multivariable circle criteria for multiparameter singularly perturbed systems a direct approach to the lur e problem for singularly perturbed systems sps is proposed in contrast to previous results the feedback connection between the linear and nonlinear parts of sps is allowed to depend essentially on both the slow and the fast variables the lur e problem for multiparameter sps is studied by the same framework

a new approach to the perfect regulation and the bounded peaking in linear multivariable control systems this paper presents a new approach to the perfect regulation p r and the bounded peaking b p in linear multivariable control systems based on the pole and the eigenvector assignment technique roughly speaking the p r represents an ideal control action which reduces the settling time to 0 while the b p simply means the bounded overshoot in this ideal situation simple frequency domain characterizations of the p r and the b p are derived they reveal some invariance properties of the p r and the b p that provide a powerful tool for achieving the p r and the b p the existence condition for the p r is derived which turns out to be identical to the result obtained in the optimal regulator theory this result is extended to a more general control objective of attaining the p r for one output while keeping the b p for another output a condition on which the p r is realized by an output feedback is also derived a simple design algorithm is proposed for achieving the p r which is essentially the eigenvector assignment procedure finally an application to a real system is discussed

microwave imaging of nonsparse domains using born iterative method with wavelet transform and block sparse bayesian learning a microwave technique utilizing the combination of wavelet transform block sparse bayesian learning bsbl and born iterative method bim is proposed to image nonsparse domains the wavelet transform is implemented to convert the nonsparse domain into a sparse domain then bsbl framework based on expectation maximization em algorithm is applied on the bim model to reconstruct the original profile of the nonsparse domain the presented imaging results of a nonsparse model indicate that the proposed technique in comparison with traditional microwave imaging or compressive sensing cs algorithms achieve very low normalized error rate ner at a short computational time using only small number of antennas the accuracy robustness and effectiveness of the proposed method are further assessed by employing it to detect a hemorrhagic brain stroke in a realistic numerical head model which is a nonsparse domain the obtained results indicate the capability for the technique to detect an early stroke in the realistic nonsparse environment of the human head using only six antennas

near aggregation the dual ghr and pole zero cancellation it is known that a linear system will aggregate if and only if it is unobservable an equivalent condition is that the transfer function has a pole zero cancellation in this paper we consider siso systems that nearly aggregate and we show that these systems have almost pole zero cancellations defining near unobservability as roughly the existence of an invariant subspace near the null space of c we also show that nearly unobservable systems exhibit almost pole zero cancellations the main tool in this analysis is the dual generalized hessenberg representation dual ghr the dual ghr extends the ghr by incorporating the input structure with the output structure of the ghr the result is a canonical form the dual ghr that relates the internal states to the input output properties of the system by exploiting this structure the main results are obtained

a probabilistic model for the nonlinear electromagnetic inverse scattering tm case electromagnetic inverse scattering emis is a noninvasive examination tool which holds the promising potential in science engineering and military applications in contrast to conventional tomography techniques the inverse scattering is a quantitative superresolution imaging method since it is capable of accommodating more realistic interactions between the wavefield and the probed scene in this paper a full probabilistic formulation of the emis is presented for the first time which is then solved by applying the well known expectation maximization method afterward the concept of the complex valued alternating direction method of multipliers has been proposed as an alternative approach to solve the resulting nonlinear optimization problem finally exemplary numerical and experimental results are provided to validate the proposed method

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

viable three dimensional medical microwave tomography theory and numerical experiments three dimensional microwave tomography represents a potentially very important advance over 2d techniques because it eliminates associated approximations which may lead to more accurate images however with the significant increase in problem size computational efficiency is critical to making 3d microwave imaging viable in practice in this paper we present two 3d image reconstruction methods utilizing 3d scalar and vector field modeling strategies respectively finite element fe and finite difference time domain fdtd algorithms are used to model the electromagnetic field interactions in human tissue in 3d image reconstruction techniques previously developed for the 2d problem such as the dual mesh scheme iterative block solver and adjoint jacobian method are extended directly to 3d reconstructions speed improvements achieved by setting an initial field distribution and utilizing an alternating direction implicit adi fdtd are explored for 3d vector field modeling the proposed algorithms are tested with simulated data and correctly recovered the position size and electrical properties of the target the adjoint formulation and the fdtd method utilizing initial field estimates are found to be significantly more effective in reducing the computation time finally these results also demonstrate that cross plane measurements are critical for reconstructing 3d profiles of the target

