new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

evidence for two discrete sources of 2f1 f2 distortion product otoacoustic emission in rabbit i differential dependence on stimulus parameters the results of studies of the physiological vulnerability of distortion product otoacoustic emissions dpoaes suggest that the dpoae at 2f1 f2 in vertebrate ears is generated by more than one source the principal aims of the present study were to provide independent evidence for the existence of more than one dpoae source and to determine the contributions of each to the ear canal 2f1 f2 signal to accomplish these aims specific stimulus parameters were separately and systematically varied to provide detailed parametric information regarding 2f1 f2 dpoae amplitude and phase in normal ears of awake rabbits the findings indicate that two discrete sources demonstrating differential dependence on stimulus parameters dominate the generation of the 2f1 f2 dpoae one source of distortion is dominant above 60 70 db spl at moderate primary frequency separations and at all stimulus levels when the primary tones are closely spaced the other source is dominant below 60 70 db spl at moderate primary frequency

pure tone threshold estimation from extrapolated distortion product otoacoustic emission i o functions in normal and cochlear hearing loss ears a new method for direct pure tone threshold estimation from input output functions of distortion product otoacoustic emissions dpoaes in humans is presented previous methods use statistical models relating dpoae level to hearing threshold including additional parameters e g age or slope of dpoae i o function here we derive a dpoae threshold from extrapolated dpoae i o functions directly cubic 2 f1 f2 distortion products and pure tone threshold at f2 were measured at 51 frequencies between f2 500 hz and 8 khz at up to ten primary tone levels between l2 65 and 20 db spl in 30 normally hearing and 119 sensorineural hearing loss ears using an optimized primary tone level setting l1 0 4l2 39 db that accounts for the nonlinear interaction of the two primaries at the dpoae generation site at f2 the pressure of the 2 f1 f2 distortion product pdp is a linear function of the primary tone level l2 linear regression yields correlation coefficients higher than 0 8 in the majority of the dpoae i o functions

robust stabilization of singularly perturbed systems abstract we discuss the problem of designing stabilizing controllers for singularly perturbed systems on the basis of simplified models in 1 it was shown that a constant gain output feedback controller designed on the basis of the simplified model need not stabilize the true system containing both fast and slow modes this phenomenon was then expanded to include the case where the simplified system is strictly proper in 2 the objectives of this note are threefold i to show that given any proper system and any stabilizing controller for it that is proper but not strictly proper there exists a singular perturbation of the system that is destabilized by that controller ii to show that any strictly proper controller for a singularly perturbed system designed on the basis of a reduced order model will stabilize the true system for sufficiently small values of the fast dynamics parameter and iii to provide a characterization in the same spirit as 3 4 of the set of all strictly proper controllers that stabilize a given proper plant by combining these results it is possible to generate the class of all robustly stabilizing controllers for a given singularly perturbed system

a sampled data control scheme for stabilization of systems with unmodeled high frequency dynamics the output feedback stabilization problem is considered for linear sampled data control systems in the presence of unmodeled high frequency dynamics sufficient conditions for stabilization of such systems were given by m vidyasagar 1985 for strictly proper systems this paper extends the class of systems in order to include the proper systems case and proposes a conceptually novel digital control scheme in this scheme the control law based on the reduced order system is applied to the full system only during a short fraction of the sampling period during the second part of the sampling period the control is taken equal to zero such that without control the neglected fast states have sufficient time to converge to their equilibrium point

robustness of dynamic output feedback control for singular perturbation systems abstract the problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated the solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so called auxiliary system of the slow subsystem some conditions are proposed to ensure the robustness of the actual closed loop system the exact upper bound of the parasitic parameter for the controlled system is also determined finally an actual model which failed in dynamic output feedback control in 4 is reexamined successfully here

a further note on the robustness of output feedback control methods to modeling errors in an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed loop system even when the neglected modes are asymptotically stable the purpose of this note is to show that this instability phenomenon might take place even when the reduced order design model is strictly proper

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

a new stable compensator design for exact and approximate loop transfer recovery abstract in this paper a new compensator structure for loop transfer recovery ltr is proposed the proposed compensator a is open loop stable b guarantees closed loop stability and above all c requires much smaller values of gain than the conventional observer based controller for the same degree of loop transfer recovery the fact that the new compensator requires much smaller values of gain than the conventional controller results in several practical advantages the most important among them being the reduction in controller band width and freedom from the woes of saturation the trade off between the value of gain and the degree of loop transfer recovery as well as the bounds on singular values of sensitivity and complementary sensitivity functions is shown clearly both full and reduced order compensators for ltr when the design specifications are reflected either at the input or at the output point of the given plant are considered numerical examples illustrate the advantages of the new compensator structure the new compensator structure is inspired by a careful and clear understanding of how loop transfer recovery occurs when conventional observer based controllers are used to motivate and deduce our new compensator structure a unified treatment of observer theory for ltr is presented in the context of such a unification some new results are also given

near optimal output feedback regulation of ill conditioned linear systems a two time scale approximation for the linear quadratic optimal output feedback regulator program is examined necessary conditions for optimality as well as an algorithm for computing locally near optimal gains are derived if it is assumed that the slow and fast subsystem initial conditions are uniformly distributed optimal gains for the two time scale problem provide a second order approximation to optimal closed loop performance in the unperturbed system this is verified with a numerical example

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

distortion product otoacoustic emission input output characteristics in normal hearing and hearing impaired human ears dpoae input output i o functions were measured at 7f2 frequencies 1 to 8 khz f2 f1 1 22 over a range of levels 5 to 95 db spl in normal hearing and hearing impaired human ears l1 l2 was level dependent in order to produce the largest 2f1 f2 responses in normal ears system distortion was determined by collecting dp data in six different acoustic cavities these data were used to derive a multiple linear regression model to predict system distortion levels the model was tested on cochlear implant users and used to estimate system distortion in all other ears at most but not all f2 s measurements in cochlear implant ears were consistent with model predictions at all f2 frequencies the ears with normal auditory thresholds produced i o functions characterized by compressive nonlinear regions at moderate levels with more rapid growth at low and high stimulus levels as auditory threshold increased dpoae threshold increased accompanied by dpoae amplitude reductions notably over the range of levels where normal ears showed compression the slope of the i o function was steeper in impaired ears the data from normal hearing ears resembled direct measurements of basilar membrane displacement in lower animals data from ears with hearing loss showed that the compressive region was affected by cochlear damage however responses at high levels of stimulation resembled those observed in normal ears

computation of the output of a function with fuzzy inputs based on a low rank tensor approximation we apply a derivative free optimization method based on novel low rank tensor methods to the problem of propagating fuzzy uncertainty through a continuous real valued function adhering to zadeh s extension principle such a problem can be reformulated as a sequence of optimization problems over nested search spaces the optimization method we use is based on a low rank tensor approximation of the function sampled on a grid and a search for the minimal and maximal entries in this low rank tensor in contrast to classical fuzzy uncertainty propagation methods such as the vertex method and the transformation method the method we propose does not exhibit an inherent exponential scaling for increasing dimension of the search space obviously no derivative free optimization algorithm can exist which shows sub exponential scaling with the dimension for all possible continuous functions the algorithm that we present here however can exploit a specific type of structure and regularity beyond continuity that is often present in real world optimization problems we illustrate this with some high dimensional numerical examples where the presented method clearly outperforms some established derivative free optimization codes

vertex method for computing functions of fuzzy variables abstract this paper is to introduce a new approach the vertex method for computing functions of fuzzy variables the method is based on the cut concept and interval analysis the vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi occurrence of variables in the functional expression by conventional interval analysis methods the algorithm is very easy to implement and can be applied to many practical problems some examples are given to illustrate the applications

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

fuzzy weighted averages and implementation of the extension principle abstract this paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and in particular to weighted average operations in risk and decision analysis a computational algorithm based on the cut representation of fuzzy sets and interval analysis is described the method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non linear programming the algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

necessary and sufficient conditions for the equality of interactive and non interactive extensions of continuous functions abstract in this contribution we find the class of n dimensional joint possibility distributions with the property that the interactive extension principle coincides with the non interactive extension principle as long as the interactive operations are determined by continuous functions strictly increasing in each argument this result completes recent studies by the authors where the particular case of interactive additions and multiplications versus non interactive additions and multiplications were investigated in addition this time we propose results that also cover the cases when we know the fuzzy numbers only from their membership functions it means that we eliminated the limitations that appear when we cannot pass from membership function representation to parametric representation of fuzzy numbers as important new applications we mention the study on the completely correlated fuzzy numbers also of note is that we propose two simple methods to extend bidimensional joint possibility distributions to n dimensional joint possibility distributions one method is based on an inductive construction while the other one is based on a pairwise construction

output feedback control of linear two time scale systems output feedback control of linear time invariant singularly perturbed systems is studied the set of all compensators that stabilize a singularly perturbed system while preserving its two time scale structure is parameterized the parameterization is used to show that any two frequency scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure in this procedure a fast high frequency compensator is designed first to stabilize the fast model of the system then a strictly proper slow low frequency compensator is designed to stabilize a modified slow model the parallel connection of the two compensators forms a two frequency scale stabilizing compensator for the singularly perturbed system

on output feedback control of singularly perturbed systems we treat the problem of robustness of output feedback controllers with respect to singular perturbations given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a possibly dynamical output feedback controller we present a sufficient condition which ensures that the system obtained by applying the same controller to the original full order singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter this condition which is less restrictive than those previously given in the literature is shown to be always satisfied when the singular perturbation is due to the presence of fast actuators and or sensors furthermore we show explicitly that in the linear time invariant case if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced order system but destabilizes the full order system

calibration of a water and energy balance model recursive parameter estimation versus particle swarm optimization 1 it is well known that one of the major problems in the application of land surface models is the determination of the various model parameters in most cases only one or a limited number of variables are used to estimate these parameters this study evaluates the use of two fundamentally different global optimization methods multistart weight adaptive recursive parameter estimation mwarpe and particle swarm optimization pso for the estimation of hydrologic model parameters on the basis of data for multiple variables mwarpe iteratively uses the linear recursive filter equations in a monte carlo setting and therefore does not rely on the explicit minimization of an objective function however a major drawback of the mwarpe method is the high dimensionality determined by the number of observations of the matrix to be inverted on the other hand pso is a stochastic optimization method based on the collective strength of a population of individuals with flocking or herding behavior as observed in a wide number of biological systems in situ observations of net radiation latent sensible and ground heat fluxes and the soil moisture profile are used to determine the parameters of a simplified water and energy balance model both optimization methods are analyzed in terms of model performance and computational efficiency comparable results expressed in terms of the root mean square error values were obtained for both methods however it was found that mwarpe tends to slightly overfit the data

the extension principle and a decomposition of fuzzy sets we give an algorithm to decompose a fuzzy interval u using this decomposition and the multilinearization of a univariate function f we obtain an approximation of the fuzzy interval where is obtained from f by applying the extension principle we provide approximation bounds some numeric illustration is provided

analytical expressions for the addition of fuzzy intervals abstract the addition of fuzzy quantities is undeniably the most important operation in fuzzy arithmetic in this paper we consider the general case of the addition of fuzzy intervals based on a continuous triangular norm we start our discussion with an extensive literature review in which we recall explicit formulae for the addition based on the strongest and the weakest triangular norm for the addition based on the algebraic product and several recent results for the addition based on a continuous archimedean triangular norm including specific theorems for strict and nilpotent triangular norms subsequently the addition based on an ordinal sum is studied and it is shown how this addition can be transformed into a series of additions based on the summands of this ordinal sum this important observation implies that the addition based on an arbitrary continuous triangular norm can be practically performed provided the summands of the corresponding ordinal sum representation and the fuzzy intervals involved fulfil the appropriate conditions mentioned in the overview this is illustrated by means of several examples

distortion product otoacoustic emission 2 f1 f2 amplitude as a function of f2 f1 frequency ratio and primary tone level separation in human adults and neonates distortion product otoacoustic emission dpoae 2 f1 f2 amplitude is dependent upon both the frequency ratio and level separation of the eliciting primary tones in adults it has been established that on average a f2 f1 ratio of 1 22 is optimal for evoking the most robust dpoae dpoae amplitude is systematically reduced when f2 f1 ratio is either increased or decreased thus forming a bandpass function harris et al 1989 the frequency ratio function dpoae amplitude f2 f1 ratio is thought to reflect the filtering properties of the cochlea allen and fahey 1993 brown et al 1993 primary tone level separation also influences dpoae amplitude with a 10 to 15 db level difference between the primary tones l1 l2 typically generating largest amplitude in adults equivalent studies have not been conducted in neonates the present study evoked the 2 f1 f2 dpoae in adults term and premature neonates to define the optimal f2 f1 ratio and l1 l2 level separation and to investigate the filtering prope

optifel a convergent heterogeneous particle swarm optimization algorithm for takagi sugeno fuzzy modeling data driven design of accurate and reliable takagi sugeno t s fuzzy systems has attracted a lot of attention where the model structures and parameters are important and often solved in an optimization framework the particle swarm optimization pso algorithm is widely applied in the field however the classical pso suffers from premature convergence and it is trapped easily into local optima which will significantly affect the model accuracy to overcome these drawbacks we have developed a new t s fuzzy system parameters searching strategy called optifel with a heterogeneous multiswarm pso mspso to enhance the searching performance mspso groups the whole population into multiple cooperative subswarms which perform different search behaviors for the potential solutions we have found that the multiple subswarms strategy proposed in this paper is greatly helpful for finding the optimal parameters suitable for the subspaces of the t s fuzzy model our theoretical proof has also demonstrated that the cooperation among the subswarms can maintain a balance between exploration and exploitation to ensure the particles converge to stable points experimental results show that mspso performs significantly better than traditional pso algorithms on six benchmark functions with the improved mspso optifel can generate a good fuzzy system model with high accuracy and strong generalization ability

the behavior of the acoustic distortion product 2f1 f2 from the human ear and its relation to auditory sensitivity the acoustic intermodulation distortion product 2f1 f2 adp was measured in human subjects to investigate 1 the dependence of adp level on stimulus parameters and 2 the relationship between adp level and auditory sensitivity the frequency ratio f2 f1 at which adp level is maximal varies only slightly across frequency and subjects the average optimal ratio is 1 225 beyond the maximum the adp level declines with increasing f2 f1 ratio at rates of up to 250 db oct as the level of one stimulus is increased relative to the other the adp grows saturates and in most cases shows a bendover maximum distortion is generated when l 1 exceeds l 2 growth rate and saturation point are dependent on which stimulus is incremented and on the level of the stationary stimulus with optimal stimulus parameters levels below 60 db spl l 1 greater than l 2 by 15 db f2 f1 1 225 adp levels are commonly 30 db below l 2 patterns of adp level across frequency vary between subjects but are repeatable within each subject as the frequency of one or both of the stimuli is varied changes in adp level exhibit a broadly featured pattern with a fine structure superimposed upon it this fine structure was compared with the features in the stimulus frequency emission spectrum in one subject with appropriate stimulus parameters half of our subjects show a statistically significant correlation across frequency between adp level and auditory sensitivity at the corresponding f1 frequency our results suggest that with low levels of stimulation adp measurements could form the basis of an objective measure of cochlear function in human subjects

on the robustness of sampled data control to unmodeled high frequency dynamics robustness of sampled data control designs to unmodeled high frequency dynamics is studied using singular perturbation theory it is argued that when the plant is preceded by a zero order hold a direct transmission term of the reduced order model which results from neglecting high frequency dynamics should be modeled as a delay element in order to ensure robustness

locus of generation for the 2 f1 f2 vs 2 f2 f1 distortion product otoacoustic emissions in normal hearing humans revealed by suppression tuning onset latencies and amplitude correlations the present study used distortion product otoacoustic emission dpoae suppression tuning curves stcs dpoae onset latencies ols and dpoae amplitude correlations to investigate the locus of generation of the 2 f1 f2 dpoae versus the 2 f2 f1 dpoae in humans the results of the tuning study revealed that for the 2 f1 f2 dpoae the tips of the stcs tuned consistently below the geometric mean gm frequency of the primary tones in contrast for the 2 f2 f1 dpoae stcs tuned above the gm of the primaries with 50 of the tip frequencies at or above the 2 f2 f1 frequency place when the average ratio of the 2 f2 f1 to the 2 f1 f2 tip frequencies was computed a factor of 1 44 provided an estimate of the frequency shift needed to align the two dpoae generation sites other results showed that ols for the 2 f2 f1 dpoae were uniformly shorter than those for the 2 f1 f2 with differences at the low frequencies amounting to as much as 6 7 ms further for both dpoaes curves describing latency decreases as

