paper pole assignment for distributed systems by finite dimensional control the question of pole assignment for a class of distributed systems by means of finite dimensional control is considered a finite dimensional compensator is usually designed based on a reduced order model and it is not a priori known what effect this will have on the original infinite dimensional system explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system for a certain compensator design estimates are derived which can be used to guarantee stability a priori numerical results are also presented

proper stable bezout factorizations and feedback control of linear time delay systems this paper deals with the existence and construction of proper stable bezout factorizations of transfer function matrices of linear time invariant systems with commensurate time delays existence of factorizations is characterized in terms of spectral controllability or spectral observability of the co canonical or canonical realization of the transfer function matrix an explicit procedure for computing proper stable bezout factorizations is given in terms of a specialized ring of pure and distributed time delays this procedure is utilized to construct finite dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed loop system

highest predictive density estimator in regression models abstract when the prior is only partially specified it is sometimes possible to estimate its unspecified part by maximizing the predictive density marginal likelihood of the data this paper examines the usefulness and the limitations of the priors of this kind hprd priors and the corresponding posterior mean hprd estimators in a regression setup the hprd estimator turns out to be a simple shrinkage estimator and it is found that there is an interesting relationship regarding the shrinkage factor of an estimator between the empirical bayes approach and the hprd approach the latter findings may provide some insight into getting the right size of shrinkage to attain the minimum risk the hprd prior can rarely serve as a reference prior however since the prior information it contains is too strong although this shortcoming is partly due to the nature of the hprd approach itself it can sometimes be alleviated by a more careful choice of the class of priors if the lower bound on the prior variance is set correctly the hprd estimator will provide a sensible candidate for the point estimate of the regression coefficients we also show a link between the hprd approach and the lower bound on the bayes factor

splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

on spectrum distribution of completely controllable linear systems this paper is concerned with the placement of the spectrum of the closed loop operator a bk resulting from use of a linear feedback control law u kx in the infinite dimensional linear control system x ax bu for a class of systems in hilbert space with certain assumptions on the spectrum of the operator a a complete characterization of the achievable spectra is obtained the proofs are carried out in an operator theoretic context

smoothness priors and nonlinear regression abstract smoothness priors represent prior information that an unknown function does not change slope quickly and hence that the function describes a simple curve e g wahba 1978 in this article such priors for the multiple nonlinear regression model are developed in such a way that estimates and standard errors can be obtained as a natural and conceptually straightforward extension of linear multiple regression estimation with the addition of dummy variables and dummy observations relations to spline and polynomial interpolation are described an illustrative example of cost function estimation is provided

on the existence of finite dimensional compensators for retarded and neutral systems in this paper we study a large class of neutral systems containing the class of retarded systems a necessary and sufficient condition is given for the existence of a finite dimensional compensator achieving exponential stability

remarks on space time codes including a new lower bound and an improved code this article presents a new asymptotically exact lower bound on pairwise error probability of a space time code as well as an example code that outperforms the comparable orthogonal design based space time odst code also contained in the article are an exact expression for pairwise error probability pep signal design guidelines and some observations relating to the reception of odst codes

perturbation of strongly and polynomially stable riesz spectral operators abstract in this paper we consider bounded and relatively bounded finite rank perturbations of a riesz spectral operator generating a polynomially stable semigroup of linear operators on a hilbert space we concentrate on a commonly encountered situation where the spectrum of the unperturbed operator is contained in the open left half plane of the complex plane and approaches the imaginary axis asymptotically we present conditions on the perturbing operator such that the spectrum of the perturbed operator is contained in the open left half plane of the complex plane and additional conditions for the strong and polynomial stabilities of the perturbed semigroup we consider two applications of the perturbation results in the first example we apply the results to the perturbation of a polynomially stabilized one dimensional wave equation in the second example we consider the perturbation of a closed loop system consisting of a distributed parameter system and an observer based feedback controller solving the robust output regulation problem related to an infinite dimensional signal generator

robustness of strongly and polynomially stable semigroups abstract in this paper we study the robustness properties of strong and polynomial stability of semigroups of operators we show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator the presented results apply to general polynomially stable semigroups and bounded perturbations the conditions on the perturbations generalize well known criteria for the preservation of exponential stability of semigroups we also show that the general results can be improved if the perturbation is of finite rank or if the semigroup is generated by a riesz spectral operator the theory is applied to deriving concrete conditions for the preservation of stability of a strongly stabilized one dimensional wave equation

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

robust stabilization of infinite dimensional systems by finite dimensional controllers abstract the problem of robustly stabilizing an infinite dimensional system with transfer function g subject to an additive perturbation is considered it is assumed that g b 0 of systems introduced by callier and desoer 3 the perturbation satisfies w1 w2 c now write w1gw2 g1 g1 where g1 is rational and totally unstable and g2 is stable generalizing the finite dimensional results of glover 12 this family of perturbed systems is shown to be stabilizable if and only if min g 1 the smallest hankel singular value of g 1 a finite dimensional stabilizing controller is then given by k w 2 k 1 i g 2 k 1 1 w 1 where 2 is a rational approximation of g2 such that g 2 g 2 min g 1 and k1 robustly stabilizes g1 to margin the feedback system g k will then be stable if w1 w2

tracking control for boundary controlled parabolic pdes with varying parameters combining backstepping and differential flatness the combination of backstepping based state feedback control and flatness based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion convection reaction system with spatially and temporally varying parameters and nonlinear boundary input for this in a first step the backstepping transformation is utilized to determine a state feedback controller which transforms the original distributed parameter system into an appropriately chosen exponentially stable distributed parameter target system of a significantly simpler structure in a second step the flatness property of the target system is exploited in order to determine the feedforward controller which allows us to realize the tracking of suitably prescribed trajectories for the system output this results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion convection reaction system with varying parameters whose applicability and tracking performance is evaluated in simulation studies

riesz basis property of a second order hyperbolic system with collocated scalar input output the closed loop form of a second order hyperbolic system with scalar collocated sensor actuator is considered the riesz basis property of the system is verified for diagonal semigroups based on an abstract result of one rank perturbation of discrete type operators in hilbert spaces a simplified proof for the abstract result is presented

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

riesz basis approach to the stabilization of a flexible beam with a tip mass using an abstract condition of riesz basis generation of discrete operators in the hilbert spaces we show in this paper that a sequence of generalized eigenfunctions of an euler bernoulli beam equation with a tip mass under boundary linear feedback control forms a riesz basis for the state hilbert space in the meanwhile an asymptotic expression of eigenvalues and the exponential stability are readily obtained the main results of siam j control optim 36 1998 pp 1962 1986 are concluded as a special case and the additional conditions imposed there are removed

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

dynamic stabilization of regular linear systems we consider a general class of infinite dimensional linear systems called regular linear systems for which convenient representations are known to exist both in time and in frequency domain for this class of systems we investigate the concepts of stabilizability and detectability in particular their invariance under feedback and their relationship to exponential stability we introduce two concepts of dynamic stabilization the first formulated as usual with the plant and the controller connected in feedback and the second with two feedback loops even for finite dimensional systems the second concept stabilization with an internal loop in the controller is more general we argue that the more general concept is the natural one and we derive sufficient conditions under which an observer based stabilizing controller with an internal loop can be constructed

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

root locii for systems defined on hilbert spaces the root locus is an important tool for analyzing the stability and time constants of linear finite dimensional systems as a parameter often the gain is varied however many systems are modelled by partial differential equations or delay equations these systems evolve on an infinite dimensional space and their transfer functions are not rational in this paper a rigorous definition of the root locus for infinite dimensional systems is given and it is shown that the root locus is well defined for a large class of infinite dimensional systems as for finite dimensional systems any limit point of a branch of the root locus is a zero however the asymptotic behavior can be quite different from that for finite dimensional systems this point is illustrated with a number of examples it is shown that the familiar pole zero interlacing property for collocated systems with a hermitian state matrix extends to infinite dimensional systems with self adjoint generator this interlacing property is also shown to hold for collocated systems with a skew adjoint generator

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

structured unitary space time autocoding constellations we previously showed that arbitrarily reliable communication is possible within a single coherence interval in rayleigh flat fading as the symbol duration of the coherence interval and the number of transmit antennas grow simultaneously this effect where the space time signals act as their own channel codes is called autocoding for relatively short e g 16 symbol coherence intervals a codebook of independent isotropically random unitary space time signals theoretically supports transmission rates that are a significant fraction of autocapacity with an extremely low probability of error the exploitation of space time autocoding requires the creation and decoding of extraordinarily large constellations typically l 2 sup 80 we make progress on the first part of the problem through a random but highly structured constellation that is completely specified by log sub 2 l independent isotropically distributed unitary matrices the distinguishing property of this construction is that any two signals in the constellation are pairwise statistically independent and isotropically distributed thus the pairwise probability of error and hence the union bound on the block probability of error of the structured constellation is identical to that of a fully random constellation of independent signals we establish the limitations of an earlier construction through a subsidiary result that is interesting in its own right the square or for that matter any integer power greater than one of an isotropically random unitary matrix is not isotropically random with the sole exception of the one by one unitary matrix

controller design for distributed systems based on hankel norm approximations a procedure for obtaining a finite dimensional reduced order model for a class of distributed systems is developed it is based on a combination of a modal approximation and an optimal hankel norm approximation and the approximation error can be accurately predicted the reduced order model can be used to design a precompensator for the original system as its performance and robust stability characteristics can be deduced from the reduced order model and finitely many modal parameters the procedure is applied to a parabolic system

computing the performance of unitary space time group codes from their character table multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment their success however depends on the design of cedes that achieve these promises it is well known that unitary matrices can be used to design differentially modulated space time codes these codes have a particularly efficient description if they form a finite group under matrix multiplication we show how to compute the parameters of such groups crucial for their use as space time codes using only the character table of the group since character tables for many groups are known and tabulated this method could be used to quickly test for a given group which of its irreducible representations can be used to design good unitary space time codes we demonstrate our method by computing the eigenvalues of all the irreducible representations of the special linear group sl sub 2 f sub q over a finite prime field f sub q of odd characteristic and study in detail the performance of a particular eight dimensional representation of sl sub 2 f sub 17

robust control of flexible structures a case study a comparison is made between three partial differential equation models for a flexible beam with different types of damping and varying parameter values robust controllers can be designed to stabilize all linear systems whose transfer functions lie within a ball in the l norm given a nominal model for our flexible beam we calculate which sets of models can be stabilized by the same finite dimensional robust controller by stabilize we mean here that the poles of the system are moved to the left of the line re s 0

estimation of some partially specified nonlinear models abstract this paper presents a procedure for analyzing a partially specified nonlinear regression model in which the nuisance parameter is an unrestricted function of a subset of regressors the procedure does not require parameteric modeling of the nuisance parameter but assumes that the model can be transformed into a partially specified linear equation by inverting some nonlinear functions the model parameters are estimated by applying robinson s 1988a procedure and the estimator is show to be n consistent and asymptotically normal one attraction of the estimator is that is to computationally simple requiring no more than least squares regressions a simulation study indicates that the estimator has practical values

on the optimum design of unitary cyclic group space time codes in this letter based on the exact pairwise error probability we derive the union bound on the symbol error probability sep of the differential unitary space time dust modulation employing group codes instead of using the rank and determinant or euclidean distance criteria we optimize the cyclic group codes such that the union bound on the sep is minimized for a predetermined scenario taking into account the number of transmit and receive antennas and the operating signal to noise ratio snr our simulation results show that for a wide range of snrs the codes with the minimum union bound for a particular snr outperform the codes designed based on rank and determinant or euclidean distance criteria

on the design of layered space time systems for autocoding hochwald et al see ieee trans inform theory nov 2001 have recognized that arbitrarily reliable communication is possible in multiantenna systems with coding over only a single coherence interval in particular they showed that reliable communication is possible for all rates r spl les c sub a with code words that extend over a single coherence interval when the number of transmit antennas and coherence interval n t spl rarr spl infin they coined the names autocoding for this phenomenon and autocapacity for c sub a they also proposed a signalling scheme based on random unitary matrices that achieves a significant fraction of this capacity the main limitation however is that currently no decoder of reasonable complexity is known for this signalling scheme we investigate the application of space time layering to autocoding we show that properly constructed layered systems can achieve the autocapacity with a reasonable complexity receiver composed of minimum mean square error mmse decision feedback multiuser detectors and single user decoders in addition to this asymptotic result we propose a specific layering approach the threaded space time layering that combines generalized bit interleaved space time coded modulation iterative signal processing and pilot symbol assisted channel estimation we show that this approach is well suited for practical systems with limited numbers of transmit antennas and small coherence intervals finally we report simulation results that demonstrate the ability of the threaded approach to achieve significant fractions of the autocapacity with a realizable receiver the simulation results also indicate significant performance gains over the cayley differential space time signalling scheme in certain scenarios

delay constrained capacity with causal feedback a block fading channel model is considered and a k block delay constraint is imposed on data transmission the key consideration is that the channel state information is fed back to the transmitter in a causal manner a general cost function spl mu x is considered in solving the delay constrained transmission problem under the short term and the long term power constraints a causal power adaptation strategy is needed to maximize the cost function hence dynamic programming is found to give the optimum solution the general cost function is then specialized to the cases of expected and outage capacities in the case of expected capacity it is observed that optimizing the transmitted power does not give much benefit at high signal to noise ratio snr but provides a substantial gain at low snr at low snr it is proved that the capacity increases by a factor of approximately log k m due to power adaptation when the channel fades according to the spl chi sub 2m sup 2 statistics in the case of outage capacity it is shown that the optimum power adaptation solution to the long term constraint problem provides a substantial snr gain at both low and high values of snr random coding bounds are derived for the outage capacity algorithms

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

a direct approach to compensator design for distributed parameter systems we present a direct approach to finite order compensator design for distributed parameter systems i e one that is not based on reduced order modelling instead we use a parametrization around an initial compensator which displays both controller order and closed loop stability in a convenient way the main result is an existence theorem which holds for a wide class of linear time invariant systems parabolic delay damped hyperbolic the most important assumptions are bounded inputs and outputs finitely many unstable modes completeness of eigenvectors an example is included to illustrate the feasibility of our method for purposes of design

finite dimensional regulators for a class of regular hyperbolic pde systems abstractin this paper the output regulation problem is addressed for a class of linear hyperbolic infinite dimensional systems with spatially varying coefficients modelling a large class of convection dominated transport reaction systems in particular distributed parameter systems with bounded input and unbounded output operators are considered first we demonstrate a general conclusion about the exponential stability of the considered system by relating the stability to the solution of an associated differential equation based on the assumption that the hyperbolic system satisfies the exponential stability conditions the main manuscript contribution is the development of two novel finite dimensional regulators output and error feedback regulators such that the controlled output of the plant tracks a reference signal generated by a known signal process exosystem in order to guarantee the feasibility of the proposed regulators the solvability of the corresponding sylvester equations is discusse

stabilization of linear distributed control systems with unbounded delay in this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space we characterize those systems that can be stabilized using a feedback control as consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control

spline smoothing in a partly linear model on donne des estimations qui minimisent la somme des sommes residuelles des carres et une penalite de difficulte

finite dimensional compensators for parabolic distributed systems with unbounded control and observation it is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback finite dimensional means here that the dynamics relating the input to the output is finite dimensional a constructive design algorithm is presented and several examples are considered

optimal signaling schemes and capacities of non coherent correlated miso channels under per antenna power constraints this paper investigates the optimal signaling schemes and capacities of non coherent correlated multiple input single output miso channels in fast rayleigh fading we consider both channels under per antenna power constraints as well as channels under joint per antenna and sum power constraints for per antenna power constraint channels we first establish the convex and compact properties of the feasible sets and demonstrate the existence of optimal input distribution and the uniqueness of optimal effective magnitude input distribution by exploiting the solutions of a quadratic optimization problem we show that the kuhn tucker condition on the optimal inputs can be simplified to a single dimension as a result we can apply the identity theorem to show the discrete and finite nature of the optimal effective magnitude distribution with a mass point located at the origin by using this distribution we then construct a finite and discrete optimal input vector distribution the use of this input allows us to determine the capacity gain of miso over siso via the phase solutions of a constrained quadratic optimization problem on a sphere which can be obtained using a proposed penalized optimization algorithm we also extend the results to miso channels subject to the joint per antenna and sum power constraints under this consideration it is shown that not all per antenna constraints are active while the finiteness and discreteness of the optimal effective magnitude and the optimal input vector distributions still hold the optimal phases and the optimal power allocation among the transmit antennas need to be determined simultaneously via a quadratic optimization problem under inequality constraints these solutions can finally be used to obtain the miso capacity gain

stabilization of time delay systems using finite dimensional compensators for linear time invariant systems with one or more noncommensurate time delays necessary and sufficient conditions are given for the existence of a finite dimensional stabilizing feedback compensator in particular it is shown that a stabilizable time delay system can always be stabilized using a finite dimensional compensator the problem of explicitly constructing finite dimensional stabilizing compensators is also considered

channels with block interference a new class of channel models with memory is presented in order to study various kinds of interference phenomena it is shown among other things that when all other parameters are held fixed channel capacity c is an em increasing function of the memory length while the cutoff rate r 0 generally is a em decreasing function calculations with various explicit coding schemes indicate that c is better than r 0 as a performance measure for these channel models as a partial resolution of this c versus r 0 paradox the conjecture is offered that r 0 is more properly a measure of coding delay rather than of coding complexity

fault detection for linear distributed parameter systems using finite dimensional functional observers abstractin this article finite dimensional residual generators are directly designed for riesz spectral systems with bounded input and output operators to detect faults this is achieved by using finite dimensional observers that can estimate linear functionals of the state without spillover these observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions then a finite dimensional residual generator is obtained by approximately decoupling the state from the residual that is generated by the observer states and the outputs it is shown that the resulting approximation error can be made small by increasing the observer order then fault detection with the finite dimensional residual generator can be assured by introducing a time varying threshold a faulty euler bernoulli beam with structural damping illustrates the proposed finite dimensional fault detection approach

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

on the design of finite dimensional stabilizing compensators for infinite dimensional feedback systems via semiinfinite optimization the computational stability criterion presented by e polak and t l wuu see ibid vol 34 p 196 200 feb 1989 is extended to a form that can be used in the design of finite dimensional stabilizing compensators for a class of feedback systems with infinite dimensional plants since in this case the characteristic function is not a polynomial there is no simple way to define a normalizing polynomial hence approximation theory has to be used the new stability test guarantees not only input output stability but also internal stability of the feedback system furthermore since the numerical implementation of the test does not depend on the use of a reduced plant model the test does not lead to spillover effects because the compensator is parametrized in the state space form the order of the compensator can be assigned by the designer

finite dimensional compensators for linear distributed control systems with delays in outputs abstract in this paper we are concerned with linear control systems of infinite dimension with delays in outputs an asymptotic compensator of finite order is proposed the compensator provides a control law that stabilizes a wide class of distributed systems moreover the compensator is invariant with respect to small bounded perturbations of the system parameters

the use of marginal likelihood for a diagnostic test for the goodness of fit of the simple linear regression model a novel test procedure is proposed to diagnose the goodness of fit of a simple regression model by applying a marginal likelihood under the assumption of smoothness of the alternative regression curve no specific form for the alternative regression function is assumed an advantage of the proposed test procedure is that it simultaneously provides an estimated regression curve spline some existing diagnostic procedures are explored in relation to the one proposed the procedure is applied to data of a spectrophotometric analysis of mixtures of two types of flour cornstarch and casein soybean

some algebraic aspects of the strong stabilizability of time delay linear systems this note considers some algebraic aspects of the output feedback strong stabilizability of time delay linear systems a sufficient condition for the existence of a stable finite dimensional stabilizing compensator for a single input single output siso time delay system is given an illustrative example is also given and two open problems are posed

bounds on packings of spheres in the grassmann manifold we derive the gilbert varshamov and hamming bounds for packings of spheres codes in the grassmann manifolds over r and c asymptotic expressions are obtained for the geodesic metric and projection frobenius chordal metric on the manifold

space time autocoding prior treatments of space time communications in rayleigh flat fading generally assume that channel coding covers either one fading interval in which case there is a nonzero outage capacity or multiple fading intervals in which case there is a nonzero shannon capacity however we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable in short space time signals are their own channel codes we call this phenomenon space time autocoding and the accompanying capacity the space time autocapacity let an m transmitter antenna n receiver antenna rayleigh flat fading channel be characterized by an m spl times n matrix of independent propagation coefficients distributed as zero mean unit variance complex gaussian random variables this propagation matrix is unknown to the transmitter it remains constant during a t symbol coherence interval and there is a fixed total transmit power let the coherence interval and number of transmitter antennas be related as t spl beta m for some constant spl beta a t spl times m matrix valued signal associated with r spl middot t bits of information for some rate r is transmitted during the t symbol coherence interval then there is a positive space time autocapacity c sub a such that for all r c sub a the block probability of error goes to zero as the pair t m spl rarr spl infin such that t m spl beta the autocoding effect occurs whether or not the propagation matrix is known to the receiver and c sub a nlog 1 spl rho in either case independently of spl beta where spl rho is the expected signal to noise ratio snr at each receiver antenna lower bounds on the cutoff rate derived from random unitary space time signals suggest that the autocoding effect manifests itself for relatively small values of t and m for example within a single coherence interval of duration t 16 for m 7 transmitter antennas and n 4 receiver antennas and an 18 db expected snr a total of 80 bits corresponding to rate r 5 can theoretically be transmitted with a block probability of error less than 10 sup 9 all without any training or knowledge of the propagation matrix

inference in semiparametric dynamic models for binary longitudinal data this article deals with the analysis of a hierarchical semiparametric model for dynamic binary longitudinal responses the main complicating components of the model are an unknown covariate function and serial correlation in the errors existing estimation methods for models with these features are of o n3 where n is the total number of observations in the sample therefore nonparametric estimation is largely infeasible when the sample size is large as in typical in the longitudinal setting here we propose a new o n markov chain monte carlo based algorithm for estimation of the nonparametric function when the errors are correlated thus contributing to the growing literature on semiparametric and nonparametric mixed effects models for binary data in addition we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications the performance of the methods is illustrated with detailed studies involving simul

spectral factorization by symmetric extraction for distributed parameter systems the spectral factorization problem of a scalar coercive spectral density is considered in the framework of the callier desoer algebra of distributed parameter system transfer functions criteria are given for the infinite product representation of a meromorphic coercive spectral density of finite order and for the convergence of infinite product representations of spectral factors i e for the convergence of the symmetric extraction method for solving the spectral factorization problem of such spectral density these convergence criteria are applied to the solution of the linear quadratic optimal control problem by spectral factorization for a specific class of semigroup hilbert state space systems with a riesz spectral generator the speed of convergence of the symmetric extraction method is also considered as an example a damped vibrating string model is handled

an approximate predictor approach to reduced order models and controllers for distributed parameter systems two reduced order digital controllers for distributed parameter systems dps are described reduced order models approximate the optimal finite past predictor and error covariance for the full system to minimize an approximation to the kullback leibler information distance klid an lqg controller based on a reduced order system model is described a reduced order controller is found to minimize the klid between the closed loop system outputs with the full and reduced order controllers noncollocated control of a flexible beam is simulated

correction to bounds on packings of spheres in the grassmann manifold in the above titled paper ibid vol 48 no 9 pp 2450 2454 sep 02 corrections were made to haar measurements in various equations

model reference adaptive control for spectral systems in this paper we investigate a model reference adaptive control problem for the class of distributed parameter systems generated by spectral operators first we present an equivalent static input output representation for the spectral system using filtered values generated from the inputs and the outputs next we design and analyse a model reference adaptive control system for systems with unknown input and output distribution functions

a note on smoothness priors and nonlinear regression abstract a generalization of a nonparametric estimator proposed by shiller 1984 is considered the estimator is shown to be directly related to penalized least squares estimation and spline smoothing some simplifications concerning the computation of shiller s estimator and corresponding posterior covariances are indicated

stabilization problem in hilbert spaces the stabilization problem for linear systems on hilbert spaces is examined necessary and sufficient conditions for the state stabilization by a linear bounded feedback are given using these results and similar methods necessary and sufficient conditions for output stabilization are given

finite dimensional regulators for a class of infinite dimensional systems abstract we show that the direct approach developed by the author for stabilization of certain classes of distributed parameter systems can be extended to cover regulation problems as well an iterative design algorithm is presented together with proof that the algorithm will converge after a finite number of steps the procedure is illustrated with an example of a constant disturbance acting on a delay system

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

further results on noncoherent block coded mpsk transactions papers a novel noncoherent block coding scheme called noncoherent block coded mpsk nbc mpsk was proposed recently in this paper we present further research results on nbc mpsk we first focus on the rotational invariance ri of nbc mpsk based on the ri property of nbc mpsk with multistage decoding a noncoherent near optimal linear complexity multistage decoder for nbc mpsk is proposed then we investigate a tree search ml decoding algorithm for nbcmpsk the derived algorithm is shown to have low complexity and excellent error performance in this paper we also utilize the idea of the nbc mpsk to design noncoherent space time block codes called noncoherent space time block coded mpsk nstbc mpsk for two transmit antennas we propose a signal set with set partitioning and derive the minimum noncohent distance of nstbc mpsk with this signal set for the decoding of nstbc mpsk we modify the ml decoding algorithm of nbc mpsk and propose an iterative hard decision decoding algorithm compared with training codes and unitary space time modulation nbc mpsk and nstbc mpsk have larger minimum noncoherent distance and thus better error performance for the noncoherent ml decoder

superimposed training based noncoherent mimo systems the training based scheme constitutes an efficient method for noncoherent multiantenna communications in this paper we propose a superimposed training based linear dispersion stld transmission scheme where the transmitted symbols are superposition of the training pilots and the data symbols the stld system enjoys simple encoding and efficient suboptimal decoding since for noncoherent multiple input multiple output systems employing the stld scheme analytical expressions of block or bit error probabilities do not exist deterministic optimization methods cannot be used to design the optimal stld system we therefore propose to design the optimal stld systems using simulation based optimization techniques together with gradient estimation simulation results show that with either maximum likelihood or suboptimal decoding the stld systems obtained by the proposed design algorithm generally outperform the conventional training based scheme employing space time codes designed for coherent channels

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

an algorithmic test for checking stability of feedback spectral systems abstract given a certain class of regular spectral systems an algorithm is presented that is designed to test the stability properties of the feedback interconnection of such a system and either a bounded state feedback operator or a finite dimensional linear time invariant controller the applicability of this test is independent of the method used to design the feedback controller and is designed to provide a separate independent method for verifying whether or not the plant controller interconnection is exponentially stable the test is particularly well suited to problems involving certain partial differential equations pde with spatially varying coefficients or complicated boundary shapes

solving the linear quadratic optimal control problem for infinite dimensional systems abstract calculation of the solutions to linear quadratic optimal control problems for infinite dimensional systems is considered the sequence of solutions to a sequence of approximating finite dimensional problems converges to the optimal control for the infinite dimensional system if certain assumptions such as uniform stabilizability are satisfied we use this result to calculate controllers for the infinite dimensional system that are arbitrarily close to optimal a one dimensional heat equation and a problem of acoustic noise control are used to illustrate the algorithm the numerical results are discussed

stabilization of hereditary distributed parameter control systems abstract in this paper we study the asymptotic stabilization of semilinear distributed parameter control systems with delay assuming that the semigroup of operators associated with the uncontrolled and undelayed equation is compact we prove that a well known rank condition which implies the feedback stabilization for lumped systems can be extended to this type of systems

a broadcast approach for a single user slowly fading mimo channel a broadcast transmission strategy for the slowly fading gaussian multiple input multiple output mimo channel is introduced this broadcast strategy is an extension of the single input single output siso broadcast approach perfect channel state information csi is assumed known at the receiver end only this strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter transmission of layered coded information is motivated by the theory of majorization we derive the basic equations characterizing achievable rates of the strategy several ad hoc approximations to the achievable region are considered and their performance is compared with the siso setting and the ergodic capacity it has been demonstrated that a single layer outage approach is reasonably efficient in the mimo setting in terms of the average reliably decoded rate a multiple access channel mac broadcast approach is also applied for the mimo case and demonstrated to be relatively efficient

unitary space time modulation via cayley transform a prevoiusly proposed method for communicating with multiple antennas over block fading channels is unitary space time modulation ustm in this method the signals transmitted from the antennas viewed as a matrix with spatial and temporal dimensions form a unitary matrix i e one with orthonormal columns since channel knowledge is not required at the receiver ustm schemes are suitable for use on wireless links where channel tracking is undesirable or infeasible either because of rapid changes in the channel characteristics or because of limited system resources previous results have shown that if suitably designed ustm schemes can achieve full channel capacity at high snr and moreover that all this can be done over a single coherence interval provided the coherence interval and number of transmit antennas are sufficiently large which is a phenomenon referred to as autocoding while all this is well recognized what is not clear is how to generate good performing constellations of nonsquare unitary matrices that lend themselves to efficient encoding decoding the schemes proposed so far either exhibit poor performance especially at high rates or have no efficient decoding algorithms we propose to use the cayley transform to design ustm constellations this work can be viewed as a generalization to the nonsquare case of the cayley codes that have been proposed for differential ustm the codes are designed based on an information theoretic criterion and lend themselves to polynomial time often cubic near maximum likelihood decoding using a sphere decoding algorithm simulations suggest that the resulting codes allow for effective high rate data transmission in multiantenna communication systems without knowing the channel however our preliminary results do not show a substantial advantage over training based schemes

robustness of polynomial stability with respect to unbounded perturbations abstract in this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator in addition we also improve recent perturbation results for bounded finite rank perturbations the results are illustrated with two examples in the first one we consider the preservation of stability of a one dimensional wave equation that has been stabilized polynomially with boundary feedback in the second example we find conditions for the preservation of polynomial stability of a multiplication semigroup under unbounded rank one perturbations

unitary signal constellations for differential space time modulation with two transmit antennas parametric codes optimal designs and bounds we focus on the design of unitary signal constellations for differential space time modulation with double transmit antennas by using the parametric form of a two by two unitary matrix we present a class of unitary space time codes called parametric codes and show that this class of unitary space time codes leads to a five signal constellation with the largest possible diversity product and a 16 signal constellation with the largest known diversity product although the parametric code of size 16 is not a group by itself we show that it is a subset of a group of order 32 furthermore the unitary signal constellations of sizes 32 64 128 and 256 obtained by taking the subsets of the parametric codes of sizes 37 75 135 and 273 respectively have the largest known diversity products we also use large diversity sum of unitary space time signal constellations as another significant property for the signal constellations to have good performance in low snr scenarios the newly introduced unitary space time codes can lead to signal constellations with sizes of 5 and 9 through 16 that have the largest possible diversity sums subsequently we construct a few sporadic unitary signal constellations with the largest possible diversity product or diversity sum a four signal constellation which has both the largest possible diversity product and the largest possible diversity sum and three unitary signal constellations with the largest possible diversity sums for sizes of 6 7 and 8 are constructed respectively furthermore by making use of the existing results in sphere packing and spherical codes we provide several upper and lower bounds on the largest possible diversity product and the largest possible diversity sum that unitary signal constellations of any size can achieve

shrinking towards subspaces in multiple linear regression the problem of multiple linear regression and the use of shrinkage estimators is considered it is pointed out that sometimes prior beliefs about the signs and orders of magnitude of the regression coefftcients for example suggest a subspace l such that it is more natural to shrink the least squares estimate towards its projection onto l than towards the origin an empirical bayes approach is used to construct such an estimator for an arbitrary design matrix the estimator is illustrated on the acetylene data previously analyzed by marquardt and snee 1975

sphere packing bounds in the grassmann and stiefel manifolds applying the riemann geometric machinery of volume estimates in terms of curvature bounds for the minimal distance of packings codes in the grassmann and stiefel manifolds will be derived and analyzed in the context of space time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length this advocates large block lengths for the code design

output regulation problem for a class of regular hyperbolic systems this paper investigates the output regulation problem for a class of regular first order hyperbolic partial differential equation pde systems a state feedback and an error feedback regulator are considered to force the output of the hyperbolic pde plant to track a periodic reference trajectory generated by a neutrally stable exosystem a new explanation is given to extend the results in the literature to solve the regulation problem associated with the first order hyperbolic pde systems moreover in order to provide the closed loop stability condition for the solvability of the regulator problems the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper this paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator riccati equation

spectral determination for a cantilever beam the eigenvalue specification problem is discussed for a beam with one end clamped and the other end free which is allowed to have some structural damping and has a moment force at the free end acting as a control the spectrum and eigenvectors of the uncontrolled system are first analyzed and are then used to construct the feedback element which solves the problem it is shown how this feedback element can be numerically approximated and a spillover result is proved for the approximation in the case where there is no damping this method yields a bounded feedback law which exponentially stabilizes the beam

on the information throughput and optimized power allocation for mimo wireless systems with imperfect channel estimation in this paper we focus on the throughput analysis outage evaluation and optimized power allocation for multiple input multiple output mimo pilot based wireless systems subject to short term constraints on the radiated power and equipped with a feedback path for communicating back to the transmitter the imperfect mimo channel estimates available at the receiver the case of the ergodic throughput for gaussian distributed input signals is analyzed and the conditions for the asymptotical achievement of the shannon capacity are pointed out the main contributions of this work may be so summarized first we develop closed form analytical expressions for the computation of the ergodic information throughput conveyed by the considered mimo system for the case of ideal feedback link second we present an iterative algorithm for the optimized power allocation over the transmit antennas that explicitly accounts for the imperfect mimo channel estimates available at the receiver third after relaxing the assumption of ideal feedback link we test the sensitivity of the proposed power allocation algorithm on errors possibly introduced by the feedback channel and then we numerically evaluate the resulting throughput loss finally we develop closed form upper and lower bounds on the outage probability that are asymptotically tight

output and error feedback regulator designs for linear infinite dimensional systems abstract this manuscript addresses the output regulation problem for linear distributed parameter systems dpss with bounded input and unbounded output operators we introduce novel methods for the design of the output feedback and error feedback regulators in the output feedback regulator design the measurements available for the regulator do not belong to the set of controlled outputs the proposed output feedback regulator with the injection of the measurement y m t and reference y r t can realize both the plant and the exosystem states estimation disturbance rejection and reference signal tracking simultaneously moreover new design approach provides an alternative choice for seeking the output injection gain in a traditional error feedback regulator design the regulator parameters are easily configured to solve the output regulation problems and to ensure the stability of the closed loop systems the results are demonstrated via computer simulation in two types of representative systems the parabolic partial differential equation pde system and the first order hyperbolic pde system

legendre tau approximation for functional differential equations part ii the linear quadratic optimal control problem a numerical scheme based on the legendre tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems the convergence property is established using the trotter kato theorem the method yields very good approximations at low orders and provides an approximation technique for computing closed loop eigenvalues of the feedback system a comparison with existing methods based on averaging and spline approximations is made

stabilization of a coupled transport diffusion system with boundary input we consider the problem of stabilizing a coupled transport diffusion system with boundary input the system is described by two linear transport diffusion equations and is not asymptotically stable in order to stabilize the system with boundary input sensor influence functions are assumed to be located at interior of the domain first we formulate the system as an evolution equation with unbounded output operators in a hilbert space using variable transformation next we derive a reduced order model with a finite dimensional state variable for the infinite dimensional system then a stabilizing controller is constructed for the reduced order model under an additional assumption it is shown that the finite dimensional controller together with a residual mode filter plays a role of a finite dimensional stabilizing controller for the original infinite dimensional system if the order of the residual mode filter is chosen sufficiently large finally the validity of the design method is demonstrated through a numerical simulation