a nested multi scaling inexact newton iterative approach for microwave imaging a microwave imaging technique based on the integration of the inexact newton method within a multi scaling strategy is proposed in the framework of the contrast field formulation of the electromagnetic inverse scattering the inversion problem is solved by means of a nested procedure that considers three different logical levels a an outer multi focusing loop aimed at implementing a synthetic zoom for focusing the scatterer support within the investigation domain b a local linearization of the original full nonlinear inverse scattering function and c a truncated landweber inner loop devoted to regularize the arising ill posed linear problem thanks to the features of the integrated approach a reliable inversion technique able to suitably face the non linearity and the ill posedness ill conditioning issues of the imaging problem is designed a numerical validation dealing with different objects measurement setups and noise conditions is carried out to assess the features and the potentialities as well as the limitations of the proposed strategy comparisons with bare approaches and other multi resolution formulations are presented as well

microwave imaging within the first order born approximation by means of the contrast field bayesian compressive sensing a new approach based the contrast field cf formulation of the microwave imaging problem that exploits the bayesian compressive sampling bcs paradigm is proposed for the reconstruction of sparse distributions of weak scatterers towards this end the original inverse scattering problem is recast to a probabilistic sparseness constrained optimization by introducing suitable hierarchical priors as sparsity constraints a fast relevance vector machine rvm is then employed to reconstruct the scatterers as well as to estimate the confidence level of the inversion representative numerical results are presented to illustrate the method as well as to assess its potentialities and limitations in terms of inversion accuracy computational efficiency and robustness comparisons with state of the art deterministic and stochastic reconstruction methodologies still within the born approximation ba are discussed as well

nevanlinna pick interpolation problem for two frequency scale systems the nevanlinna pick interpolation problem for a parametric set of data is considered sufficient conditions are obtained that guarantees a two frequency scale solution decomposition of the problem into two nevanlinna pick interpolation problems with smaller data size is presented an algorithm is developed which computes the solution as the result of combining the solutions for these two smaller problems

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

optimization of convex risk functions we consider optimization problems involving convex risk functions by employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models and optimality and duality theory for problems with convex risk functions

wavelet based compressive imaging of sparse targets the application of the compressive sensing cs paradigm to retrieve non single pixels contrast profiles is discussed by exploiting a wavelet representation to model complex scatterer distributions with sparse vectors of coefficients an efficient bayesian cs bcs strategy is adopted to solve the arising inverse scattering problem a set of representative numerical examples is presented to illustrate the advantages and the limitations of the proposed approach also with respect to comparable state of the art inversion methods

frequency domain results for systems with multiple time scales the mathematical treatment of systems with multiple time scales has traditionally employed the use of singular perturbation theory for differential equations this paper treats such systems from a frequency domain viewpoint previously existing two frequency scale results involving approximation and algebraic characterization are extended in addition an exact frequency scale decomposition is presented

microwave imaging using the finite element method and a sensitivity analysis approach a method for reconstructing the constitutive parameters of two dimensional 2 d penetrable scatterers from scattered field measurements is presented this method is based on the differential formulation of the forward scattering problem which is solved by applying the finite element method fem given a set of scattered field measurements the objective is to minimize a cost function which consists of two terms the first is the standard error term which is related to the measurements and their estimates while the second term which is related to the tikhonov regularization is used to heal the ill posedness of the inverse problem the iterative polak ribiere nonlinear conjugate gradient algorithm is applied to the minimization of the cost function during each iteration of the algorithm the direction of correction is computed by using a sensitivity analysis approach which is carried out by an elaborate finite element scheme the adoption of the finite element method results in sparse systems of equations while the computational burden is further reduced by applying the adjoint state vector methodology finally a microwave medical imaging application which is related to the detection of proliferated bone marrow is examined while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated

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

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

two time scaled parameter identification by coordination of local identifiers abstract contradictory requirements on the precision in l and l 2 norms prevent the classical least square procedure from identifying two time scaled systems accurately a new identification procedure explicitly using the time scale structure of the system is proposed here and is proved to solve the problem of accurate parameter estimation

the dual theory of choice under risk in this essay a new theory of choice under risk is being proposed it is a theory which in a sense that will become clear is dual to expected utility theory hence the title dual theory risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility except that the roles of payments and probabilities are reversed this theme the reversal of the roles of probabilities and payments will recur throughout the paper i should emphasize that playing games with probabilities masquerading as payments and payments masquerading as probabilities is not my object rather i hope to convince the reader that the dual theory has intrinsic economic significance and that in some areas its predictions are superior to those of expected utility theory while in other areas the reverse will be the case two reasons have prompted me to look for an alternative to expected utility theory the first reason is methodological in expected utility theory the agent s attitude towards risk and the agent s attitude towards wealth are forever bonded together at the level of fundamental principles risk aversion and diminishing marginal utility of wealth which are synonymous under expected utility theory are horses of different colors the former expresses an attitute towards risk increased uncertainty hurts while the latter expresses an attitude towards wealth the loss of a sheep hurts more when the agent is poor than when the agent is rich a question arises therefore as to whether these two notions can be kept separate from each other in a full fledged theory of cardinal utility the dual theory will have this property the second reason that leads me to look for an alternative to expected utility theory is empirical behavior patterns which are systematic yet inconsistent with expected utility theory have often been observed two prominent references among many others are allais 1953 and kahneman tversky 1979 so deeply

multivariable singularly perturbed feedback systems with time delay multivariable singularly perturbed systems with both small and large time delays in the feedback loop are considered conditions for stability of the full order closed loop system are given in terms of properties of the slow and fast subsystems

conditional risk mappings we introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties in particular we prove a representation theorem for conditional risk mappings in terms of conditional expectations we also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings

state space realization of multiple frequency scale transfer matrices the class of linear time variant singularly perturbed systems is considered in which all poles are o 1 or o 1 epsilon as epsilon to o with coefficient matrices that are analytic functions of epsilon it has been shown previously that transfer matrices of systems in the above class are two frequency scale this means that such transfer matrices behave as dynamical systems in two separate frequency ranges it is shown that any two frequency scale transfer matrix can be realized in state space form as a system in the above mentioned class of singularly perturbed systems the result is generalized to n frequency scales

high gain predictor based output feedback control for time delay nonlinear systems this paper designs a high gain predictor for output feedback control of nonlinear systems in the presence of input output and state delays the high gain predictor realizes the states appearing in the output feedback control in terms of predictive state delayed state and current state the system includes internal and external dynamics and the closed loop system under state feedback is required to be asymptotically stable and locally exponentially stable positively invariant sets are found to verify boundedness exponential stability and performance recovery in the simulation a saturated sliding mode control is applied to demonstrate the performance recovery of the closed loop system and the fact that the high gain predictor parameter has a lower bound related to time delays

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

stochastic optimization methods applied to microwave imaging a review stochastic methods are now very common in electromagnetics among the various applications they have been recently proposed for solving inverse problems arising in radio frequency and microwave imaging some of the recently proposed stochastic inversion procedures are critically discussed e g genetic algorithms differential evolution methods memetic algorithms particle swarm optimizations hybrid techniques etc and the way they have been applied in this area the use of the ant colony optimization method which is a relatively new method in electromagnetics is also proposed various imaging modalities are considered tomography buried object detection and borehole sensing finally the main features making these approaches useful for imaging purposes are discussed and the currently considered strategies to reduce the computational load associated with stochastic optimization procedures delineated

microwave imaging via distorted iterated virtual experiments the linearity of the scattering phenomenon with respect to primary sources allows to recombine a posteriori the available experiments and build in a synthetic fashion new virtual experiments starting from this circumstance an iterative procedure is proposed as an effective approach to tackle nonlinear inverse scattering problems in this procedure the virtual experiments the green s function and the corresponding physical inspired field approximations are updated at each iteration the structure and the complexity of the approach are comparable with those of the widely adopted distorted born iterative method but its performances are remarkably better thanks to extended validity of the exploited field approximation the overall approach also takes advantage of a compressive sensing inspired regularization scheme to promote sparsity in the search of piecewise constant dielectric profiles and further improve the accuracy of the imaging results examples with numerical and experimental data are given to assess the method

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

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

balanced realizations of singularly perturbed systems abstract balanced realizations of linear time invariant singularly perturbed systems are studied the reduced model of a singularly perturbed system that is obtained based on the balanced realization is compared to that obtained by time scale considerations an approximate balancing transformation for singularly perturbed systems is constructed based on balancing transformations of the approximating slow and fast subsystems

inverse scattering using a joint l1 l2 norm based regularization inverse scattering problems suffer from ill posedness and ill conditioning necessitating the use of regularization methods to get meaningful solutions commonly used regularizations are l2 norm based but these generate over smooth solutions we propose a regularization method using both the l1 and l2 norms to obtain sharp object boundaries while also achieving good interior reconstruction of the object permittivity knowledge about the permittivity can also be used as a priori information the applicability of the method is demonstrated on synthetically generated data for two dimensional 2 d microwave imaging using the born iterative method bim the optimization routine systematically estimates all parameters while minimizing the cost function different objects chosen to represent realistic features have been considered to evaluate the performance the reconstructed images indicate that the method can produce accurate object localization shape identification and good permittivity estimation

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

compressive sensing imaging of non sparse 2d scatterers by a total variation approach within the born approximation the problem of imaging two dimensional non sparse scatterers with piecewise constant contrast is solved through an innovative total variation compressive sensing tv cs technique under born approximation ba the time harmonic two dimensional inverse scattering problem is reformulated into an equivalent augmented lagrangian one according to the tv cs formulation the resulting unconstrained functional is then minimized by means of a deterministic alternating direction algorithm selected results from a numerical assessment are discussed to give the interested reader some insights on the accuracy the flexibility the robustness and the efficiency of the tv cs inversion scheme also in comparison with available implementations of state of the art inversion methods still formulated within the ba

sparsening conformal arrays through a versatile bcs based method sparsening conformal arrangements is carried out through a versatile multi task bayesian compressive sensing mt bcs strategy the problem formulated in a probabilistic fashion as a pattern matching synthesis is that of determining the sparsest excitation set locations and weights fitting a reference pattern subject to user defined geometrical constraints results from a set of representative numerical experiments are presented to illustrate the key features of the proposed approach as well as to assess also through comparisons its potentials in terms of matching accuracy element saving and computational costs

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

near field radar imaging via compressive sensing a novel two dimensional 2 d compressive sensing cs based method is presented for near field radar imaging first an accurate near field approximation is proposed based on which the circular wavefront curvature of spherical waves can be compensated by mapping the images to a rectified new grid more importantly the near field approximation makes the two dimensions of the scattered data separable for the range and cross range directions which makes it possible to solve the 2 d reflectivity matrix for the image reconstruction directly then a 2 d proximal subgradient algorithm for near field radar imaging based on a fast iterative shrinkage thresholding algorithm fista is introduced to resolve the memory usage and computation time issues simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional fourier based method and to the conjugate gradient cg based method which proves that the proposed method is an effective way to solve the near field radar imaging problem

spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor a reconstruction algorithm to simultaneously estimate the shape and location of three dimensional breast cancer tumor is presented and its utility is analyzed the approach is based on a spherical harmonic decomposition to capture the shape of the tumor we combine a gradient descent optimization method with a direct electromagnetic solver to determine the coefficients in the harmonic expansion as well as the coordinates of the center of the tumor the results demonstrate the potential advantage of collecting data using a multiple view tomographic type strategy we show how the order of the harmonic expansion must be increased to capture increasingly irregularly shaped tumors and explore the resulting increase in the central processing unit cpu time required by the algorithm our approach shows accurate reconstruction of the tumor image regardless of the source polarization this work demonstrates the promise of the algorithm when used on data corrupted with gaussian noise and when perfect knowledge of the tumor electrical properties is not available

nonlinear microwave imaging for breast cancer screening using gauss newton s method and the cgls inversion algorithm breast cancer screening using microwave imaging is emerging as a new promising technique as a supplement to x ray mammography to create tomographic images from microwave measurements it is necessary to solve a nonlinear inversion problem for which an algorithm based on the iterative gauss newton method has been developed at dartmouth college this algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the tikhonov algorithm in this paper a new algorithm for determining the iteration update values in the gauss newton algorithm is presented which is based on the conjugate gradient least squares cgls algorithm the iterative cgls algorithm is capable of solving the update problem by operating on just the jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations the new algorithm is compared to the gauss newton algorithm with tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations

comparison of an enhanced distorted born iterative method and the multiplicative regularized contrast source inversion method for 2d transverse magnetic tm microwave inversion multiplicative regularized contrast source inversion mr csi and the distorted born iterative method dbim are compared the comparison is based on a computational resource analysis inversion of synthetic data and inversion of experimentally collected data from both the fresnel and upc barcelona data sets all inversion results are blind but appropriate physical values for the reconstructed contrast are maintained the data sets used to test the algorithms vary widely in terms of the background media antennas and far near field considerations to ensure that the comparison is replicable an automatic regularization parameter selection method is used for the additive regularization within the dbim which utilizes a fast implementation of the l curve method and the laplacian regularizer while not used in the classical dbim we introduce an mr term to the dbim in order to provide comparable results to mr csi the introduction of this mr term requires only slight modifications to the classical dbim algorithm and adds little computational complexity the results show that with the addition of the mr term in the dbim the two algorithms provide very similar inversion results but with the mr csi method providing advantages for both computational resources and ease of implementation

characterization of zeros in two frequency scale systems we study the asymptotic behavior of the zeros of a two frequency scale transfer function in terms of the zeros of its slow and fast transfer functions by introducing the notion of type index we will show that all zeros of a two frequency scale transfer function with the type index of either spl nu spl ges 0 or spl nu 1 can be completely characterized in a manner that is quite similar to the characterization of the poles we also give a partial characterization for all other zeros in terms of the cardinality of their zero sets

equilibrium routing under uncertainty we provide a brief introduction to the basic models used to describe traffic on congested networks both in urban transport and telecommunications we discuss traffic equilibrium models covering atomic and non atomic routing games with emphasis on situations where the travel times are subject to random fluctuations we use convex optimization to present the models in a unified framework that stresses the common underlying structures as a prototypical example of traffic equilibrium with elastic demands we discuss some models for routing and congestion control in telecommunications we also describe a class of stochastic dynamics that model the adaptive behavior of agents and which provides a plausible micro foundation for the equilibrium finally we present some recent ideas on how risk averse behavior might be incorporated in the equilibrium models

additive consistency of risk measures and its application to risk averse routing in networks we investigate the use of risk measures and theories of choice to model risk averse routing and traffic equilibrium on networks with random travel times we interpret the postulates of these theories in the context of routing identifying additive consistency as a plausible condition that allows to reduce risk averse route choice to a standard shortest path problem within the classical theories of choice we show that the only preferences that satisfy this condition are the ones induced by the entropic risk measures

a relationship between sensitivity and stability of multivariable feedback systems both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design although the two bodies of work have developed about a decade apart the basic philosophies are similar both attempt to maintain a system property sensitivity reduction versus stability in the presence of plant modeling errors this paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

common mathematical foundations of expected utility and dual utility theories we show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas the separation principle of convex analysis and integral representations of continuous linear functionals from functional analysis our analysis reveals the dual character of utility functions we also derive new integral representations of dual utility models

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

singular perturbation analysis of high frequency filter design the control design of systems with lightly damped high frequency oscillatory modes is treated systems exhibiting these lightly damped modes include turbine generators and large flexible structures frequently the dynamics of these high frequency modes are not known very accurately as a result the design objective is to improve the slow dynamics without destabilizing the high frequency modes from a classical frequency domain design viewpoint this is in part a filtering problem requiring some kind of high frequency filter the singular perturbation method is used to systematically develop a two time scale method to design these high frequency filters and provides guidelines on the kind of high frequency filter to be used in addition the method provides an asymptotic error analysis the design is illustrated with an example representative of a power system model with a two mass turbine generator model

two time scale distributions and singular perturbations two time scale tts distributions are introduced for a class of stable systems it is shown that every tts distribution has a two frequency scale tfs laplace transform conversely it is shown that the impulse response of any stable tfs transfer function and hence any stable standard singularly perturbed system can be characterized in terms of a stable tts distribution a time domain decomposition for tts distributions is obtained which parallels the slow and fast decomposition of singularly perturbed systems and also the frequency domain decomposition of tfs transfer functions it is shown that every stable tts distribution can be decomposed in terms of two simpler distributions represented in two different time scales a composite distribution is constructed from these two which approximates the tts distribution arbitrarily closely in the l 1 norm

h model matching problem for singularly perturbed systems abstract the model matching problem for single input single output singularly perturbed systems is considered two sets of sufficient conditions are obtained to guarantee the existence of a two frequency scale solution one for the optimal and one for a suboptimal case both the minimum phase and the non minumum phase cases are treated the sub optimal two frequency scale solution constructed in this paper uses the solutions of two well defined lower order problems and therefore it is numerically better conditioned and computationally less demanding than the traditional optimal methods a two stage algorithm for the computation of the suboptimal tfs solution is presented

time inconsistent multistage stochastic programs martingale bounds abstract multistage stochastic programs show time inconsistency in general if the objective is neither the expectation nor the maximum functional this paper considers distortion risk measures in particular the average value at risk at the final stage of a multistage stochastic program such problems are not time consistent however it is shown that by considering risk parameters at random level and by extending the state space appropriately the value function corresponding to the optimal decisions evolves as a martingale and a dynamic programming principle is applicable in this setup the risk profile has to be accepted to vary over time and to be adapted dynamically further a verification theorem is provided which characterizes optimal decisions by sub and supermartingales these enveloping martingales constitute a lower and an upper bound of the optimal value function the basis of the analysis is a new decomposition theorem for the average value at risk which is given in a time consistent formulation

conjugate gradient method applied to inverse scattering problem a new reconstruction algorithm for diffraction tomography is presented the algorithm is based on the minimization of a functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated object function by using the conjugate gradient method to minimize the functional one can derive an iterative formula for getting the object function numerical results for some two dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first order born approximation can not be applied in addition the number of iterations is reduced by using a priori information about the outer boundary of the objects furthermore the method is not so sensitive to the presence of noise in the scattered field data

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