linear and nonlinear algorithms for identification in h sub infinity with error bounds a linear algorithm and a nonlinear algorithm for the problem of system identification in h sub infinity posed by helmicki et al 1990 for discrete time systems are presented the authors derive some error bounds for the linear algorithm which indicate that it is not robustly convergent however the worst case identification error is shown to grow as log n where n is the model order a robustly convergent nonlinear algorithm is derived and bounds on the worst case identification error in the h sub infinity norm are obtained

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

h sub spl infin nonlinear filtering of discrete time processes this correspondence investigates the problem of h sub spl infin estimation of a discrete time nonlinear process an estimator which may be nonlinear is introduced so that an h sub spl infin norm like of what we call a generalized estimation error is guaranteed to be bounded by a prescribed level conditions for the existence of such an estimator and formulae for its derivation are obtained utilizing a discrete time analog of the hamilton jacobi inequality an approximate filter based on linearization is developed this filter relates to the extended kalman filter in the same way that the linear h sub spl infin filter relates to the kalman filter

an extended robust h _infty filter for nonlinear constrained uncertain systems in this correspondence a robust filter is proposed to effectively estimate the system states in the case where system model uncertainties as well as disturbances are present the proposed robust filter is constructed based on the linear approximation methods for a general nonlinear uncertain system with an integral quadratic constraint we also derive the important characteristic of the proposed filter a modified hinfin performance index analysis results show that the proposed filter has robustness against disturbances such as process and measurement noises and against parameter uncertainties simulation results show that the proposed filter provides a performance improvement

the dirichlet problem for the p fractional laplace equation abstract we deal with a class of equations driven by nonlocal possibly degenerate integro differential operators of differentiability order s 0 1 and summability growth p 1 whose model is the fractional p laplacian operator with measurable coefficients we review several recent results for the corresponding weak solutions supersolutions as comparison principles a priori bounds lower semicontinuity boundedness holder continuity up to the boundary and many others we then discuss the good definition of s p superharmonic functions and the nonlocal counterpart of the perron method in nonlinear potential theory together with various related results we briefly mention some basic results for the obstacle problem for nonlinear integro differential equations finally we present the connection amongst the fractional viscosity solutions the weak solutions and the aforementioned s p superharmonic functions together with other important results for this class of equations when involving general measure data and a surprising fractional version of the gehring lemma we sketch the corresponding proofs of some of the results presented here by especially underlining the development of new fractional localization techniques and other recent tools various open problems are listed throughout the paper

maximum likelihood estimators and worst case optimal algorithms for system identification abstract for system identification problems with stochastic noise maximum likelihood estimators are frequently used if noise is deterministic worst case optimal algorithms should be considered in this paper we study the following problem under what circumstances are maximum likelihood estimators optimal in the worst case

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

brief paper h filtering for nonlinear discrete time stochastic systems with randomly varying sensor delays this paper is concerned with the h filtering problem for a general class of nonlinear discrete time stochastic systems with randomly varying sensor delays where the delayed sensor measurement is governed by a stochastic variable satisfying the bernoulli random binary distribution law in terms of the hamilton jacobi isaacs inequalities preliminary results are first obtained that ensure the addressed system to possess an l 2 gain less than a given positive scalar c next a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the h performance constraint for all nonzero exogenous disturbances under the zero initial condition such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation furthermore it is shown that our main results can be readily specialized to the case of linear stochastic systems finally a numerical simulation example is used to demonstrate the effectiveness of the results derived

optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors the problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed the measurements are assumed to be corrupted by an unknown but bounded additive noise the sampling design assumes that the number of samples is unconstrained and no replication is allowed two main results are shown 1 for particular classes of linear models the optimal number of measurements is equal to the number of parameters as in the statistical context 2 the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori knowing only the model and the error structure

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

regularity of the free boundary of an american option on several assets we establish the c regularity of the free boundary for an american option on several assets in the case where the payoff is convex and the assets follow correlated geometric brownian motions our work builds on results concerning the qualitative properties and initial regularity of the free boundary by broadie and detemple jaillet lamberton and lapeyre and villeneuve 2008 wiley periodicals inc

optimal and robust memoryless discrimination from dependent observations discrimination is considered between two possible sources based on dependent observations of their output the discrimination problem is modeled by means of a general binary hypothesis test the main emphasis being on situations that cannot be modeled as signals in additive noise the observations are modeled as stationary m dependent or rho mixing processes the structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic which is then compared to a threshold only fixed sample size tests are considered four different performance measures which resemble the signal to noise ratios encountered in the signal in additive noise problems are derived under different problem formulations the optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations for three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations computer simulation results that demonstrate the advantage of using these nonlinearities over the i i d nonlinearity under the probability of error criterion are presented

approximation of infinite dimensional systems a fourier series based method for approximation of stable infinite dimensional linear time invariant system models is discussed the basic idea is to compute the fourier series coefficients of the associated transfer function t sub d z and then take a high order partial sum two results on h sup infinity convergence and associated error bounds of the partial sum approximation are established it is shown that the fourier coefficients can be replaced by the discrete fourier transform coefficients while maintaining h sup infinity convergence thus a fast fourier transform algorithm can be used to compute the high order approximation this high order finite dimensional approximation can then be reduced using balanced truncation or optimal hankel approximation leading to the final finite dimensional approximation to the original infinite dimensional model this model has been tested on several transfer functions of the time delay type with promising results

fuzzy h_ infty filter design for a class of nonlinear discrete time systems with multiple time delays this paper studies the fuzzy hinfin filter design problem for signal estimation of nonlinear discrete time systems with multiple time delays and unknown bounded disturbances first the takagi sugeno t s fuzzy model is used to represent the state space model of nonlinear discrete time systems with time delays next we design a stable fuzzy hinfin filter based on the t s fuzzy model which guarantees asymptotic stability and a prescribed hinfin index for the filtering error system irrespective of the time delays and uncertain disturbances a sufficient condition for the existence of such a filter is established by using the linear matrix inequality lmi approach the proposed lmi problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm simulation examples are provided to illustrate the design procedure of the present method

discrete fourier transform and h sub infinity approximation it is shown that uniform rational approximation of nonrational transfer functions can always be obtained by means of the discrete fourier transform dft as long as such approximants exist based on this fact it is permissible to apply the fast fourier transform fft algorithm in carrying out rational approximations without being apprehensive of convergence the dft is used to obtain traditional approximations for transfer functions of infinite dimensional systems justification is provided for using the dft in such approximations it is established that whenever a stable transfer function can be approximated uniformly on the right half plane by a rational function its approximants can always be recognized by means of a dft

robust identification and interpolation in h abstract we consider system identification in h in the framework proposed by helmicki jacobson and nett an algorithm using the jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems it is shown that this and similar identification algorithms can be successfully combined with a model reduction procedure to produce low order models connections with the nevanlinna pick interpolation problem are explored and an algorithm is given in which the identified model interpolates the given noisy data some numerical results are provided for illustration finally the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions

robust filtering for discrete time systems with saturation and its application to transmultiplexers this paper considers the problem of robust filtering for discrete time linear systems subject to saturation a generalized dynamic filter architecture is proposed and a filter design method is developed our approach incorporates the conventional linear h sub 2 and h sub spl infin filtering as well as a regional l sub 2 gain filtering feature developed specially for the saturation nonlinearity and is applicable to the digital transmultiplexer systems for the purpose of separating filterbank design it turns out that our filter design can be carried out by solving a constrained optimization problem with linear matrix inequality lmi constraints simulations show that the resultant separating filters possess satisfactory reconstruction performance while working in the linear range and less degraded reconstruction performance in the presence of saturation

