construction does not need any assumption and it constructs n/sub 1/+n/sub 2/-1 EDSTs in G/spl times/F. By applying the proposed methods, it is easy to construct the maximum numbers of EDSTs in many important Cartesian product networks, such as hypercubes, tori, generalized hypercubes, mesh connected trees, and hyper Petersen networks.     

Computation of the frequency-response gain of sampled-data systems via projection in the lifted domain

This note addresses the computation of the frequency-response gain of sampled-data systems with their intersample behavior taken into account. The proposed method is based upon a novel necessary and sufficient condition for the frequency-response gain to be less than a given /spl gamma/ > o and thus can be used as a basis for a bisection algorithm. Unlike all currently existing results, the proposed procedure requires the operator /spl gamma//sup 2/I - D /sub 11/D/spl breve//sub 11/* neither to be positive nor even to be invertible, thus eliminating unnecessary restrictions of the existing approaches (here D/spl breve//sub 11/ stands for the feedthrough term of the lifted system).