recursive estimators of signals from measurements with stochastic delays using covariance information least squares linear one stage prediction filtering and fixed point smoothing algorithms for signal estimation using measurements with stochastic delays contaminated by additive white noise are derived the delay is considered to be random and modelled by a binary white noise with values zero or one these values indicate that the measurements arrive in time or they are delayed by one sampling time recursive estimation algorithms are obtained without requiring the state space model generating the signal but just using covariance information about the signal and the additive noise in the observations as well as the delay probabilities

computer assisted bounds for the rate of decay of correlations the rate of decay of correlations quantitatively describes the rate at which a chaotic system mixes the state space we present a new rigorous method to estimate a bound for this rate of mixing the technique may be implemented on a computer and is applicable to both multidimensional expanding and hyperbolic systems the bounds produced are significantly less conservative than current rigorous bounds in some situations it is possible to approximate resonant eigenfunctions and to strengthen our bound to an estimate of the decay rate order of convergence results are stated

optimal recursive estimation for networked stochastic uncertain systems with fading measurements and time correlated channel noises abstract this paper is concerned with the optimal linear estimation problem for discrete time stochastic system with time correlated channel noises correlated multiplicative noises and fading measurements the time correlated channel noises are described by a seemingly arma autoregressive moving average model by an equivalent transformation the original system is transformed into the same dimension system with finite step correlated virtual noises and multiple measurement delays the statistical properties of correlation functions among noise state and measurement are analyzed further the optimal linear state estimators including filter predictor and smoother are derived by using an innovation analysis approach a simulation example shows the effectiveness of the proposed algorithms

linear estimation for networked control systems with random transmission delays and packet dropouts in networked control systems random delays and packet dropouts are inevitable during data transmissions due to the limited communication capacity the phenomena of random delays and packet dropouts of both sides from a sensor to an estimator and from a controller to an actuator are modeled via employing two groups of bernoulli random variables by defining some new variables the original system with random delays and packet dropouts is equivalently transformed into a stochastic parameterized system the optimal linear filter predictor and smoother in the linear minimum variance sense are presented via the orthogonality projection approach they depend on the probabilities of the stochastic parameters the solutions to the optimal linear estimators are given by three equations including a riccati a lyapunov and a simple difference the stability of the proposed estimators is analyzed at last a sufficient condition for the existence of the steady state estimators is given for time invariant systems two examples are provided to verify the effectiveness of the proposed algorithms

phase transition and correlation decay in coupled map lattices for a coupled map lattice with a specific strong coupling emulating stavskaya s probabilistic cellular automata we prove the existence of a phase transition using a peierls argument and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling this implies the exponential decay in space and in time of the correlation functions of the invariant measures

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

rigorous approximation of diffusion coefficients for expanding maps we use ulam s method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps an algorithm is provided and its implementation is illustrated using lanford s map

modeling and estimation for networked systems with multiple random transmission delays and packet losses abstract in networked systems data packets are transmitted through networks from a sensor to a data processing center due to the unreliability of communication channels a packet may be delayed even lost during the transmission at each moment the data processing center may receive one or multiple data packets or nothing at all a novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of bernoulli distributed random variables it is transformed to a measurement model with multiple random delayed states and noises based on the model an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate it does not have a steady state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment so it needs to be computed online to reduce the online computational cost a suboptimal linear filter dependent on the probabilities of random variables is also proposed however it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities it can be computed offline since it has the steady state performance a sufficient condition of existence for the steady state performance is given a simulation example shows the effectiveness

technical communique a kushner approach for small random perturbations of the duffing van der pol system the stochastic version of the duffing van der pol system sdvdp which assumes the structure of a non linear stochastic differential equation is an appealing and a standard case from the stochastic systems point of view since it involves linear and non linear vector fields i e system non linearities state independent and state dependent stochastic accelerations this paper discusses and explores the efficacy of three non linear filters which are developed using the kushner equation for the stochastic differential system of concern here this paper introduces the notion of a qualitative analysis to decide a structure of the observation equation for non linear stochastic filtering as well

sampled data fuzzy control for a class of nonlinear systems with missing data and disturbances this paper considers the sampled data fuzzy control of nonlinear systems in strict feedback form with disturbances and random missing input data we propose a novel method in which a state observer and a disturbance observer are combined to construct a sampled data fuzzy output feedback controller the stochastic variables with a bernoulli distributed sequence are used to model missing input data fuzzy logic systems are applied to approximate nonlinearities without requiring prior knowledge the relation between observer gain and sampling period is established the output feedback controller designed guarantees that the nonlinear system is globally stable a simulation example of four degrees of freedom robotic arm is used to demonstrate the effectiveness and applicability of the proposed control scheme

ergodic properties of invariant measures for piecewise monotonic transformations during the last decade a lot of research has been done on onedimensional dynamics different kinds of invariant measures for certain classes of piecewise monotonic transformations have been considered in most of these cases the perron frobenius operator plays an important role in this paper we try to unify these different examples which are discussed in detail below first we give a discription of the results proved in this paper

invariant densities and escape rates rigorous and computable approximations in the l norm abstract in this article we study piecewise linear discretization schemes for transfer operators perron frobenius operators associated with interval maps we show how these can be used to provide rigorous pointwise approximations for invariant densities of markov interval maps we also derive the order of convergence of the approximate invariant density to the real one in the l norm the outcome of this paper complements recent results on the formulae of escape rates of open dynamical systems keller and liverani 2009 7 in particular the novelty of our work over previous results on b v and l approximations is that it provides a method for explicit computation of the approximation error

harmonic averages and new explicit constants for invariant densities of piecewise expanding maps of the interval the statistical behavior of families of maps is important in studying the stability properties of chaotic maps for a piecewise expanding map whose slope 2 in magnitude much is known about the stability of the associated invariant density however when the map has slope magnitude 2 many different behaviors can occur as shown in keller in monatsh math 94 4 313 333 1982 for w maps the main results of this note use a harmonic average of slopes condition to obtain new explicit constants for the upper and lower bounds of the invariant probability density function associated with the map as well as a bound for the speed of convergence to the density since these constants are determined explicitly the results can be extended to families of approximating maps

zeta functions and transfer operators for piecewise monotone transformations given a piecewise monotone transformationt of the interval and a piecewise continuous complex weight functiong of bounded variation we prove that the ruelle zeta function z of t g extends meromorphically to z 1 where lim g tn 1 g tg 1 n and thatz is a pole of if and only ifz 1 is an eigenvalue of the corresponding transfer operator l we do not assume that l leaves a reference measure invariant

linear estimation for measurement delay systems with periodic coefficients and multiplicative noise this technical note is concerned with the remote estimation problem for measurement delay systems with multiplicative noise and periodic coefficients the multiplicative noise in every communication channel is described by an independent and identically distributed i i d bernoulli process the quality of the estimation achieved by an admissible filter is measured by a performance criterion described by the cesaro limit of the mean square of the deviation between the remote signal and the estimated signal the filter is designed in terms of the unique periodic solution of a lyapunov equation together with the periodic stabilizing solution of a riccati equation in the end we supply a numerical example to show the effectiveness of our proposed estimation approach

linear optimal estimation for discrete time systems with measurement delay and packet dropping this paper is concerned with the remote estimation problem for measurement delay system over a packet dropping network the packet dropping phenomenon in every communication channel is described by an independent and identically distributed bernoulli process an optimal linear filter is provided in the linear minimum mean square error sense by applying the reorganized innovation analysis approach the solution to the filter is given in terms of two riccati difference equations and one lyapunov difference equation further the infinite horizon filter is investigated under the condition of system stability in the end we supply a numerical example to show the effectiveness of our proposed estimation approach

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

decay of correlations for piecewise expanding maps this paper investigates the decay of correlations in a large class of non markov one dimensional expanding maps the method employed is a special version of a general approach recently proposed by the author explicit bounds on the rate of decay of correlations are obtained

linear estimation for random delay systems this paper is concerned with the linear estimation problems for discrete time systems with random delayed observations when the random delay is known online i e time stamped the random delayed system is reconstructed as an equivalent delay free one by using measurement reorganization technique and then an optimal linear filter is presented based on the kalman filtering technique however the optimal filter is time varying stochastic and does not converge to a steady state in general then an alternative suboptimal filter with deterministic gains is developed under a new criteria the estimator performance in terms of their error covariances is provided and its mean square stability is established finally a numerical example is presented to illustrate the efficiency of proposed estimators

mmse state estimation approach for linear discrete time systems with time delay and multi error measurements this technical note focuses on designing a novel optimal estimation approach for linear discrete time systems with time delay and multi error measurements inspired by the measurement demands of the five hundred meter aperture spherical radio telescope measurement errors from different measurement channels which are considered equal in many previous estimation methods are usually negatively correlated with time delays measurements with higher time delays usually have less errors than the ones with lower delays our approach improves the estimation accuracy by decreasing the usage rate of measurements with larger errors to prove the optimality of the approach in the minimum mean square error sense a derivation procedure is presented a numerical example and comparison are also given to demonstrate the feasibility and advantage of the proposed approach

iterates of expanding maps the iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic process when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random in this paper we show that the sequence of iterates can be closely tied to an m dependent process this enables us to prove good bounds on the accuracy of gaussian approximations our main tools are coupling and stein s method

optimal filtering with random sensor delay multiple packet dropout and uncertain observations this paper studies the problem of optimal filtering of discrete time systems with random sensor delay multiple packet dropout and uncertain observation the random sensor delay multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation a new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data based on a stochastic definition of the norm of a system with a stochastic parameter new relations for stochastic norm are derived the stochastic norm of the estimation error is used as a criterion for the filter design the relations derived for the new norm definition are used to obtain a set of linear matrix inequalities lmis to solve the filter design problems simulation examples show the effectiveness of the proposed method

decay of correlations for certain quadratic maps we prove exponential decay of correlations for f wheref belongs in a positive measure set of quadratic maps of the interval and is its absolutely continuous invariant measure these results generalize to other interval maps

optimal full order and reduced order estimators for discrete time systems with multiple packet dropouts this paper is concerned with the estimation problem for discrete time stochastic linear systems with multiple packet dropouts based on a recently developed model for multiple packet dropouts the original system is transferred to a stochastic parameter system by augmentation of the state and measurement the optimal full order linear filter of the form of employing the received outputs at the current and last time instants is investigated the solution to the optimal linear filter is given in terms of a riccati difference equation governed by packet arrival rate the optimal filter is reduced to the standard kalman filter when there are no packet dropouts the steady state filter is also studied a sufficient condition for the existence of the steady state filter is given and the asymptotic stability of the optimal filter is analyzed at last a reduced order filter is investigated

produits aleatoires d operateurs matrices de transfert nous etudions le comportement asymptotique de produits aleatoires d operateurs de ruelle perron frobenius nous etendons le travail de ruelle obtenu dans le cas homogene au cas aleatoire

almost sure invariance principle for sequential and non stationary dynamical systems we establish almost sure invariance principles a strong form of approximation by brownian motion for non stationary time series arising as observations on dynamical systems our examples include observations on sequential expanding maps perturbed dynamical systems non stationary sequences of functions on hyperbolic systems as well as applications to the shrinking target problem in expanding systems

quadratic estimation problem in discrete time stochastic systems with random parameter matrices this paper addresses the least squares quadratic filtering problem in discrete time stochastic systems with random parameter matrices in both the state and measurement equations defining a suitable augmented system this problem is reduced to the least squares linear filtering problem of the augmented state based on the augmented observations under the assumption that the moments up to the fourth order one of the original state and measurement vectors are known a recursive algorithm for the optimal linear filter of the augmented state is designed from which the optimal quadratic filter of the original state is obtained as a particular case the proposed results are applied to multi sensor systems with state dependent multiplicative noise and fading measurements and finally a numerical simulation example illustrates the performance of the proposed quadratic filter in comparison with the linear one and also with other filters in the existing literature

state estimators for systems with random parameter matrices stochastic nonlinearities fading measurements and correlated noises using the innovation analysis approach the optimal linear state estimators including the filter predictor and smoother in the linear minimum variance lmv sense are presented for a class of nonlinear discrete time stochastic uncertain systems with fading measurements and correlated noises stochastic uncertainties of parameter matrices are depicted by correlated multiplicative noises stochastic nonlinearities are characterized by a known conditional mean and covariance different sensor channels have different fading measurement rates the process and measurement noises are finite step auto and or cross correlated with each other two simulation examples verify the effectiveness of the proposed algorithms

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

a new suboptimal approach to the filtering problem for bilinear stochastic differential systems the aim of this paper is to present a new approach to the filtering problem for the class of bilinear stochastic multivariable systems consisting in searching for suboptimal state estimates instead of the conditional statistics as a first result a finite dimensional optimal linear filter for the considered class of systems is defined then the more general problem of designing polynomial finite dimensional filters is considered the equations of a finite dimensional filter are given producing a state estimate which is optimal in a class of polynomial transformations of the measurements with arbitrarily fixed degree numerical simulations show the effectiveness of the proposed filter

optimal linear filters for discrete time systems with randomly delayed and lost measurements with without time stamps a novel model is developed to describe possible random delays and losses of measurements transmitted from a sensor to a filter by a group of bernoulli distributed random variables based on the new developed model an optimal linear filter dependent on the probabilities is presented in the linear minimum variance sense by the innovation analysis approach when packets are not time stamped the solution to the optimal linear filter is given in terms of a riccati difference equation and a lyapunov difference equation a sufficient condition for the existence of the steady state filter is given at last the optimal filter is given by kalman filter when packets are time stamped

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

a strong pair correlation bound implies the clt for sinai billiards we investigate the possibility of proving the central limit theorem clt for dynamical systems using only information on pair correlations a strong bound on multiple correlations is known to imply the clt chernov and markarian in chaotic billiards 2006 in chernov s paper j stat phys 122 6 2006 such a bound is derived for dynamically holder continuous observables of dispersing billiards here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations thus a strong bound on pair correlations alone implies the clt for a wider class of observables the result is extended to anosov diffeomorphisms in any dimension some non invertible maps are also considered

lyapunov exponents for small random perturbations of hamiltonian systems consider the stochastic nonlinear oscillator equation ddot x x x 3 varepsilon 2 beta dot x varepsilon sigma x dot w t with beta 0 and sigma neq 0 if 4 beta sigma 2 0 then for small enough varepsilon 0 the system x dot x is positive recurrent in bf r 2 setminus 0 0 now let overline lambda varepsilon denote the top lyapunov exponent for the linearization of this equation along trajectories the main result asserts that overline lambda varepsilon varepsilon 2 3 overline lambda o varepsilon 4 3 qquad mbox as varepsilon to 0 with overline lambda 0 this result depends crucially on the fact that the system above is a small perturbation of a hamiltonian system the method of proof can be applied to a more general class of small perturbations of two dimensional hamiltonian systems the techniques used include i an extension of results of pinsky and wihstutz for perturbations of nilpotent linear systems and ii a stochastic averaging argument involving

h sub spl infin control for networked systems with random communication delays this note is concerned with a new controller design problem for networked systems with random communication delays two kinds of random delays are simultaneously considered i from the controller to the plant and ii from the sensor to the controller via a limited bandwidth communication channel the random delays are modeled as a linear function of the stochastic variable satisfying bernoulli random binary distribution the observer based controller is designed to exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed h sub spl infin disturbance attenuation level the addressed controller design problem is transformed to an auxiliary convex optimization problem which can be solved by a linear matrix inequality lmi approach an illustrative example is provided to show the applicability of the proposed method

filtering for a duffing van der pol stochastic differential equation the stochastic duffing van der pol sdvdp system is a non trivial case in stochastic system theory since it involves linear non linear vector fields and state dependent stochastic accelerations notably analyzing specific and non trivial cases brings greater theoretical insights as well as reveals joining points between different topics in the theory of stochastic differential systems the filtered estimates are more accurate in contrast to the predicted since the observation correction terms associated with the filtering equations contribute to the effectiveness of the estimation procedure thus it becomes reasonable to analyze the stochastic duffing van der pol system from the filtering viewpoint in this paper we wish to revisit the stochastic duffing van der pol filtering in the fokker planck setting in lieu of the filtering in the kushner setting in the fokker planck setting observations are accounted at discrete time instants as a result of this we arrive at continuous discrete filtering equations the duffing van der pol filtering equations of this paper can be regarded as a consequence of the two stage estimation procedure since this paper utilizes stochastic differential equation formalism for the stochastic system of this paper on the other hand a discrete time stochastic evolution of the observation is accounted for in this study notably filtering equations of the paper explain explicit contributions of the predicted estimate and the observation noise to the filtered estimate as a result of this the filtering approach of this paper offers greater convenience for examining the filtering efficacy via simulations for specific cases the filtering theory of this paper will be of interest to applied mathematicians control theorists aspiring for understanding the continuous discrete filtering better especially for stochastic problems arising from technology where observation rates are less

brief paper optimal linear estimation for systems with multiple packet dropouts this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with multiple packet dropouts based on a packet dropout model the optimal linear estimators including filter predictor and smoother are developed via an innovation analysis approach the estimators are computed recursively in terms of the solution of a riccati difference equation of dimension equal to the order of the system state plus that of the measurement output the steady state estimators are also investigated a sufficient condition for the convergence of the optimal linear estimators is given simulation results show the effectiveness of the proposed optimal linear estimators

decay of correlations dedicated to micheline ishay i would like to thank p boyland l chierchia v donnay g de martino c gole j l lebowitz m lyubich m rychlik i g schwarz s vaienti and especially g gallavotti for helpful and enlightening discussions particularly warm thanks go to n chernov for carefully reading and finding a mistake in an early version the present paper benefits from several improvements due to his sharp criticism in addition i am indebted to p collet and most of all m wojtkowski for introducing me to the magical world of cones finally i thank j milnor director of the institute for mathematical sciences at stony brook university where i was visiting during part of this work and the italian c n r gnfm for providing travel funds

rls wiener estimators from observations with multiple and random delays in linear discrete time stochastic systems this paper designs a new recursive least squares rls wiener fixed point smoother and filter from randomly delayed observed values by multiple sampling times in linear discrete time stochastic systems the actual observed value is generated in terms of the observed values email protected k j 1 with the probability p j k 1

nonlinear weighted measurement fusion unscented kalman filter with asymptotic optimality for the general nonlinear systems a universal weighted measurement fusion wmf algorithm is presented via the taylor series expansion method based on the proposed fusion algorithm and the well known unscented kalman filter ukf the wmf ukf is presented it is proven that the proposed wmf ukf asymptotically approaches to the centralized measurement fusion ukf cmf ukf with the increase of the order of taylor series expansion so it has the asymptotical global optimality we find that wmf ukf has less computational cost than the cmf ukf does with the increase of the number of sensors two examples are given to show the effectiveness of the proposed algorithms

regularity of the metric entropy for expanding maps the main result of the current paper is an estimate of the radius of the nonperipheral part of the spectrum of the perron frobenius operator for expanding mappings as a consequence we are able to show that the metric entropy of an expanding map has modulus of continuity x log 1 x on the space of c2 expandings we also give an explicit estimate of the rate of mixing for cl functions in terms of natural constants it seems that the method we present can be generalized to other classes of dynamical systems which have a distinguished invariant measure like axiom a diffeomorphisms it also can be adopted to show that the entropy of the quadratic family f x 1 ux2 computed with respect to the absolutely continuous invariant measure found in jakobson s theorem varies continuously the last result is going to appear somewhere else

chains of infinite order chains with memory of variable length and maps of the interval we show how to construct a topological markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order in particular we characterize the maps corresponding to stochastic chains with memory of variable length the problem treated here is the converse of the classical construction of the gibbs formalism for markov expanding maps of the interval