on identification of stable systems and optimal approximation abstract approximative modelling of stable continuous time possibly infinite dimensional systems is studied based on an optimal approximation approach both approximation of analytical system representations system approximation as well as approximation of input output data based system estimates system identification are considered while special emphasis is given to approximative modelling in the h and hankel norms the l1 and l2 norm cases are also discussed the model sets considered here are finite dimensional systems and time shifted systems simple delay systems the theory of approximation numbers is shown to provide a convenient tool to study problems of identification of stable continuous time systems in a deterministic framework with close connections to complexity considerations laguerre fourier series methods and hankel operator techniques can be utilized to develop fully practical identification methods for continuous time possibly infinite dimensional systems

from time series to linear system part ii exact modelling abstract in the second part of this paper the problem of finding an exact model for a q dimensional infinite time series is considered first a mathematical vocabulary for discussing exact modelling is developed it is then shown how the results of part i guarantee the existence of a most powerful ar model for an observed time series two algorithms for obtaining such an ar model are subsequently derived one of these algorithms gives a shortest lag input output model the problem of obtaining a minimal state space realization of the observed time series is also considered in order to do that realization theory based on the truncated behaviour is developed as an extensive example the classical situation with impulse response measurements is discussed

a class of algorithms for identification in h abs traet in this paper a class of algorithms for the problem of system identification in are investigated these algorithms are characterized by a two stage structure and involve a class of window functions some conditions in terms of properties of the window functions are derived which guarantee robust convergence of the algorithms identification errors are analyzed for several common window functions this leads to some insights into the trade off between the error induced by approximation and that due to noise

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

envelope constrained h filtering for nonlinear systems with quantization effects the finite horizon case abstract this paper is concerned with the envelope constrained h filtering problem for a class of discrete nonlinear stochastic systems subject to quantization effects over a finite horizon the system under investigation involves both deterministic and stochastic nonlinearities the stochastic nonlinearity described by statistical means is quite general that includes several well studied nonlinearities as its special cases the output measurements are quantized by a logarithmic quantizer two performance indices namely the finite horizon h specification and the envelope constraint criterion are proposed to quantify the transient dynamics of the filtering errors over the specified time interval the aim of the proposed problem is to construct a filter such that both the prespecified h requirement and the envelope constraint are guaranteed simultaneously over a finite horizon by resorting to the recursive matrix inequality approach sufficient conditions are established for the existence of the desired filters a numerical example is finally proposed to demonstrate the effectiveness of the developed filtering scheme

time domain h sub spl infin identification the problem of parameter identification for single input single output arx systems is considered recent results in h sub spl infin nonlinear filtering are used to formulate a nonlinear h sub spl infin time domain prediction error modeling pem identification method the performance of the new method is guaranteed by a preassigned bound on the ratio between the energy of the prediction error of the obtained model and the energy of the exogenous disturbances the potential usefulness of the h sub spl infin time domain identification method is illustrated by a numerical example

obstacle problems for integro differential operators higher regularity of free boundaries abstract we study the higher regularity of free boundaries in obstacle problems for integro differential operators our main result establishes that once free boundaries are c 1 then they are c this completes the study of regular points initiated in 5 in order to achieve this we need to establish optimal boundary regularity estimates for solutions to linear nonlocal equations in c k domains these new estimates are the core of our paper and extend previously known results by grubb for k and by the second author and serra for k 1

partial update lms algorithms partial updating of lms filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations this paper presents an analysis of convergence of the class of sequential partial update lms algorithms s lms under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random which we call the stochastic partial update lms algorithm spu lms specifically under the standard independence assumptions for wide sense stationary signals the s lms algorithm converges in the mean if the step size parameter spl mu is in the convergent range of ordinary lms relaxing the independence assumption it is shown that s lms and lms algorithms have the same sufficient conditions for exponential stability however there exist nonstationary signals for which the existing algorithms s lms included are unstable and do not converge for any value of spl mu on the other hand under broad conditions the spu lms algorithm remains stable for nonstationary signals expressions for convergence rate and steady state mean square error of spu lms are derived the theoretical results of this paper are validated and compared by simulation through numerical examples

parameter identification for uncertain plants using h methods abstract we demonstrate the effective use of h filtering and cost to come methods for parameter identification in deterministic uncertain plants that are linear in the unknown parameters but nonlinear otherwise the cost to come method is an approach that has been used earlier to solve linear and nonlinear h optimal control and filtering problems it consists of constructing a cost to come function which assists in the design of an optimal observer scheme the method is used here in the design of a parameter identification scheme for uncertain plants where measurements on the state of the system are available but not on its derivative two approaches are adopted in both of which the parameter estimation problem is formulated as an h filtering problem one of the approaches uses a more standard prefiltering of the past states input and disturbance signals the other approach is a novel design method which leads to a new class of identification schemes it involves two subproblems fsdi full state derivative information problem where it is assumed that both the state and its derivative are available to the parameter estimator and npfsi noise perturbed fsi problem where the estimator is assumed to measure a noise perturbed measurement of the state in the latter problem we use singular perturbation methods to prove asymptotic convergence of the performance of the identifier to that of the unperturbed case thus providing an asymptotically optimal solution to the fsi full state measurement problem to illustrate both approaches several simulation studies on a numerical example are provided

robust detection of signals a large deviations approach robust detection of a signal is considered for the case of independent and identically distributed observations following an asymptotic but nonlocal approach the exponential rates of decrease of the error probabilities are considered as measure of performance under this measure a robust detection structure for the symmetric density case is derived this detection structure is a generalization of an existing result for the local case and is reduced to it when the signal magnitude tends to zero

a maximum variance model for robust detection and estimation with dependent data a model that accounts for uncertain data dependency is developed by generating a large class of stationary stochastic processes each with the same univariate distribution this class can be considered to be a contamination class about the nominal independent and identically distributed i i d process distribution the class is developed specifically for application to robust detector and estimator design based on asymptotic variance application of this dependency class leads to an intuitively pleasing result the minimax variance estimators and the maximin efficacy detectors are the same as obtained using i i d asymptotic estimation and detection theory thus our technique generalizes previously obtained robust design results for i i d data to this dependent data case

higher regularity of the free boundary in the elliptic signorini problem abstract in this paper we study the higher regularity of the free boundary for the elliptic signorini problem by using a partial hodograph legendre transformation we show that the regular part of the free boundary is real analytic the first complication in the study is the invertibility of the hodograph transform which is only c 0 1 2 which can be overcome by studying the precise asymptotic behavior of the solutions near regular free boundary points the second and main complication in the study is that the equation satisfied by the legendre transform is degenerate however the equation has a subelliptic structure and can be viewed as a perturbation of the baouendi grushin operator by using the l p theory available for that operator we can bootstrap the regularity of the legendre transform up to real analyticity which implies the real analyticity of the free boundary

laguerre series approximation of infinite dimensional systems laguerre fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems specifically time domain supremum and l1 norm convergence results and frequency domain h norm convergence results are given for laguerre fourier approximations it is also shown that the theory of laguerre polynomials solves explicitly the problem of determining laguerre fourier approximations for a large class of delay systems furthermore it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems

regularity estimates for the solution and the free boundary of the obstacle problem for the fractional laplacian we use a characterization of the fractional laplacian as a dirichlet to neumann operator for an appropriate differential equation to study its obstacle problem we write an equivalent characterization as a thin obstacle problem in this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

a variational scheme for hyperbolic obstacle problems abstract we consider an obstacle problem for possibly non local wave equations and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme we provide the corresponding numerical implementation and raise some open questions

distributed h state estimation with stochastic parameters and nonlinearities through sensor networks the finite horizon case this paper deals with the distributed h state estimation problem for a class of discrete time varying nonlinear systems with both stochastic parameters and stochastic nonlinearities the system measurements are collected through sensor networks with sensors distributed according to a given topology the purpose of the addressed problem is to design a set of time varying estimators such that the average estimation performance of the networked sensors is guaranteed over a given finite horizon through available output measurements from not only the individual sensor but also its neighboring sensors a necessary and sufficient condition is established to achieve the h performance constraint and then the estimator design scheme is proposed via a certain h 2 type criterion the desired estimator parameters can be obtained by solving coupled backward recursive riccati difference equations rdes a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed estimator design approach

single snapshot robust direction finding the paper presents a novel approach for recursively estimating the directions of arrival of incident signals as measurements are received along a sensor array using a single snapshot and without any statistical assumptions the proposed method employs a robust performance criterion which is based on worst case gain minimization the criterion aims to reduce the estimation error induced by worst case amplitude and phase perturbations as well as additive noise in the array model an algorithm that guarantees the criterion within a first order approximation is developed and shown to converge moreover instead of using a trial and error method to find a constant minimum worst case gain the minimum worst case gain is updated as each sensor measurement is processed a step by step implementation of the algorithm is presented and its computational complexity is analyzed the performance of the new approach is evaluated by simulating the estimation algorithm for a linear array and comparing its performance with that of an existing single snapshot algorithm

the change of variance function for dependent data the infinitesimal stability of the asymptotic variance is considered form estimators of a location parameter when the nominal sample with i i d data is contaminated by a possibly dependent process it is shown that the resulting change of variance function can be expressed as a sum of two terms one corresponding contamination of the univariate distribution and one to contamination of the bivariate distributions a change of variance sensitivity is introduced the form of which is closely related to the average patch length of the outliers finally optimalv robust and mostv robust score functions are derived the resulting family of estimators is the same as for independent data in the general case but the truncation point approaches zero when dependency is accounted for for redescending score functions the family of estimators is changed

nonlinear fractional laplacian problems with nonlocal gradient terms let n 2 be a smooth bounded domain for s 1 2 1 we consider a problem of the form where 0 is a real parameter f belongs to a suitable lebesgue space and is a nonlocal gradient square term given by depending on the real parameter 0 we derive existence and non existence results the proof of our existence result relies on sharp calderon zygmund type regularity results for the fractional poisson equation with low integrability data we also obtain existence results for related problems involving different nonlocal diffusion terms

a nonlocal approach for asymptotic memoryless detection theory corresp previous literature on detector design has presented many tractable results using efficacy as a performance functional which is a small signal or local approach some nonlocal issues of memoryless detection are considered we argue that the asymptotic exponential rate of decrease of error probabilities or bayes risk provides the appropriate asymptotic measure of performance a main contribution is the development of an approximation for nonlocal design that retains the tractability of the efficacy approach we have proved the local consistency of our approximation also as a consequence of the analysis new proofs for pitman noether like theorems have been obtained

second order extended h_ infty filter for nonlinear discrete time systems using quadratic error matrix approximation in this paper the second order extended soe h filter for nonlinear discrete time systems is derived based on an approximation to the quadratic error matrix the solution is obtained by the game theory approach it is shown that the result bears a strong resemblance to the soe kalman filter when the performance bound goes to infinity an example of vehicle state tracking is simulated to compare the performances of the soe kalman filter the first order extended and the soe h filter noises with unknown bias are injected into both process dynamics and measurements the results show that the soe h filter has the smallest state tracking error

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

dissipative control for state saturated discrete time varying systems with randomly occurring nonlinearities and missing measurements in this paper the dissipative control problem is investigated for a class of discrete time varying systems with simultaneous presence of state saturations randomly occurring nonlinearities as well as multiple missing measurements in order to render more practical significance of the system model some bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements the purpose of the addressed problem is to design a time varying output feedback controller such that the dissipativity performance index is guaranteed over a given finite horizon by introducing a free matrix with its infinity norm less than or equal to 1 the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities a novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities

robust locally optimum detection of signals in dependent noise a robust locally optimum detector of a signal embedded in additive dependent nongaussian noise is presented the performance criterion is bayes risk the sample size is finite and the uncertainty class of multivariate inputs is the in contamination model the locally optimum detector is shown to be a censored version of the nominal likelihood ratio

insight into detection of deterministic and gaussian signals in correlated plus impulsive noise environments the authors present a different view of the discrete time detection problem in impulsive noise the approach used is to examine the geometry from a subspace viewpoint of two detectors the clairvoyant matched filter and the clairvoyant power detector they are clairvoyant in that the locations of the impulses in the received data sample are assumed known in the presence of impulses both detectors use this knowledge for properly weighting these samples to reduce the effects of the impulses unfortunately since it is never reasonable to assume that the impulse locations are known these are unrealizable detectors however these clairvoyant detectors provide insight into the problem of detection in an impulsive environment when the nominal component is correlated and suggest detectors which are realizable the results can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection

brief paper robust h filtering for nonlinear stochastic systems with uncertainties and markov delays this paper investigates the h filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by markov chains simultaneously the general algebraic hamilton jacobi inequality hji is established first for general nonlinear stochastic systems with uncertainties and random markovian delays then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level moreover the developed results are specialized for a special class of nonlinear stochastic systems by presenting the sufficient conditions in terms of matrix inequalities simulation results demonstrate the effectiveness of the proposed approach

approximation and identification of continuous time systems an approximation approach to the identification of stable continuous time possibly infinite dimensional systems is studied for this purpose concrete exponential leg endre series methods are proposed and analysed here for the l1 and l2 approximations of continuous time systems rate of approximation results are given for the proposed methods for an important class of delay systems the proposed exponential legendre series method for the l2 approximation has a certain optimal rate of approximation property for this class of delay systems these results show that exponential legendre series techniques have promising properties in connection with the l1 and l2 identifications of stable continuous time systems the proposed l1 identification method has a direct application to the robust design of control systems

robust extended kalman filtering linearization errors inherent in the specification of an extended kalman filter ekf can severely degrade its performance this correspondence presents a new approach to the robust design of a discrete time ekf by application of the robust linear design methods based on the h sub spl infin norm minimization criterion the results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications

holder estimates for non local parabolic equations with critical drift abstract in this paper we extend previous results on the regularity of solutions of integro differential parabolic equations the kernels are non necessarily symmetric which could be interpreted as a non local drift with the same order as the diffusion we provide a growth lemma and a harnack inequality which can be used to prove higher regularity estimates

parameter identification in the presence of non parametric dynamic uncertainty abstract this paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs but in the presence of non parametric dynamic uncertainty unmodelled dynamics this paper considers two non parametric uncertainty sets motivated by robust control the weighted ball in h and the weighted ball in the induced l2 norm the non parametric uncertainty produces signals which corrupt the signals used in identification this paper shows that the corruption is non conservatively bounded in an l2 sense this l2 bound is then compared with the signal energy with the result used to enable disable the parameter adjustment of a gradient least squares adjustment mechanism it is proved that the resulting parameter adjustment yields non increasing parameter errors with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories

min max detection of weak signals in phi mixing noise detection of weak signals in a special varphi mixing noise class is considered the detector structure is restricted to sums of memoryless nonlinear transformations of the observations correlated with the data sequence and compared to a fixed threshold using the efficacy to measure performance the nonlinearity that has min max performance is derived

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

optimality of central and projection algorithms for bounded uncertainty this paper investigates optimality properties of central and projection algorithms for linear problems in the field of system identification in a context in which uncertainty is described in a deterministic rather than statistical way particular attention is devoted to least squares algorithms when the measurement noise is assumed to be unknown but bounded in a hilbert norm a major contribution of this paper consists in proving that least squares algorithms enjoy strong optimality properties on the contrary it is pointed out that these properties do not hold for other frequently used projection algorithms such as least absolute values or minimax algorithms corresponding to a description of the measurement error in h or l norm respectively

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

on nonlinear h_ infty filtering for discrete time stochastic systems with missing measurements in this paper the h infin filtering problem is investigated for a general class of nonlinear discrete time stochastic systems with missing measurements the system under study is not only corrupted by state dependent white noises but also disturbed by exogenous inputs the measurement output contains randomly missing data that is modeled by a bernoulli distributed white sequence with a known conditional probability a filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies h infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero initial condition the existence conditions of the desired filter are described in terms of a second order nonlinear inequality such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the lyapunov functionals as a consequence a linear time invariant filter design problem is discussed for the benefit of practical applications and some simplified conditions are obtained finally two numerical simulation examples are given to illustrate the main results of this paper

robust detection of signals in dependent noise the robust detection of signals in additive dependent noise is considered the solution to the finite sample problem is obtained when the bayes risk is used as the performance measure for the multivariate densities involved we assume that they belong to an e contamination model the robust detection structure is shown to be optimum for the least favorable density and is a censored version of the nominal likelihood ratio

strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions we present some comparison results for solutions to certain non local elliptic and parabolic problems that involve the fractional laplacian operator and mixed boundary conditions given by a zero dirichlet datum on part of the complementary of the domain and zero neumann data on the rest these results represent a non local generalization of a hopf s lemma for elliptic and parabolic problems with mixed conditions in particular we prove the non local version of the results obtained by davila and davila and dupaigne for the classical case s 1 in 23 24 respectively

obstacle problems for integro differential operators regularity of solutions and free boundaries we study the obstacle problem for integro differential operators of order 2s with s in 0 1 our main result establish that the free boundary is c 1 gamma and u in c 1 s near all regular points namely we prove the following dichotomy at all free boundary points x 0 in partial u varphi i either u x varphi x c d 1 s x o x x 0 1 s alpha for some c 0 ii or u x varphi x o x x 0 1 s alpha where d is the distance to the contact set u varphi moreover we show that the set of free boundary points x 0 satisfying i is open and that the free boundary is c 1 gamma and u in c 1 s near those points these results were only known for the fractional laplacian 2 and are completely new for more general integro differential operators the methods we develop here are purely nonlocal and do not rely on any monotonicity type formula for the operator thanks to this our techniques can be applied in the much more general context of fully nonlinear integro differential operators we establish similar regularity results for obstacle problems with convex operators

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

direct filtering a new approach to optimal filter design for nonlinear systems optimal filters for nonlinear systems are in general difficult to derive or implement the common approach is to use approximate solutions such as extended kalman filters ensemble filters or particle filters however no optimality properties can be guaranteed by these approximations and even the stability of the estimation error cannot often be ensured another relevant issue is that in most practical situations the system whose variables have to be estimated is not known and a two step procedure is adopted based on model identification from data and filter design from the identified model however the designed filter may display large performance deteriorations in the case of modeling errors in this paper a new approach overcoming these issues is proposed allowing the design of optimal filters for nonlinear systems in both the cases of known and unknown system the approach is based on the direct filter design from a set of data generated by the system either experimental or simulated data can be used for design a bound on the number of data necessary to ensure a given filter accuracy is also provided showing that the proposed approach is not affected by the curse of dimensionality

h robustness of adaptive filters against measurement noise and parameter drift recently the issue of robustness of adaptive filtering algorithms has been investigated using the h paradigm in particular in the constant parameter case the celebrated normalized lms algorithm has been shown to coincide with the central h filter ensuring the minumum achievable disturbance attenuation level in this paper the problem is re examined by taking into account the robust performance of three classical algorithms normalized lms kalman filter central h filter with respect to both measurement noise and parameter drift it turns out that normalized lms does not guarantee any finite level of h robustness on the other hand it is shown that striving for the minimum achievable attenuation level leads to a trivial nondynamic estimator with poor h performance this motivates the need for a design approach balancing h and h performance criteria in this regard an illustrative example is presented showing that the central h filter is best suited to achieve a satisfactory tradeoff between the two performances

h sub spl infin fuzzy estimation for a class of nonlinear discrete time dynamic systems this paper studies h sub spl infin fuzzy filtering design for state estimation of nonlinear discrete time systems with bounded but unknown disturbances first the takagi and sugeno 1985 fuzzy model is proposed to represent a nonlinear system next using a linear matrix inequality lmi approach the h sub spl infin fuzzy filtering problems are characterized in terms of a linear matrix inequality problem lmip the lmip can be efficiently solved using convex optimization techniques simulation examples are given to illustrate the design procedure and the applicability of the proposed method the results indicate that the proposed method is suitable for practical applications

signal detection in the presence of weakly dependent noise i optimum detection the problem of designing robust systems for detecting constant signals in the presence of weakly dependent noise with uncertain statistics is considered as in part i of this study which treated optimum detection in weakly dependent noise a moving average representation is used to model the dependence structure of the noise process with the degree of dependence being parameterized by the averaging weights weak dependence is then modeled as the situation in which quantities depending to second or higher order on the averaging weights can be considered to be negligible uncertainty in the noise statistics is introduced within this framework by allowing a general type of uncertainty in the univariate statistics of the independent sequence that drives the moving average to find robust detectors for signals in this type of weakly dependent noise environment related results concerning robust location estimation in an analogous dependent situation are applied to modify a robust detection system for the corresponding independent noise case it is argued here that a robust detector for this dependent noise model is characterized by a least favorable noise distribution which coincides with the distribution that is least favorable for the corresponding independent noise case however the resulting detector design for dependent noise differs from that for independent noise in particular the robust detector for dependent noise is based on a linearly corrected version of the influence curve that defines the independent noise robust detector the worst case performance of the proposed robust detector relative to that of the independent noise robust detector is also analyzed with the conclusion that the performance of the proposed technique is better to first order in the averaging weights in this respect a modification of this robust detector is also proposed which eliminates some practical disadvantages of this system while retaining equivalent performance to first order the specific situation of contaminated gaussian noise is treated in order to illustrate the analysis

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

quadrature mirror filter design in the time domain a new technique for designing quadrature mirror filters is described the formulation carried out in the time domain is shown to result in an optimization problem requiring minimization of a quartic multinomial an iterative solution is suggested which involves computation of the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps our experiments show that convergence to the optimum tap weights is stable and the accuracy of the final solution is limited only by the accuracy of the eigenvalue eigenvector routine as in an earlier technique the user can specify the stop band frequency the relative weights of the passband ripple energy and the stopband residual energy and of course the number of filter taps

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

some new monotonicity formulas and the singular set in the lower dimensional obstacle problem we construct two new one parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem the first one is a family of weiss type formulas geared for points of any given homogeneity and the second one is a family of monneau type formulas suited for the study of singular points we show the uniqueness and continuous dependence of the blowups at singular points of given homogeneity this allows to prove a structural theorem for the singular set our approach works both for zero and smooth non zero lower dimensional obstacles the study in the latter case is based on a generalization of almgren s frequency formula first established by caffarelli salsa and silvestre

stabilization of discrete time nonlinear systems by smooth state feedback abstract for a class of nonlinear discrete time systems of the form x k 1 x k g x k u k we investigate conditions under which a nonlinear system can be rendered globally asymptotically stable via smooth state feedback our main result is that any nonlinear system with lyapunov stable unforced dynamics can always be globally stabilized by smooth state feedback if suitable controllability like rank conditions are satisfied several examples are presented to demonstrate the applications of the stability results developed in this paper

optimum detection of a weak signal with minimal knowledge of dependency the optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available specifically it is assumed that the observations form a one dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known it is assumed that the bivariate densities involved can be represented as diagonal series using orthonormal polynomials using efficacy as a performance measure the optimum nonlinearity is required to satisfy a saddle point condition over this class of bivariate densities

regularity theory for general stable operators parabolic equations abstract we establish sharp interior and boundary regularity estimates for solutions to t u l u f t x in i with i r and r n the operators l we consider are infinitesimal generators of stable levy processes these are linear nonlocal operators with kernels that may be very singular on the one hand we establish interior estimates obtaining that u is c 2 s in x and c 1 2 s in t whenever f is c in x and c 2 s in t in the case f l we prove that u is c 2 s in x and c 1 in t for any 0 on the other hand we study the boundary regularity of solutions in c 1 1 domains we prove that for solutions u to the dirichlet problem the quotient u d s is holder continuous in space and time up to the boundary where d is the distance to this is new even when l is the fractional laplacian

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed