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.     

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.     

Channel assignment with separation for interference avoidance in wireless networks

Given an integer /spl sigma/>1, a vector (/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/), of nonnegative integers, and an undirected graph G=(V, E), an L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers, such that |f(u)-f(v)|/spl ges//spl delta//sub i/, if d(u,v)=i, for 1相似文献   

Stochastic stabilization of nonlinear systems in feedforward form with noisy outputs

We study the problem of globally stabilizing through measurement feedback a class of uncertain stochastic nonlinear systems in feedforward (or upper triangular) form, with state equations affected by a Wiener process adapted to a given filtration of /spl sigma/-algebras and measurements affected by a sample continuous and strongly Markov stochastic process adapted to the same filtration of /spl sigma/-algebras. We propose a step-by step design, based on splitting the system /spl Sigma/ into one-dimensional interconnected systems /spl Sigma//sub j/, j=1,...,n. Moreover, we introduce the notion of practical stability in probability, which corresponds to having a large probability of being the state small in norm whenever the noise affecting the measurements has a "small" second order moment.     

Learning capability and storage capacity of two-hidden-layer feedforward networks

The problem of the necessary complexity of neural networks is of interest in applications. In this paper, learning capability and storage capacity of feedforward neural networks are considered. We markedly improve the recent results by introducing neural-network modularity logically. This paper rigorously proves in a constructive method that two-hidden-layer feedforward networks (TLFNs) with 2/spl radic/(m+2)N (/spl Lt/N) hidden neurons can learn any N distinct samples (x/sub i/, t/sub i/) with any arbitrarily small error, where m is the required number of output neurons. It implies that the required number of hidden neurons needed in feedforward networks can be decreased significantly, comparing with previous results. Conversely, a TLFN with Q hidden neurons can store at least Q/sup 2//4(m+2) any distinct data (x/sub i/, t/sub i/) with any desired precision.     

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.     

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.     

Efficient algorithms for the all nearest neighbor and closest pair problems on the linear array with a reconfigurable pipelined bus system

We present two O(1)-time algorithms for solving the 2D all nearest neighbor (2D/spl I.bar/ANN) problem, the 2D closest pair (2D/spl I.bar/CP) problem, the 3D all nearest neighbor (3D/spl I.bar/ANN) problem and the 3D-closest pair (3D/spl I.bar/CP) problem of n points on the linear array with a reconfigurable pipelined bus system (LARPBS) from the computational geometry perspective. The first O(1) time algorithm, which invokes the ANN properties (introduced in this paper) only once, can solve the 2D/spl I.bar/ANN and 2D/spl I.bar/CP problems of n points on an LARPBS of size 1/2n/sup 5/3+c/, and the 3D/spl I.bar/ANN and 3D/spl I.bar/CP problems pf n points on an LARPBS of size 1/2n/sup 7/4+c/, where 0 < /spl epsi/ = 1/2/sup c+1/-1 /spl Lt/ 1, c is a constant and positive integer. The second O(1) time algorithm, which recursively invokes the ANN properties k times, can solve the kD/spl I.bar/ANN, and kD/spl I.bar/CP problems of n points on an LARPBS of size 1/2n/sup 3/2+c/, where k = 2 or 3, 0 < /spl epsi/ = 1/2/sup n+1/-1 /spl Lt/ 1, and c is a constant and positive integer. To the best of our knowledge, all results derived above are the best O(1) time ANN algorithms known.     

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).     

Optimal quantization of periodic task requests on multiple identical processors

We simplify the periodic tasks scheduling problem by making a trade off between processor load and computational complexity. A set N of periodic tasks, each characterized by its density /spl rho//sub i/, contains n possibly unique values of /spl rho//sub i/. We transform N through a process called quantization, in which each /spl rho/i /spl isin/ N is mapped onto a service level s/sub j/ /spl isin/ L, where |L| = l /spl Lt/ n and /spl rho//sub i/ /spl les/ s/sub j/, (this second condition differentiates this problem from the p-median problem on the real line). We define the periodic task quantization problem with deterministic input (PTQ-D) and present an optimal polynomial time dynamic programming solution. We also introduce the problem PTQ-S (with stochastic input) and present an optimal solution. We examine, in a simulation study, the trade off penalty of excess processor load needed to service the set of quantized tasks over the original set, and find that, through quantization onto as few as 15 or 20 service levels, no more than 5 percent processor load is required above the amount requested. Finally, we demonstrate that the scheduling of a set of periodic tasks is greatly simplified through quantization and we present a fast online algorithm that schedules quantized periodic tasks.     

A necessary algebraic condition for controllability and observability of linear time-varying systems

In this note, we give an algebraic condition which is necessary for the system x'(t)=A(t)x(t)+B(t)u(t), y(t)=C(t)x(t), either to be totally controllable or to be totally observable, where x/spl isin//spl Ropf//sup d/, u/spl isin//spl Ropf//sup p/, y/spl isin//spl Ropf//sup q/, and the matrix functions A, B and C are (d-2), (d-1) and (d-1) times continuously differentiable, respectively. All conditions presented here are in terms of known quantities and therefore easily verified. Our conditions can be used to rule out large classes of time-varying systems which cannot be controlled and/or observed no matter what the nonzero time-varying coefficients are. This work is motivated by the deep result of Silverman and Meadows.     

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.     

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.     

Many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements

A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. We deal with the graph G/sub 0/ /spl oplus/ G/sub 1/ obtained from connecting two graphs G/sub 0/ and G/sub 1/ with n vertices each by n pairwise nonadjacent edges joining vertices in G/sub 0/ and vertices in G/sub 1/. Many interconnection networks such as hypercube-like interconnection networks can be represented in the form of G/sub 0/ /spl oplus/ G/sub 1/ connecting two lower dimensional networks G/sub 0/ and G/sub 1/. In the presence of faulty vertices and/or edges, we investigate many-to-many disjoint path coverability of G/sub 0/ /spl oplus/ G/sub 1/ and (G/sub 0/ /spl oplus/ G/sub 1/) /spl oplus/ (G/sub 2/ /spl oplus/ G/sub 3/ ), provided some conditions on the Hamiltonicity and disjoint path coverability of each graph G/sub i/ are satisfied, 0 /spl les/ i /spl les/ 3. We apply our main results to recursive circulant G(2/sup m/, 4) and a subclass of hypercube-like interconnection networks, called restricted HL-graphs. The subclasses includes twisted cubes, crossed cubes, multiply twisted cubes, Mobius cubes, Mcubes, and generalized twisted cubes. We show that all these networks of degree m with f or less faulty elements have a many-to-many k-DPC joining any k distinct source-sink pairs for any k /spl ges/ 1 and f /spl ges/ 0 such that f+2k /spl les/ m - 1.     

On nonlinear controllability of homogeneous systems linear in control

This paper considers small-time local controllability (STLC) of single- and multiple-input systems, x/spl dot/=f/sub 0/(x)+/spl Sigma//sub i=1//sup m/f/sub i/u/sub i/ where f/sub 0/(x) contains homogeneous polynomials and f/sub 1/,...,f/sub m/ are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree homogeneous systems STLC is equivalent to accessibility, provides a complete characterization of STLC for this class of systems. In the multiple-input case, transformations on the input space are applied to homogeneous systems of degree two, an example of this type of system being motion of a rigid-body in a plane. Such input transformations are related via consideration of a tensor on the tangent space to congruence transformation of a matrix to one with zeros on the diagonal. Conditions are given for successful neutralization of bad type (1,2) brackets via congruence transformations.     

A note on deciding controllability in pushdown systems

Consider an event alphabet /spl Sigma/. The supervisory control theory of Ramadge and Wonham asks the question, given a plant model G, with language K L/sub M/(G)/spl sube//spl Sigma//sup */ and another language K/spl sube/ L/sub M/(G), is there a supervisor /spl psi/ such that L/sub M/(/spl psi//G)=K. Ramadge and Wonham showed that a necessary condition for this to be true is the so-called controllability of K with respect to L/sub M/(G). They showed that when G is a finite state automaton and K is a regular language (also generated by a finite state automaton), then the controllability property was decidable for K. The class of languages generated by pushdown automata properly includes the regular languages. They are accepted by finite state machines coupled with pushdown stack memory. This makes them interesting candidates as supervisory languages, since the supervisor will have nonfinite memory. In this note, we show the following: i) If S is a specification given by a deterministic pushdown automaton and L is generated by a finite state machine, then there is an algorithm to decide whether K=S/spl cap/L is controllable with respect to L. ii) It is undecidable for an arbitrary specification S generated by a nondeterministic pushdown automaton and plant language L generated by a finite state machine whether K=S/spl cap/L is controllable with respect to L.     

The critical role of environment in fatigue damage accumulation in deep-reactive ion-etched single-crystal silicon structural films

The importance of service environment to the fatigue resistance of n/sup +/-type, 10 /spl mu/m thick, deep-reactive ion-etched (DRIE) silicon structural films used in microelectromechanical systems (MEMS) was characterized by testing of electrostatically actuated resonators (natural frequency, f/sub 0/, /spl sim/40 kHz) in controlled atmospheres. Stress-life (S-N) fatigue tests conducted in 30/spl deg/C, 50% relative humidity (R.H.) air demonstrated the fatigue susceptibility of silicon films. Further characterization of the films in medium vacuum and 25% R.H. air at various stress amplitudes revealed that the rates of fatigue damage accumulation (measured via resonant frequency changes) are strongly sensitive to both stress amplitude and, more importantly, humidity. Scanning electron microscopy of high-cycle fatigue fracture surfaces (cycles to failure, N/sub f/>1/spl times/10/sup 9/) revealed clear failure origins that were not observed in short-life (N/sub f/<1/spl times/10/sup 4/) specimens. Reaction-layer and microcracking mechanisms for fatigue of silicon films are discussed in light of this empirical evidence for the critical role of service environment during damage accumulation under cyclic loading conditions.     

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.     

An analog neural network implementation in fixed time of adjustable-order statistic filters and applications

In this paper, we show a neural network implementation in fixed time of adjustable order statistic filters, including sorting, and adaptive-order statistic filters. All these networks accept an array of N numbers X/sub i/=S/sub Xi/M/sub Xi/2/sup EXi/ as input (where S/sub Xi/ is the sign of X/sub i/, M/sub Xi/ is the mantissa normalized to m digits, and Ex is the exponent) and employ two kinds of neurons, the linear and the threshold-logic neurons, with only integer weights (most of the weights being just +1 or -1) and integer threshold. Therefore, this will greatly facilitate the actual hardware implementation of the proposed neural networks using currently available very large scale integration technology. An application of using minimum filter in implementing a special neural network model neural network classifier (NNC) is given. With a classification problem of l classes C/sub 1/,C/sub 2/,...,C/sub 1/, NNC classifies in fixed time an unknown vector to one class using a minimum-distance classification technique.