the influence of systematic primary tone level variation l2 l1 on the acoustic distortion product emission 2f1 f2 in normal human ears the purpose of the present study was to determine the effect of primary tone level variation l2 l1 on the amplitude of distortion product otoacoustic emissions dpoaes the dpoae at the frequency 2f1 f2 f2 f1 was measured in 20 ears of ten normally hearing subjects acoustic distortion products were generated by primaries f1 and f2 with geometric mean frequencies of 1 2 and 4 khz the f2 f1 ratios were 1 25 1 khz 1 23 2 khz and 1 21 4 khz the primary tone level l1 was kept constant at either 65 or 75 db spl while the second primary tone level l2 was varied between 20 and 90 db spl in 5 db steps the level differences l2 l1 generating maximal dpoae amplitudes depended on l1 and on the geometric mean frequency of f1 and f2 there were large interindividual differences overall the l2 l1 evoking maximal mean dpoae amplitudes was 10 db for geometric mean frequencies of 1 and 2 khz with both l1 65 db spl and l1 75 db spl for 4 khz l2 l1 was 5 db with l1 65 db spl and 0 db with l1 75 db sp

characterization and computation for the bound e in linear time variantsingularly perturbed systems abstract this paper gives a complete solution to the bound problem in a linear time invariant singularly perturbed system a criterion is presented to determine the existence of the bound

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

on interactive fuzzy numbers in this paper we will introduce a measure of interactivity between marginal distributions of a joint possibility distribution c as the expected value of the interactivity relation between the level sets of its marginal distributions

on the design of stabilizing controllers for singularly perturbed systems the robustness of output feedback control designs for singularly perturbed systems based on the reduced systems is discussed a frequency domain approach is presented to determine the conditions for the stability of linear time invariant systems subject to neglected high frequency dynamics in contrast with the qualitative analyses for robust stability that have appeared in the literature this approach gives an explicit computable bound on unmodeled dynamics which does not destabilize the systems stability conditions for various feedback control schemes are presented it is noted that the approach extended to systems with mixed singular regular perturbations can be used to derive the robust stability condition

the recursive algorithm for the optimal static output feedback control problem of linear singularity perturbed systems a recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of singularly perturbed linear systems the algorithm is very efficient from the numerical point of view since only low order systems are involved in algebraic calculations and the required solution can be easily obtained up to an arbitrary order of accuracy that is o epsilon sup k where epsilon is a small perturbation parameter the real world example demonstrates the failure of o epsilon theory used so far in the study of this problem and the necessity for the existence of o epsilon sup k theory

computing expensive multivariate functions of fuzzy numbers using sparse grids fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models with zadeh s extension principle one can obtain a fuzzy extension of any objective function computing expensive multivariate functions of fuzzy numbers however often poses a difficult problem due to non applicability of common fuzzy arithmetic algorithms severe overestimation or very high computational complexity this paper proposes a new approach based on sparse grids consisting of two parts first we compute a surrogate function using sparse grid interpolation second we perform the fuzzy valued evaluation of the surrogate function by a suitable implementation of the extension principle based on real or interval arithmetic the new approach gives accurate results and requires only few function evaluations

a new approach to robust guaranteed cost control for uncertain multimodeling systems the guaranteed cost control problem for multimodeling systems with norm bounded uncertainty is investigated the main contribution in this paper is that a new independent controller is derived by solving the reduced order slow and fast algebraic riccati equations ares whose dimension is smaller than the dimension of full order multiparameter algebraic riccati equation mare it is shown that if these ares have a positive definite stabilizing solution then the closed loop system is quadratically stable and has the cost bound

zadeh s extension principle for continuous functions of non interactive variables a parallel optimization approach there is a growing interest in the use of fuzzy intervals in many engineering applications however a direct implementation of zadeh s extension principle which forms the basis for computing with fuzzy intervals is still computationally too demanding for practical use in the case of a continuous function and fuzzy intervals that describe non interactive variables as inputs the output is a fuzzy interval as well and can be determined for each cut separately the problem thus reduces to finding the endpoints of these cuts which amounts to a number of interwoven optimization problems in the case of a non monotone continuous function however these optimization problems are non trivial in this paper different optimization algorithms are applied for that purpose gradient descent based on sequential quadratic programming simplex simulated annealing particle swarm optimization and particle swarm optimization combined with gradient descent in addition two approaches are followed to determine a suitable number of cuts either a fixed predetermined number is used or an initially very small number is chosen that is subsequently increased according to a linearity criterion both a non parallel and a parallel implementation are designed the parallel version is restricted to work with particle swarm optimization and employs communication to optimize its internal performance by exploiting the dependence between the various optimization problems different configurations are evaluated on a set of benchmark functions in terms of the mean area under the output fuzzy interval and the number of function evaluations particle swarm optimization combined with gradient descent starting from a small number of cuts leads to the most accurate fuzzy intervals at the cost of a relatively large number of function evaluations

comparison of nine methods to estimate ear canal stimulus levels the reliability of nine measures of the stimulus level in the human ear canal was compared by measuring the sensitivity of behavioral hearing thresholds to changes in the depth of insertion of an otoacoustic emission probe four measures were the ear canal pressure the eardrum pressure estimated from it and the pressure measured in an ear simulator with and without compensation for insertion depth the remaining five quantities were derived from the ear canal pressure and the thevenin equivalent source characteristics of the probe forward pressure initial forward pressure the pressure transmitted into the middle ear eardrum sound pressure estimated by summing the magnitudes of the forward and reverse pressure integrated pressure and absorbed power two sets of behavioral thresholds were measured in 26 subjects from 0 125 to 20 khz with the probe inserted at relatively deep and shallow positions in the ear canal the greatest dependence on insertion depth was for transmitted pressure and absorbed power the measures with the least dependence on insertion depth throughout the frequency range best performance included the depth compensated simulator eardrum forward and integrated pressures among these forward pressure is advantageous because it quantifies stimulus phase

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

technical communique on the klimushchev krasovskii theorem the klimushchev krasovskii theorem describes a sufficient condition for the asymptotic stability of singularly perturbed systems motivated by some subtle examples this note presents a new necessary and sufficient condition by imposing an additional assumption on the statement of the klimushchev krasovskii theorem this note also extends the main inertia theorem to singularly perturbed systems

multistage parametric eigenstructure assignment by output feedback control this paper develops an efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output feedback control the sets of closed loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages this allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions the number of effective free parameters beyond eigenvalue assignment is determined and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced numerical examples are included to demonstrate the design procedure

frequency domain results for systems with slow and fast dynamics the mathematical treatment of systems with slow and fast dynamics has traditionally involved singular perturbation theory for differential equations this paper suggests a set of conditions to be placed on a frequency domain description of a system to guarantee two time scale behavior some basic stability and approximation results are presented

robust stabilization for composite observer based control of discrete systems abstract design criteria of robust observer based controllers for linear discrete time singularly perturbed systems with slow and fast modes are considered the developed stability measure complements the quantitative information for unmodeled fast modes that cannot be provided by the usual qualitative robustness analyses a numerical example is provided to show the analytical results obtained

paper optimal output feedback design of systems with ill conditioned dynamics singular perturbation concepts are exploited to develop a procedure for designing a constant gain output feedback control system it is assumed that the original system is ill conditioned in the sense that the plant contains widely separated dynamics and that an accurate description for the high frequency behavior may not be available the design procedure attempts to stabilize the system by minimizing a quadratic cost function made up of the control and states associated with a reduced order low frequency model for the plant and a measure of stability for the neglected fast dynamics the resulting design procedure does not require knowledge of the fast dynamics

the transformation method for the simulation and analysis of systems with uncertain parameters in this paper the transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters based on the concept of cuts the method represents a special implementation of fuzzy arithmetic that avoids the well known effect of overestimation which usually arises when fuzzy arithmetic is reduced to interval computation systems with uncertain model parameters can thus be simulated without any artificial widening of the simulation results as a by product of the implementation scheme the transformation method also provides a measure of influence to quantitatively analyze the uncertain system with respect to the effect of each uncertain model parameter on the overall uncertainty of the model output by this a special kind of sensitivity analysis can be defined on the basis of fuzzy arithmetic finally to show the efficiency of the transformation method the method is applied to the simulation and analysis of a model for the friction interface between the sliding surfaces of a bolted joint connection

approximating a cuts with the vertex method if f rn r is continuous and monotonic in eachvariable and if i is a fuzzy number on the ith coordinate then the membership on r induced by and by the membership onfrn given by x min 1 x1 n xn can be evaluated by determining the membership at the endpoints of the level cuts of each i here more general conditions are given for both the function and the manner in which the fuzzy numbers i are combined so that this simple method for computing induced membership may be used in particular a geometric condition is given so that the cuts computed when the fuzzy numbers are combined using min is an upper bound for the actual induced membership

comparing the optimal signal conditions for recording cubic and quadratic distortion product otoacoustic emissions odd and even order distortion products dps evoked by two primary tones f1 f2 f1 f2 represent different aspects of cochlear nonlinearity the cubic and quadratic difference tones cdt 2f1 f2 and qdt f2 f1 are prominent representatives of the odd and even dps distortion product otoacoustic emissions dpoaes were measured within a primary level l1 l2 space over a wide range of f2 f1 ratios to compare the optimal signal conditions for these dps for cdt the primary level difference decreased as l1 increased with a rate proportional to the f2 f1 ratio moreover the optimal ratio increased with l1 a set of two formulas is proposed to describe the optimal signal conditions however for a given level of a primary increasing the other tone level could maximize the qdt amplitude the frequency ratio at the maximal qdt was about 1 3 and quite constant across different primary levels a notch was found in the qdt amplitude at the f2 f1 ratio of about 1 22 1 25 these opposite behaviors suggest that the optimal recording conditions are different for cdt and qdt due to the different aspects in the cochlear nonlinearity optimizing the dpoae recordings could improve the reliability in clinical or research practices

brief paper on the use of reduced order models in output feedback design of discrete systems the problem of designing output feedback controllers for discrete systems using reduced order models is investigated in this paper it is shown that neglecting nondominant modes does not generally guarantee the stability of the closed loop system certain special structures have been identified for which the use of static and dynamic feedback controllers can provide a stabilizing effect examples are presented to illustrate these structures

linear compensator designs based exclusively on input output information are never robust with respect to unmodeled dynamics the effects of unmodeled higher order dynamics or parasitics on the stability of linear control systems are investigated a description is first given of a class of perturbations of a given state equation that cannot be distinguished from the original on the basis of input output measurements alone then it is shown that given any plant compensator pair perturbations of each system of this type can always be found that destabilize the closed loop configuration the effect of destabilizing perturbations on output behavior is explored

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

toward a theory of robust compensation for systems with unknown parasitics the problem of designing a robust compensator based on a plant model with order uncertainty is considered the uncertainty is characterized mathematically as a class of generalized singular perturbations of the plant the case of static compensation is examined a necessary and sufficient condition is established under which actual closed loop behavior is close to that predicted by the plant model under sufficiently small singular perturbations the condition is shown to be generic

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

dependence of distortion product otoacoustic emissions on primary levels in normal and impaired ears i effects of decreasing l2 below l1 the 2f1 f2 distortion product otoacoustic emission dpoae is evoked by two primary tones of frequencies f1 f2 and levels l1 and l2 previous reports indicate that decreasing l2 below l1 l2 can 1 increase dpoae amplitude in normal ears and 2 increase the degree to which dpoae amplitudes are reduced by cochlear trauma although both of these factors could be advantageous for clinical applications of dpoaes neither has been explored in detail in the present study 2f1 f2 dpoae amplitude frequency functions were collected from normal and impaired ears of rabbits and humans with l1 l2 and with l2 l1 at each of three values of l1 in rabbits controlled tonal or noise overexposures were used to produce permanent reductions of dpoae amplitudes comparison of pre and postexposure dpoae amplitude frequency functions demonstrated that the frequency specific reductions of dpoaes were enhanced by decreasing l2 below l1 in humans dpoae amplitude frequency functions obtained with the various l1 and l2 c

robustness of linear feedback control systems to unmodelled high frequency dynamics a basic issue in the control of linear time invariant plants is the effect of neglected high frequency dynamics on the performance in particular on the closed loop stability of the control system in this paper the robustness of various output feedback control designs based on a reduced order model with neglected high frequency dynamics is investigated using singular perturbation techniques a general robust design rule is to avoid static output feedback for systems with unmodelled high frequency dynamics from a frequency domain standpoint the robust design rule is to avoid closing high frequency plant loops by using strictly proper controllers or controllers with a low pass filtering property

cooperative coevolution for large scale optimization based on kernel fuzzy clustering and variable trust region methods large scale optimization arises in a variety of scientific and engineering applications in this paper a particle swarm optimization pso approach with dynamic neighborhood that is based on kernel fuzzy clustering and variable trust region methods called ft dnpso is proposed for large scale optimization the cooperative coevolution incorporated with a kernel fuzzy c means clustering strategy is introduced to divide high dimensional problems in to subproblems and explore their search spaces furthermore the independent variable ranges change adaptably by using the variable trust region learning method which expedites the convergence process and explores in the effective space in addition the dynamic neighborhood topology assists the pso algorithm in cooperating with neighbor particles and avoids the problem of premature convergence simulation results substantiate the effectiveness of the proposed algorithm to solve large scale optimization problems with many well known benchmark functions

optimal output feedback control of discrete linear singularly perturbed stochastic systems the static output feedback control problem for discrete linear singularly perturbed stochastic systems is studied a recursive algorithm is presented to solve the corresponding coupled non linear algebraic equations the algorithm removes the ill conditioning by decomposing the higher order equations into lower order equations and develops a technique which enables us to obtain an arbitrary accuracy that is 0 ej j 1 2 3 a approximation for this problem a numerical example is presented to support the theoretical results communicated by professor a a ioannou

singular perturbation of strictly positive realness abstract the robustness of the strictly positive real spr condition of linear time invariant multi input multi output lti mimo singularly perturbed systems is examined a necessary and sufficient condition under which the full system is spr is proved this robustness result is an extension of the analysis for the popov kalman yakubovich lemma by v r saksena and p v kokotovic 7

fast suboptimal solution to the static output control problem of linear singularly perturbed systems abstract the reduced order suboptimal solution to the static output control problem of linear singularly perturbed system is obtained in terms of the fast variables only assuming the special structure of initial conditions for the slow and fast variables the problem of big initial conditions of the fast variables is considered

feedback systems and multiple time scales we study feedback design for systems with multiple time scale structure uncovering an intrinsic time scale structure for a state feedback system with full state output from this we construct a multiple time scale asymptotic observer and consider a system with state feedback via a two time scale asymptotic observer finally we obtain more general results for a restricted class of systems

the discrete time h sub spl infin control problem with strictly proper measurement feedback this paper is concerned with the discrete time h sub spl infin control problem with strictly proper measurement feedback we derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given h sub spl infin norm bound note that contrary to the continuous time in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator finally we give an explicit formula for one controller which achieves this bound

level dependence of distortion product otoacoustic emissions measured at high frequencies in humans given that high frequency hearing is most vulnerable to cochlear pathology it is important to characterize distortion product otoacoustic emissions dpoaes measured with higher frequency stimuli in order to utilize these measures in clinical applications the purpose of this study was to explore the dependence of dpoae amplitude on the levels of the evoking stimuli at frequencies greater than 8 khz and make comparisons with those data that have been extensively measured with lower frequency stimuli to accomplish this dpoae amplitudes were measured at six different f2 frequencies 2 5 10 12 14 and 16 khz with a frequency ratio f2 f1 of 1 2 at five fixed levels 30 to 70 db spl of one primary either f1 or f2 while the other primary was varied in level 30 to 70 db spl generally the level separation between the two primary tones l1 l2 generating the largest dpoae amplitude referred to as the optimal level separation decreased as the level of the fixed primary increased additional

gradual numbers and their application to fuzzy interval analysis in this paper we introduce a new way of looking at fuzzy intervals instead of considering them as fuzzy sets we see them as crisp sets of entities we call gradual real numbers they are a gradual extension of real numbers not of intervals such a concept is apparently missing in fuzzy set theory gradual numbers basically have the same algebraic properties as real numbers but they are functions a fuzzy interval is then viewed as a pair of fuzzy thresholds which are monotonic gradual real numbers this view enables interval analysis to be directly extended to fuzzy intervals without resorting to alpha cuts in agreement with zadeh s extension principle several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds our approach is illustrated on two known problems computing fuzzy weighted averages and determining fuzzy floats and latest starting times in activity network scheduling

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods