on the mean field and classical limits of quantum mechanics the main result in this paper is a new inequality bearing on solutions of the n body linear schrodinger equation and of the mean field hartree equation this inequality implies that the mean field limit of the quantum mechanics of n identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation this result applies to the case of c1 1 interaction potentials the quantity measuring the approximation of the n body quantum dynamics by its mean field limit is analogous to the monge kantorovich or wasserstein distance with exponent 2 the inequality satisfied by this quantity is reminiscent of the work of dobrushin on the mean field limit in classical mechanics func anal appl 13 115 123 1979 our approach to this problem is based on a direct analysis of the n particle liouville equation and avoids using techniques based on the bbgky hierarchy or on second quantization

the cauchy problem in one dimensional nonlinear viscoelasticity abstract the initial value problem for a nonlinear hyperbolic volterra equation which models the motion of an unbounded viscoelastic bar is studied under physically motivated assumptions the existence of a unique globally defined classical solution is established provided the initial data are sufficiently smooth and small boundedness and asymptotic behavior are also discussed this analysis is based on energy estimates in conjunction with properties of strongly positive definite kernels

paper error propagation properties of recursive least squares adaptation algorithms the numerical properties of implementations of the recursive least squares identification algorithm are of great importance for their continuous use in various adaptive schemes here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates it is shown that conventional ls algorithms including bierman s ud factorization algorithm are exponentially stable with respect to such errors i e the effect of the error decays exponentially the base of the decay is equal to the forgetting factor the same is true for fast lattice algorithms the fast least squares algorithm sometimes known as the fast kalman algorithm is however shown to be unstable with respect to such errors

exponential stability of general tracking algorithms tracking and adaptation algorithms are from a formal point of view nonlinear systems which depend on stochastic variables in a fairly complicated way the analysis of such algorithms is thus quite complicated a first step is to establish the exponential stability of these systems this is of interest in its own right and a prerequisite for the practical use of the algorithm it is also a necessary starting point to analyze the performance in terms of tracking and adaptation because that is how close the estimated parameters are to the time varying true ones in this paper we establish some general conditions for the exponential stability of a wide and common class of tracking algorithms this includes least mean squares recursive least squares and kalman filter based adaptation algorithms we show how stability of an averaged linear and deterministic equation and stability of the actual algorithm are linked to each other under weak conditions on the involved stochastic processes we also give explicit conditions for exponential stability of the most common algorithms the tracking performance of the algorithms is studied in a companion paper

on well posedness for general hierarchy equations of gross pitaevskii and hartree type gross pitaevskii and hartree hierarchies are infinite systems of coupled pdes emerging naturally from the mean field theory of bose gases their solutions are known to be related to initial value problems in particular the gross pitaevskii and hartree equations due to their physical and mathematical relevance the issues of well posedness and uniqueness for these hierarchies have recently been studied thoroughly using specific nonlinear and combinatorial techniques in this article we introduce a new approach for the study of such hierarchy equations by firstly establishing a duality between them and certain liouville equations and secondly solving the uniqueness and existence questions for the latter as an outcome we formulate a hierarchy equation starting from any initial value problem which is u 1 invariant and prove a general principle which can be stated formally as follows in particular several new well posedness results as well as a counterexample to uniqueness for the gross pitaevskii hierarchy equation are proved the novelty in our work lies in the aforementioned duality and the use of liouville equations with powerful transport techniques extended to infinite dimensional functional spaces

adaptive linear filtering using interior point optimization techniques we propose a novel approach for the linear adaptive filtering problem using techniques from interior point optimization the main idea is to formulate a feasibility problem at each iteration and obtain as an estimate a filter near the center of the feasible region it is shown under some mild conditions that this algorithm generates a sequence of filters converging to the optimum linear filter at the rate o 1 n where n is the number of data samples furthermore we show that the algorithm can be made recursive with a per sample complexity of o m sup 2 3 where m is the filter length the potential of the algorithm for practical applications is demonstrated via numerical simulations where the new algorithm is shown to have superior transient behavior and improved robustness to the source signal statistics when compared to the recursive least squares rls method

on the uniqueness of solutions to the periodic 3d gross pitaevskii hierarchy abstract in this paper we present a uniqueness result for solutions to the gross pitaevskii hierarchy on the three dimensional torus under the assumption of an a priori spacetime bound we show that this a priori bound is satisfied for factorized solutions to the hierarchy which come from solutions of the nonlinear schrodinger equation in this way we obtain a periodic analogue of the uniqueness result on r 3 previously proved by klainerman and machedon 75 except that in the periodic setting we need to assume additional regularity in particular we need to work in the sobolev class h for 1 by constructing a specific counterexample we show that on t 3 the existing techniques from the work of klainerman and machedon approach do not apply in the endpoint case 1 this is in contrast to the known results in the non periodic setting where these techniques are known to hold for all 1 in our analysis we give a detailed study of the crucial spacetime estimate associated to the free evolution operator in this step of the proof our methods rely on lattice point counting techniques based on the concept of the determinant of a lattice this method allows us to obtain improved bounds on the number of lattice points which lie in the intersection of a plane and a set of radius r depending on the number theoretic properties of the normal vector to the plane we are hence able to obtain a sharp range of admissible sobolev exponents for which the spacetime estimate holds

recursive identification of switched arx systems we consider the problem of recursively identifying the parameters of a deterministic discrete time switched auto regressive exogenous sarx model under the assumption that the number of models the model orders and the mode sequence are unknown the key to our approach is to view the identification of multiple arx models as the identification of a single though more complex lifted dynamical model built by applying a polynomial embedding to the input output data we show that the dynamics of this lifted model do not depend on the value of the discrete state or the switching mechanism and are linear on the so called hybrid model parameters therefore one can identify the parameters of the lifted model using a standard recursive identifier applied to the embedded input output data the estimated hybrid model parameters are then used to build a polynomial whose derivatives at a regressor give an estimate of the parameters of the arx model generating that regressor the estimated arx model parameters are shown to converge exponentially to their true values under a suitable persistence of excitation condition on a projection of the embedded input output data such a condition is a natural generalization of the well known result for arx models although our algorithm is designed for perfect input output data our experiments also evaluate its performance as a function of the level of noise for different choices of the number of models and model orders we also present an application to temporal video segmentation

randomization and the gross pitaevskii hierarchy we study the gross pitaevskii hierarchy on the spatial domain mathbb t 3 by using an appropriate randomization of the fourier coefficients in the collision operator we prove an averaged form of the main estimate which is used in order to contract the duhamel terms that occur in the study of the hierarchy in the averaged estimate we do not need to integrate in the time variable an averaged spacetime estimate for this range of regularity exponents then follows as a direct corollary the range of regularity exponents that we obtain is alpha frac 3 4 it was shown in our previous joint work with gressman j funct anal 266 7 4705 4764 2014 that the range alpha 1 is sharp in the corresponding deterministic spacetime estimate this is in contrast to the non periodic setting which was studied by klainerman and machedon commun math phys 279 1 169 185 2008 where the spacetime estimate is known to hold whenever alpha geq 1 the goal of our paper is to extend the range of in this class of estimates in a probabilistic sense we use the new estimate and the ideas from its proof in order to study randomized forms of the gross pitaevskii hierarchy more precisely we consider hierarchies similar to the gross pitaevskii hierarchy but in which the collision operator has been randomized for these hierarchies we show convergence to zero in low regularity sobolev spaces of duhamel expansions of fixed deterministic density matrices we believe that the study of the randomized collision operators could be the first step in the understanding of a nonlinear form of randomization

rls parameter convergence with overparametrized models abstract this paper through the concept of quotient space generalizes the rls parameter convergence results obtained previously using the lyapunov type function approach 14 1 12 7 to overparameterized systems the system signals do not have to be quasi stationary as assumed by ljung 10 and a priori knowledge of the degree of overparameterization is not required the excitation condition is the weakest possible and it is shown that under this excitation condition limiting set of parameter estimates always belongs to a set h each element of which contains the irreducible plant model plus a monic common factor polynomial it is further shown that the common factor polynomials defined by the limiting set of parameter estimates are quantitatively related to the initial conditions of the algorithm for example if the condition number of the initial covariance matrix is unity then the limiting set of parameter estimates is the singleton on h closest to the initial parameter estimate

sufficient excitation and stable reduced order adaptive iir filtering a perturbed error system is used to describe the parameter and output error behaviors of reduced order application of adaptive identifier filters such as the hyperstable adaptive recursive filter harf given satisfaction of a sufficient excitation condition this error system is shown to exhibit a bounded input bounded state bibs property this implies that despite order insufficiency the output and parameter estimates of harf and similar adaptive identifier filter algorithms remain bounded

locally optimum adaptive signal processing algorithms we propose a new analytic method for comparing constant gain adaptive signal processing algorithms specifically estimates of the convergence speed of the algorithms allow for the definition of a local measure of performance called the efficacy that can be theoretically evaluated by definition the efficacy is consistent with the fair comparison techniques used in signal processing applications using the efficacy as a performance measure we prove that the lms newton algorithm is optimum and is thus the fastest algorithm within a very rich algorithmic class furthermore we prove that regular lms is better than any of its variants that apply the same nonlinear transformation on the elements of the regression vector such as signed regressor quantized regressor etc for an important class of input signals simulations support all our theoretical conclusions

the decay rate for a fractional differential equation abstract we consider the fractional differential equation u tt t x 0 t k t s u sxx s x ds u xx t x t 0 x 0 1 with dirichlet boundary conditions and initial values this problem with a particular kernel may be looked at as an internally damped wave equation with a strong damping of order less than one it is proved that the solution of this problem with a weakly singular kernel decays exponentially to zero

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

derivation of hartree s theory for generic mean field bose systems in this paper we provide a novel strategy to prove the validity of hartree s theory for the ground state energy of bosonic quantum systems in the mean field regime for the well known case of trapped bose gases this can be shown using the strong quantum de finetti theorem which gives the structure of infinite hierarchies of k particles density matrices here we deal with the case where some particles are allowed to escape to infinity leading to a lack of compactness our approach is based on two ingredients 1 a weak version of the quantum de finetti theorem and 2 geometric techniques for many body systems our strategy does not rely on any special property of the interaction between the particles in particular our results cover those of benguria lieb and lieb yau for respectively bosonic atoms and boson stars

interior point least squares estimation transient convergence analysis and application to mmse decision feedback equalization in many communication systems training sequences are used to help the receiver identify and or equalize the channel the amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization in this paper we propose the use of a new adaptive filtering method called interior point least squares ipls for adaptive equalization first we show that ipls converges exponentially fast in the transient phase then we use the ipls algorithm to update the weight vector for a minimum mean square error decision feedback equalizer mmse dfe in a cdma downlink scenario numerical simulations show that when training sequences are short ipls consistently outperforms rls in terms of system bit error rate and packet error rate as the training sequence gets longer ipls matches the performance of the rls algorithm

adaptive system stability robustness via burst recovery abstract adaptive systems which are based on a posteriori parameter update algorithms are shown to possess a specific type of self stabilization property termed burst recovery this results in bounded disturbance bounded error stability provided that unbounded parameter drift does not occur persistent excitation prevents unbounded parameter drift but only when both upper and lower bounds on excitation exist for many adaptive systems an upper bound on excitation cannot be assured using standard perturbation analyses which require the disturbance to be suitably small compared to the lower bound on excitation this paper proves that burst recovery in conjunction with only a lower bound on excitation provides bounded disturbance bounded error stability the disturbance need not be small and additional algorithm modifications such as parameter projection are not necessary

technical communique convergence analysis of recursive identification algorithms with forgetting factor a convergence analysis of a modified version of the least squares recursive identification algorithm with forgetting factor is given it is shown that the parametric distance converges to a zero mean random variable it is also shown that under persistent excitation condition on both system input and output the condition number of the adaptation gain matrix is bounded the variance of the parametric distance is bounded by the product of the noise variance times the upper bound of the condition number of the gain matrix this is done by normalizing the measurement vector entering in the identification algorithm and by using a forgetting factor verifying l t 0

on the size of chaos in the mean field dynamics we consider the error arising from the approximation of an n particle dynamics with its description in terms of a one particle kinetic equation we estimate the distance between the j marginal of the system and the factorized state obtained in a mean field limit as n our analysis relies on the evolution equation for the correlation error rather than on the usual bbgky hierarchy the rate of convergence is shown to be o j 2 n in any bounded interval of time size of chaos as expected from heuristic arguments our formalism applies to an abstract hierarchical mean field model with bounded collision operator and a large class of initial data covering a stochastic jump processes converging to the homogeneous boltzmann and the povzner equation and b quantum systems giving rise to the hartree equation

nonasymptotic results for finite memory wls filters a nonasymptotic analysis of properties of weighted least squares wls adaptive filters used for identification of time varying systems is presented it is shown that the problem of mean square boundedness of wls estimates is closely related to the problem of invertibility in the mean sense of the corresponding regression matrix necessary and sufficient conditions are discussed for such invertibility to hold based on that a number of results are derived paralleling those already obtained for least mean square lms filters and the problem of statistical robustness of the wls estimator is briefly discussed

the recursive generalized predictive feedback control theory and experiments the proposed adaptive control algorithm combines the recursive least squares system identification algorithm and the generalized predictive control gpc design algorithm referred to as recursive generalized predictive control rgpc in the gpc design process the prediction horizon and control horizon are the constants to be chosen two new parameters are defined to describe the effects of the prediction and control horizons and those parameters provide the effective ranges of the horizons the rgpc algorithm adjusts the control penalty based on the stability of a closed loop system model a time varying algorithm for the control penalty allows to design an aggressive controller the multi sampling rate algorithm is added between the system identification and the control design in order to design a higher order controller the rgpc algorithm is applied to three different systems a cantilevered beam a sound enclosure and an optical jitter suppression testbed

adaptive rls algorithms under stochastic excitation l sup 2 convergence analysis a very general class of rls recursive least squares algorithms having a forgetting factor is considered the basic assumptions are that the data generation mechanism is free of disturbances and that the observation vector is a stochastic process satisfying a phi mixing condition a stochastic characterization of persistent excitation is first given then it is proved that the algorithm is exponentially convergent in the mean square sense

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

on parameter convergence in adaptive control it is well known that the parameter error as well as the model plant mismatch error in a model reference adaptive scheme tends exponentially to zero iff a certain sufficient richness condition holds for signals inside the time varying plant control loop in this paper we give conditions on the reference signal the exogenous input to the adaptive loop namely that it have as many spectral lines as there are unknown parameters in order to guarantee parameter convergence

a simple proof of convergence to the hartree dynamics in sobolev trace norms the derivation of the hartree equation from many body systems of bosons in the mean field limit has been very intensively studied in the last couple of years however very few results exist showing convergence of the kth marginal of the n body density matrix to the projection to the k fold tensor product of the solution of the hartree equation in stronger trace norms like the energy trace norm see the work of michelangeli and schlein commun math phys 311 3 645 687 2012 and luhrmann j math phys 53 2 022105 2012 this issue is from a physical view point very important the reason is that one can then approximate expectation values of certain observables of the n body system by means of the hartree equation with relaxation of the very restrictive assumption that the observables are bounded operators here we consider the non relativistic case we prove assuming only h1 regularity of the initial data convergence in the energy trace norm without rates and convergence in any other weaker

recursive parameter identification algorithm stability analysis via pi sharing pi sharing is introduced as an extension of the application of passivity and hyperstability concepts for discrete time systems providing connections between input output and state space stability notions using tools developed within the pi sharing framework new stability results for the output error class identification algorithm are derived this approach offers a clear interpretation of the role of the spr condition in the work of landau and silveira and its absence in the work of tomizuka and altay

robust sequential learning algorithms for linear observation models this paper presents a study of sequential parameter estimation based on a linear non gaussian observation model to develop robust algorithms we consider a family of heavy tailed distributions that can be expressed as the scale mixture of gaussian and extend the development to include some robust penalty functions we treat the problem as a bayesian learning problem and develop an iterative algorithm by using the laplace approximation for the posterior and the minorization maximization mm algorithm as an optimization tool we then study a one step implementation of the iterative algorithm this leads to a family of generalized robust rls type of algorithms which include several well known algorithms as special cases using a further simplification that the covariance is fixed leads to a family of generalized robust lms type of algorithms through mathematical analysis and simulations we demonstrate the robustness of these algorithms

on the mean field approximation of many boson dynamics abstract we show under general assumptions that the mean field approximation for quantum many boson systems is accurate our contribution unifies and improves most of the known results the proof uses general properties of quantization in infinite dimensional spaces phase space analysis and measure transportation techniques

tracking properties and steady state performance of rls adaptive filter algorithms adaptive signal processing algorithms derived from ls least squares cost functions are known to converge extremely fast and have excellent capabilities to track an unknown parameter vector this paper treats analytically and experimentally the steady state operation of rls recursive least squares adaptive filters with exponential windows for stationary and nonstationary inputs a new formula for the estimation noise has been derived involving second and fourth order statistics of the filter input as well as the exponential windowing factor and filter length furthermore it is shown that the adaptation process associated with lag effects depends solely on the exponential weighting parameter in addition the calculation of the excess mean square error due to the lag for an assumed markov channel provides the necessary information about tradeoffs between speed of adaptation and steady state error it is also the basis for comparison to the simple lms algorithm in a simple case of channel identification it is shown that the lms and rls adaptive filters have the same tracking behavior finally in the last part we present new rls restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise namely finite precision arithmetic

quantum fluctuations and rate of convergence towards mean field dynamics the nonlinear hartree equation describes the macroscopic dynamics of initially factorized n boson states in the limit of large n in this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting hartree dynamics more precisely we prove bounds on the difference between the one particle density associated with the solution of the n body schrodinger equation and the orthogonal projection onto the solution of the hartree equation

a central limit theorem in many body quantum dynamics we study the many body quantum evolution of bosonic systems in the mean field limit the dynamics is known to be well approximated by the hartree equation so far the available results have the form of a law of large numbers in this paper we go one step further and we show that the fluctuations around the hartree evolution satisfy a central limit theorem interestingly the variance of the limiting gaussian distribution is determined by a time dependent bogoliubov transformation describing the dynamics of initial coherent states in a fock space representation of the system

optimal adaptive control and consistent parameter estimate for deterministic systems with quadratic cost in this paper an adaptive control is designed for deterministic systems on the basis of the projection algorithm so that the quadratic loss function approaches its minimum at a rate of n e e 0 and the parameter estimate converges to its true value with a near exponential rate

the derivation of the mathbb t 3 t 3 energy critical nls from quantum many body dynamics we derive the 3d energy critical quintic nls from quantum many body dynamics with 3 body interaction in the mathbb t 3 periodic setting due to the known complexity of the energy critical setting previous progress was limited in comparison to the 2 body interaction case yielding energy subcritical cubic nls previously the only result for the 3d energy critical case was hong et al j funct anal 270 1 34 67 2016 which proved the uniqueness part of the argument in the case of small solutions in the main part of this paper we develop methods to prove the convergence of the bbgky hierarchy to the infinite gross pitaevskii gp hierarchy and separately the uniqueness of large gp solutions since the trace estimate used in the previous proofs of convergence is the false endpoint trace estimate in our setting we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de finetti theorem for the large solution uniqueness argument we discover the new hierarchical uniform frequency localization hufl property for the gp hierarchy and use it to prove a new type of uniqueness theorem the hufl property reduces to a new statement even for nls with the help of colliander et al ann math 2 167 3 767 865 2008 and ionescu and pausader duke math j 161 1581 1612 2012 which proved the global well posedness for the quintic nls this new uniqueness theorem establishes global uniqueness

derivation of the time dependent gross pitaevskii equation without positivity condition on the interaction using a new method pickl in a simple derivation of mean field limits for quantum systems 2010 it is possible to derive mean field equations from the microscopic n body schrodinger evolution of interacting particles without using bbgky hierarchies in this paper we wish to analyze scalings which lead to the gross pitaevskii equation which is usually derived assuming positivity of the interaction erdos et al in commun pure appl math 59 12 1659 1741 2006 invent math 167 515 614 2007 the new method for dealing with mean field limits presented in pickl 2010 allows us to relax this condition the price we have to pay for this relaxation is however that we have to restrict the scaling behavior of the interaction and that we have to assume fast convergence of the reduced one particle marginal density matrix of the initial wave function mu psi 0 to a pure state 0 0

quantitative derivation of the gross pitaevskii equation starting from first principle many body quantum dynamics we show that the dynamics of bose einstein condensates can be approximated by the time dependent nonlinear gross pitaevskii equation giving a bound on the rate of the convergence initial data are constructed on the bosonic fock space applying an appropriate bogoliubov transformation on a coherent state with expected number of particles mathit n the bogoliubov transformation plays a crucial role it produces the correct microscopic correlations among the particles our analysis shows that on the level of the one particle reduced density the form of the initial data is preserved by the many body evolution up to a small error that vanishes as mathit n 1 2 in the limit of large mathit n

convergence analysis of the least squares identification algorithm with a variable forgetting factor the time varying linear systems abstract this paper studies the convergence of the least squares identification algorithm with a variable forgetting factor the evolution of the parameter estimator with respect to initial conditions actual parameter changes and stochastic perturbations is analysed bounds on the deterministic and stochastic parts of their estimator error are found and their relation to a persistent excitation condition is discussed this relation explains the possibility of having bursting phenomena during the identification process special attention is paid to the consistency of these results with the classical ones obtained for the ordinary least squares algorithm when the forgetting factor tends to unity

local existence of solutions to randomized gross pitaevskii hierarchies in this paper we study the local in time existence of solutions to randomized forms of the gross pitaevskii hierarchy on periodic domains in particular we study the independently randomized gross pitaevskii hierarchy and the dependently randomized gross pitaevskii hierarchy which were first introduced in the author s joint work with staffilani 2013 for these hierarchies we construct local in time low regularity solutions in spaces which contain a random component the constructed density matrices will solve the full randomized hierarchies thus extending the results from the author and staffilani s joint work where solutions solving arbitrarily long subhierarchies were given our analysis will be based on the truncation argument which was first used in the deterministic setting in the work of t chen and pavlovic 2013 the presence of randomization in the problem adds additional difficulties most notably to estimating the duhamel expansions that are crucial in the truncation argument these difficulties are overcome by a detailed analysis of the duhamel expansions in the independently randomized case we need to keep track of which randomization parameters appear in the duhamel terms whereas in the dependently randomized case we express the duhamel terms directly in terms of the initial data in both cases we can obtain stronger results with respect to the time variable if we assume additional regularity on the initial data

blow up of solutions for a nonlinear beam equation with fractional feedback abstract a nonlinear beam equation describing the transversal vibrations of a beam with boundary feedback is considered the boundary feedback involves a fractional derivative we discuss the asymptotic behavior of solutions in fact we prove that solutions blow up in finite time under certain assumptions on the nonlinearity

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

study of the transient phase of the forgetting factor rls we investigate the convergence properties of the forgetting factor rls algorithm in a stationary data environment using the settling time as our performance measure we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level specifically when the observation noise level is low high snr rls when initialized with a matrix of small norm it has an exceptionally fast convergence convergence speed decreases as we increase the norm of the initialization matrix in a medium snr environment the optimum convergence speed of the algorithm is reduced as compared with the previous case however rls becomes more insensitive to initialization finally in a low snr environment we show that it is preferable to initialize the algorithm with a matrix of large norm

fast newton transversal filters a new class of adaptive estimation algorithms a class of adaptive algorithms for the estimation of fir finite impulse response transversal filters is presented the main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters the method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order m where m can be much smaller than the order of the filter to be estimated under this assumption the covariance matrix of the input signal is estimated by extending in a min max way the m order sample covariance matrix this estimate can be regarded as a generalization of the diagonal covariance matrix used in lms and leads to an efficient computation of the gain needed for the adaptation the new class of algorithms contains the lms and the fast versions of ls as special cases the complexity changes linearly with m starting from the complexity of the lms for m 0 and ending at the complexity of the fast versions of ls

mean field limit for bosons with compact kernels interactions by wigner measures transportation we consider a class of many body hamiltonians composed of a free kinetic part and a multi particle potential interaction with a compactness assumption on the latter part we investigate the mean field limit of such quantum systems following the wigner measures approach we prove the propagation of these measures along the flow of a nonlinear hartree field equation this enhances and complements some previous results in the subject

mean field dynamics singular potentials and rate of convergence we consider the time evolution of a system of n identical bosons whose interaction potential is rescaled by n 1 we choose the initial wave function to describe a condensate in which all particles are in the same one particle state it is well known that in the mean field limit n the quantum n body dynamics is governed by the nonlinear hartree equation using a nonperturbative method we extend previous results on the mean field limit in two directions first we allow a large class of singular interaction potentials as well as strong possibly time dependent external potentials second we derive bounds on the rate of convergence of the quantum n body dynamics to the hartree dynamics

brief paper reduced order performance of parallel and series parallel identifiers with weakly observable parasitics the stability properties of discrete time parallel and series parallel identifiers with respect to a specific model plant order mismatch are analyzed while in a deterministic environment with no modeling error the two schemes give identical results when used in a deterministic environment with modeling error their performance is different we assume a singularly perturbed state representation for the plant where the modeling error consists of fast parasitics which are weakly observable in the plant output detailed bounds on parameter and output estimate errors are established and the robustness of the adaptive identifiers is established by showing that the error bound goes to zero as the modeling error goes to zero i e as the parasitics become infinitely fast the dependence of this residual identification error on the input signal the neglected parasitics and the initial error conditions is shown to be crucial the bounds indicate possibilities for reducing the error by a proper choice of the input signal

optimal convergence rate and regularity of nonrelativistic limit for the nonlinear pseudo relativistic equations abstract in this paper we are concerned with the nonrelativistic limit of the following pseudo relativistic equation with hartree nonlinearity or power type nonlinearity 2 c 2 m 2 c 4 m c 2 u u n u where c denotes the speed of light we prove that as c the ground states of this equation converges to the ground state of its nonrelativistic counterpart 2 2 m u u n u with convergence rate 1 c 2 in every h s norms moreover we show that this rate is optimal

strong consistency of a class of recursive stochastic gradient algorithms in this work strong consistency results for a class of stochastic gradient algorithms are developed where the system is not necessarily minimum phase or stable and is assumed to be of the carma form the analysis uses only standard martingale results and strong consistency is shown to hold under certain persistent excitation conditions

quantum dynamics with mean field interactions a new approach we propose a new approach for the study of the time evolution of a factorized n particle bosonic wave function with respect to a mean field dynamics with a bounded interaction potential the new technique which is based on the control of the growth of the correlations among the particles leads to quantitative bounds on the difference between the many particle schrodinger dynamics and the one particle nonlinear hartree dynamics in particular the one particle density matrix associated with the solution to the n particle schrodinger equation is shown to converge to the projection onto the one dimensional subspace spanned by the solution to the hartree equation with a speed of convergence of order 1 n for all fixed times

sharf convergence properties a class of stable algorithms for adapting infinite impulse response iir digital filters based on the concepts of nonlinear stability theory prominent in the control literature is emerging while this class of adaptive filters offers much promise in practical applications little has been done toward providing a characterization that would guide selection of design parameters such as adaptation constants and error smoothing coefficients this paper focuses on the simplest well behaved member of this class of adaptive recursive filters sharf progression from a local linearization of the nonlinear parameter estimate convergence behavior through an idealized eigenvalue eigenvector analysis of the parameter estimate time varying recursion to lyapunov function establishment for the full output and parameter error system reveals the exponential local nongradient descent convergence character of sharf and provides initial insight into the effects of adaptation constants and error smoothing coefficients on these characteristics

fluctuations around hartree states in the mean field regime we consider the dynamics of a large system of n interacting bosons in the mean field regime where the interaction is of order 1 n we prove that the fluctuations around the nonlinear hartree state are generated by an effective quadratic hamiltonian in fock space which is derived from bogoliubov s approximation we use a direct method in the n particle space which is different from the one based on coherent states in fock space

normalized standing waves for the hartree equations abstract in this paper we study the existence and stability instability of standing waves with a prescribed l 2 norm for the following hartree equation 0 1 i u t u a x 2 u x u 2 u 0 t x r r n where t is time n 3 0 n and a 0 is a constant to get such solutions we look for normalized solutions of the associated stationary equation 0 2 u a x 2 u u x u 2 u 0 x r n two cases are considered i the system is free a 0 and i i a harmonic trapping potential is added in the system a 0 in case i by constructing a suitable submanifold of a l 2 sphere we prove the existence of a normalized solution for problem 0 2 with least energy in the l 2 sphere which corresponds to a normalized ground state standing wave of problem 0 1 then we show that each normalized ground state of problem 0 2 coincides a ground state of problem 0 2 in the usual sense furthermore we give a global existence result for problem 0 1 and also show that any normalized ground state standing wave is strongly unstable in case i i for small a 0 we prove the existence of two different standing waves one corresponds to a topological local minimizer of the constrained energy functional the other corresponds to a mountain pass type solution of problem 0 2 with its energy strictly larger than that of the normalized ground state moreover we show that the set of normalized ground state solutions for problem 0 2 is stable under the associated flow finally to connect case i and case i i we analyze the asymptotic behavior of the two solutions to problem 0 2 obtained in case i i as the trapping frequency a vanishes

the gross pitaevskii hierarchy on general rectangular tori in this work we study the gross pitaevskii hierarchy on general rational and irrational rectangular tori of dimensions two and three this is a system of infinitely many linear partial differential equations which arises in the rigorous derivation of the nonlinear schrodinger equation we prove a conditional uniqueness result for the hierarchy in two dimensions this result allows us to obtain a rigorous derivation of the defocusing cubic nonlinear schrodinger equation from the dynamics of many body quantum systems on irrational tori this question was posed as an open problem in the previous work of kirkpatrick schlein and staffilani

performance analysis of general tracking algorithms a general family of tracking algorithms for linear regression models is studied it includes the familiar least mean square gradient approach recursive least squares and kalman filter based estimators the exact expressions for the quality of the obtained estimates are complicated approximate and easy to use expressions for the covariance matrix of the parameter tracking error are developed these are applicable over the whole time interval including the transient and the approximation error can be explicitly calculated

weak convergence and local stability properties of fixed step size recursive algorithms a recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation ode the odes describing the motion of several common adaptive filters are examined in some simple settings including the least mean square lms algorithm and all three of its signed variants the signed regressor the signed error and the sign sign algorithms stability and instability results are presented in terms of the eigenvalues of a correlation like matrix this generalizes known results for lms signed regressor lms and signed error lms and gives new stability criteria for the sign sign algorithm the ability of the algorithms to track moving parameterizations can be analyzed in a similar manner by relating the time varying system to a forced ode the asymptotic distribution about the forced ode is an ornstein uhlenbeck process the properties of which can be described in a straightforward manner

global existence and asymptotic behavior for a fractional differential equation this paper is concerned with the global existence and asymptotic behavior of solutions to an initial boundary value problem of hyperbolic type we investigate the interaction between a polynomial source and a dissipation of fractional order this fractional dissipation is defined by a temporal nonlocal term

mean field evolution of fermionic mixed states in this paper we study the dynamics of fermionic mixed states in the mean field regime we consider initial states that are close to quasi free states and prove that under suitable assumptions on the initial data and on the many body interaction the quantum evolution of such initial data is well approximated by a suitable quasi free state in particular we prove that the evolution of the reduced one particle density matrix converges as the number of particles goes to infinity to the solution of the time dependent hartree fock equation our result holds for all times and gives effective estimates on the rate of convergence of the many body dynamics towards the hartree fock evolution 2015 wiley periodicals inc

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms