fake algebraic riccati techniques and stability conditions sufficient and necessary for monotonic behavior of the solutions of the riccati differential equation and riccati difference equation are derived for the optimal filtering respectively control equation these results are derived without the usual requirement of detectability respectively stabilizability the monotonic behavior allows proof of stabilizing properties of the solutions subject only to requirements on the initial conditions

optimal control over multiple erasure channels using a data dropout compensation scheme in this paper we focus on networked control systems subject to data dropouts we consider that the controller communicates with the plant through multiple independent erasure channels and that each actuator sends acknowledgement packages to the controller we restrict our attention to the optimal design of a class of controllers that embeds a data dropout compensator and where besides this compensation mechanism all processing is an affine function of the available data our first result shows that the optimal design consists in solving separately an estimation problem and a control problem the optimal controller is a linear function of the estimated state which is obtained exploiting the information given by the acknowledgement packages and the data dropout compensator since we focus on a specific class of controllers our proposal is suboptimal however unlike the optimal lqg controller found in the literature our proposal is easier to implement and its steady state behaviour can be simply determined we also show that under standard conditions the affine part of the optimal controller converges to an lti filter which can be used as a simple alternative to the time varying controller

kuhn tucker based stability conditions for systems with saturation this paper presents a new approach to deriving stability conditions for continuous time linear systems interconnected with a saturation the method presented can be extended to handle a dead zone or in general nonlinearities in the form of piecewise linear functions by representing the saturation as a constrained optimization problem the necessary kuhn tucker conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation after selecting a candidate lyapunov function we pose the question of whether the lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization and the time derivative of the lyapunov function this leads to stability conditions in terms of linear matrix inequalities which are obtained by an application of the s procedure to the implication an example is provided where the proposed technique is compared and contrasted with previous analysis methods

asymptotic stability of the mmse linear filter for systems with uncertain observations corresp sufficient conditions for uniform asymptotic stability in the large of the optimal minimum mean square error mmse linear filter are developed for discrete linear systems whose observations may contain noise alone and where only the probability of occurrence of such cases is known to the estimator conditions for existence uniqueness and stability of the steady state optimal filter are also considered for the case when the system is time invariant

gain constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays this paper is concerned with the gain constrained recursive filtering problem for a class of time varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises the stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case the phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of bernoulli distributed random variables taking values of 1 or 0 which means that the sensors may experience randomly occurring delays with individual delay characteristics the process noise is finite step autocorrelated the purpose of the addressed gain constrained filtering problem is to design a filter such that for all probabilistic sensor delays stochastic nonlinearities gain constraint as well as correlated noises the cost function concerning the filtering error is minimized at each sampling instant where the filter gain satisfies a certain equality constraint a new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre specified filter gain constraint a simulation example is provided to illustrate the effectiveness of the proposed filter design approach

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

an algorithm for the computation of eigenvalues spectral zeta functions and zeta determinants on hyperbolic surfaces we present a rigorous scheme that makes it possible to compute eigenvalues of the laplace operator on hyperbolic surfaces within a given precision the method is based on an adaptation of the method of particular solutions to the case of locally symmetric spaces and on explicit estimates for the approximation of eigenfunctions on hyperbolic surfaces by certain basis functions it can be applied to check whether or not there is an eigenvalue in an e neighborhood of a given number 0 this makes it possible to find all the eigenvalues in a specified interval up to a given precision with rigorous error estimates the method converges exponentially fast with the number of basis functions used combining the knowledge of the eigenvalues with the selberg trace formula we are able to compute values and derivatives of the spectral zeta function again with error bounds as an example we calculate the spectral determinant and the casimir energy of the bolza surface and other surfaces

robust h finite horizon filtering with randomly occurred nonlinearities and quantization effects in this paper the robust h finite horizon filtering problem is investigated for discrete time varying stochastic systems with polytopic uncertainties randomly occurred nonlinearities as well as quantization effects the randomly occurred nonlinearity which describes the phenomena of a nonlinear disturbance appearing in a random way is modeled by a bernoulli distributed white sequence with a known conditional probability a new robust h filtering technique is developed for the addressed ito type discrete time varying stochastic systems such a technique relies on the forward solution to a set of recursive linear matrix inequalities and is therefore suitable for on line computation it is worth mentioning that in the filtering process the information of both the current measurement and the previous state estimate is employed to estimate the current state finally a simulation example is exploited to show the effectiveness of the method proposed in this paper

an alternative look at the constant gain kalman filter for state estimation over erasure channels this technical note studies state estimation problems subject to data loss we consider a class of switched estimators where missing data is replaced by optimal estimates the considered class of estimators encompasses a number of estimation schemes proposed in the literature we show that the estimator that minimizes the steady state estimation error covariance within that class is given by a constant gain kalman filter which was previously proposed as an alternative to the kalman filter with intermittent observations as a by product of our results we derive expressions that allow one to compare analytically popular suboptimal data dropout compensation mechanisms

robust control strategies for multi inventory systems with average flow constraints in this paper we consider multi inventory systems in the presence of uncertain demand we assume that i demand is unknown but bounded in an assigned compact set and ii the control inputs controlled flows are subject to assigned constraints given a long term average demand we select a nominal flow that feeds such a demand in this context we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average we provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows such conditions are based on linear programming and thus they are constructive in the special case of a static flow i e a system with 0 capacity buffers we show that the strategy must be affine the dynamic problem can be solved by a linear saturated control strategy inspired by the previous one we provide numerical analysis and illustrative examples

lmi approach to state feedback stabilization of multidimensional systems an lmi approach to design an appropriate state feedback controller for linear multidimensional discrete systems in roesser s state space model structure is described a numerical example is employed to illustrate the results developed in the paper and the numerical advantages of using lmi techniques

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

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

a network design problem for a distribution system with uncertain demands a class of production distribution planning problems with nonstochastic uncertain demands is modeled as a dynamic game between two players who control flows on a network with node and arc capacity constraints simple conditions are derived for determining which player wins the game these conditions are then used to design a minimum cost network with the property that its feasible control strategies are allowed to meet the demand without violating the capacity constraints

local stabilization of linear systems under amplitude and rate saturating actuators this note addresses the problem of local stabilization of linear systems subject to control amplitude and rate saturation considering the actuator represented by a first order system subject to input and state saturation a condition for the stabilization of an a priori given set of admissible initial states is formulated from certain saturation nonlinearities representation and quadratic stability results from this condition an algorithm based on the iterative solution of linear matrix inequalities based problems is proposed in order to compute the control law

calculation of spectral determinants a method for regularizing spectral determinants is developed which facilitates their computation from a finite number of eigenvalues this is used to calcu late the determinant for the hyperbola billiard over a range which includes 46 quantum energy levels the result is compared with semiclassical periodic orbit evaluations of using the dirichlet series euler product and a riemann siegel type formula it is found that the riemann siegel type expansion which uses the least number of orbits gives the closest approximation this provides explicit numerical support for recent conjectures concerning the analytic proper ties of semiclassical formulae and in particular for the existence of resummation relations connecting long and short pseudo orbits

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

anti windup design with guaranteed regions of stability for discrete time linear systems abstract the purpose of this paper is to study the determination of stability regions for discrete time linear systems with saturating controls through anti windup schemes considering that a linear dynamic output feedback has been designed to stabilize the linear discrete time system without saturation a method is proposed for designing an anti windup gain that maximizes an estimate of the basin of attraction of the closed loop system in the presence of saturation it is shown that the closed loop system obtained from the controller plus the anti windup gain can be locally modeled by a linear system with a deadzone nonlinearity then based on the use of a new sector condition and quadratic lyapunov functions stability conditions in an lmi form are stated these conditions are then considered in a convex optimization problem in order to compute an anti windup gain that maximizes an estimate of the basin of attraction of the closed loop system moreover considering asymptotically stable open loop systems it is shown that the conditions can be slightly modified in order to determine an anti windup gain that ensures global stability an extension of the proposed results to the case of dynamic anti windup synthesis is also presented in the paper

variance constrained cal h _ infty filtering for a class of nonlinear time varying systems with multiple missing measurements the finite horizon case this paper is concerned with the robust h finite horizon filtering problem for a class of uncertain nonlinear discrete time varying stochastic systems with multiple missing measurements and error variance constraints all the system parameters are time varying and the uncertainty enters into the state matrix the measurement missing phenomenon occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval the stochastic nonlinearities under consideration here are described by statistical means which can cover several classes of well studied nonlinearities sufficient conditions are derived for a finite horizon filter to satisfy both the estimation error variance constraints and the prescribed h performance requirement these conditions are expressed in terms of the feasibility of a series of recursive linear matrix inequalities rlmis simulation results demonstrate the effectiveness of the developed filter design scheme

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

uncertain convex programs randomized solutions and confidence levels many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or instance parameter two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty robust optimization and chance constrained optimization robust optimization is a deterministic paradigm where one seeks a solution which simultaneously satisfies all possible constraint instances in chance constrained optimization a probability distribution is instead assumed on the uncertain parameters and the constraints are enforced up to a pre specified level of probability unfortunately however both approaches lead to computationally intractable problem formulations

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

optimal linear estimators for systems with random sensor delays multiple packet dropouts and uncertain observations this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with random sensor delays packet dropouts and uncertain observations we develop a unified model to describe the mixed uncertainties of random delays packet dropouts and uncertain observations by three bernoulli distributed random variables with known distributions based on the proposed model the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach their solutions are given in terms of a riccati equation and a lyapunov equation they can deal with the optimal linear filtering prediction and smoothing for systems with random sensor delays packet dropouts and uncertain observations in a unified framework simulation results show the effectiveness of the proposed optimal linear estimators

an antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation the article considers linear systems subject to actuator saturation an antiwindup technique is used to enlarge the domain of attraction of the closed loop system under an a priori designed linear dynamic feedback law the design of the antiwindup compensation gain is formulated and solved as an iterative optimization problem with lmi constraints numerical examples are used to demonstrate the effectiveness of the proposed design technique

optimal linear estimation with square based sampling this paper is concerned with the problem of event based sampling for the purpose of reducing the number of data transferred in control systems and the corresponding modified kalman filter a mathematical description based upon square based sampling is proposed in which the sampling occured when the accumulated difference between two adjacent sampling points satisfies the specified event condition then by utilizing the square based sampling method a modified kalman filter algorithm is adopted in which the measurement is sent when the output exceeds a given event the simulation results illustrate the advantage of the new event based sampling scheme and the effectiveness of modified kalman filter

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

mean square stability of difference equations with a stochastic delay the paper describes mean square stability conditions for nonlinear delay difference equations with a stochastic delay the first part develops a formula for the infinitesimal operator using this formula asymptotic mean square stability conditions are derived a final example is provided

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

attainability in repeated games with vector payoffs we introduce the concept of attainable sets of payoffs in two player repeated games with vector payoffs a set of payoff vectors is called attainable by a player if there is a positive integer such that the player can guarantee that in all finite game longer than that integer the distance between the set and the cumulative payoff is arbitrarily small regardless of the strategy player 2 is using we provide a necessary and sufficient condition for the attainability of a convex set using the concept of b sets we then particularize the condition to the case in which the set is a singleton and provide some equivalent conditions we finally characterize when all vectors are attainable

periodic orbit resummation and the quantization of chaos we study the spectral determinant e which has by construction zeros at the quantum energy levels of a given system if the classical motion of the system in question is chaotic then e has a semiclassical representation as a sum over combinations of periodic orbits there are however a number of fundamental problems associated with its convergence properties imposing upon the sum the condition that like e itself it is real for real e we obtain formal resummation equations relating the contributions from asymptotically long orbits to those of the short orbits these then lead to a formal derivation of the previously conjectured riemann siegel lookalike formula which involves only a finite orbit sum and thus represents in principle a semiclassical rule for quantizing chaos

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

periodic orbit sum rules for the hadamard gutzwiller model abstract it is shown how a variety of periodic orbit sum rules can be used to extract information about a quantum mechanical system whose classical counterpart is completely chaotic from knowledge only of the classical system and vice versa the basis is the selberg trace formula an exact analogue for the hadamard gutzwiller model of the semiclassical periodic orbit theory of gutzwiller which relates the quantal energies to the lengths of the periodic orbits of the classical system statistical properties of the quantal energies in the low energy region are studied where we restrict ourselves to the level spacing and spectral rigidity

recursive filtering for discrete time linear systems with fading measurement and time correlated channel noise this paper is concerned with the recursive filtering problem for discrete time linear systems with fading measurement and time correlated channel noise the phenomenon of measurement fading appears in a random way and the fading phenomenon for each sensor is described by an individual random variable taking a value in a given interval the time correlated channel noise is depicted as a linear system model with white noise using the measurement differencing method and some results obtained in this paper a recursive filtering algorithm for the system under consideration is proposed the proposed algorithm is optimal in the sense of linear minimum mean square error and does not increase computation and storage load with time computer simulations are carried out to evaluate the performance of the proposed algorithm

semiclassical limits for the hyperbolic plane we study the concentration properties of high energy eigenfunctions for the laplace beltrami operator of the hyperbolic plane with special consideration of automorphic eigenfunctions at the center of our investigation is the microlocal lift of an eigenfunction to sl 2 introduced by s zelditch the microlocal lift is based on s helgason s fourier transform and has a straightforward description in terms of the lie algebra sl 2 we begin with an elementary demonstration of zelditch s exact differential equation for the microlocal lift further for a sequence of suitably bounded eigenfunctions with eigenvalues tending to infinity we show that the limit of microlocal lifts is a geodesic flow invariant positive measure our main consideration is the microlocal lifts of the elementary eigenfunctions constructed from the macdonald bessel functions we find that with a scaling of auxiliary parameters the corresponding high energy limit converges to the positive dirac measure for the lift to sl 2 of a single geodesic on the upper half plane in particular at high energy the microlocal lift of a macdonald bessel function is concentrated along the lift of a single geodesic we further find that the convergence is uniform in parameters and thus our considerations can be applied to study automorphic eigenfunctions in particular the maass cusp forms for certain cofinite subgroups of sl 2 a formula is presented for the microlocal lift of a cusp form as an integral of a family of dirac measures and a measure given directly by sums of products of the classical fourier coefficients of the cusp form the formula establishes that questions on quantum chaos for automorphic eigenfunctions are equivalent to classically stated questions on twisted sums of coefficients in particular we find that the uniform distribution for the microlocal limit is equivalent to a uniform distribution for the limit of twisted coefficient sums we extend the considerations to the case of the nonholomorphic eisenstein series for the modular group we find that a result of w luo and p sarnak is equivalent to a limit sum formula involving the riemann zeta function and the elementary divisor function the formula is suggestive of a formula of s ramanujan

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

optimal cal h _ 2 filtering in networked control systems with multiple packet dropout this note studies the problem of optimal h2 filtering in networked control systems ncss with multiple packet dropout a new formulation is employed to model the multiple packet dropout case where the random dropout rate is transformed into a stochastic parameter in the system s representation by generalization of the h2 norm definition new relations for the stochastic norm of a linear discrete time stochastic parameter system represented in the state space form are derived the stochastic h2 norm of the estimation error is used as a criterion for filter design in the ncs framework a set of linear matrix inequalities lmis is given to solve the corresponding filter design problem a simulation example supports the theory

from classical periodic orbits to the quantization of chaos we present a quantitative analysis of selberg s trace formula viewed as an exact version of gutzwiller s semiclassical periodic orbit theory for the quantization of classically chaotic systems two main applications of the trace formula are discussed in detail i the periodic orbit sum rules giving a smoothing of the quantal energy level density ii the selberg zeta function as a prototype of a dynamical zeta function defined as an euler product over the classical periodic orbits and its analytic continuation across the entropy barrier by means of a dirichlet series it is shown how the long periodic orbits can be effectively taken into account by a universal remainder term which is explicitly given as an integral over an orbit selection function numerical results are presented for the free motion of a point particle on compact riemann surfaces hadamard gutzwiller model which is the primary testing ground for our ideas relating quantum mechanics and classical mechanics in the case of strong chaos our results demonstrate clearly the crucial role played by the long periodic orbits an exact rule for quantizing chaos is derived for such systems where the dirichlet series representing the selberg zeta function converges on the critical line explicit formulae are given for the computation of the abscissae of absolute and conditional convergence respectively of these dynamical dirichlet series for the two riemann surfaces considered it turns out that one can cross the entropy barrier but that the critical line cannot be reached by a convergent dirichlet series it would seem that this is the main reason why the riemann siegel lookalike formula recently conjectured by m v berry and j p keating fails in generating the lower lying quantal energies for these strongly chaotic systems

periodic orbits on the regular hyperbolic octagon abstract the length spectrum of closed geodesics on a compact riemann surface corresponding to a regular octagon on the poincare disc is investigated the general form of the elements of the octagon group a discrete subgroup of nu su 1 1 1 in terms of 2 2 matrices is derived and the previously conjectured law for the length of periodic orbits is proved analytically an algorithm for the multiplicity of geodesics with a given length is developed which leads to an efficient enumeration of the periodic orbits of this strongly chaotic system

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

scheduled controllers for linear systems with bounded actuators state and output feedback controllers are designed for disturbance attenuation in linear systems with bounded actuators the controller is scheduled according to the proximity to the origin of the state of the plant in the state feedback case and the compensator state in the case of output feedback this procedure yields a linear parameter varying structure for the controller that allows higher gain and hence higher performance controllers as the states move closer to the origin the main results give sufficient conditions for the satisfaction of a parameter dependent performance measure without violating the saturation bounds linear splines are used to obtain solutions that can be obtained by standard lmi software examples including an open loop unstable system highlight the application of the results

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

optimal computer control via communication channels with irregular transmission times we study a linear discrete time partially observed system perturbed by white noises the observations are transmitted to the controller via communication channels with random transmission times various measurement signals may incur independent delays be lost or corrupted under certain assumptions a recursive minimum variance state estimator is proposed a finite horizon linear quadratic optimal control problem is solved we also find a solution for the problem of minimizing the average cost per unit time over the infinite planning horizon

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

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

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

the modulus of continuity for γ0 m semi classical limits we study the behavior of a large eigenvalue limit of eigenfunctions for the hyperbolic laplacian for the modular quotient sl 2 fejer summation and results of s zelditch are used to show that the microlocal lifts of eigenfunctions have large eigenvalue limit a geodesic flow invariant measure for the modular unit cotangent bundle the limit is studied for hecke maass forms joint eigenfunctions of the hecke operators and the hyperbolic laplacian the first modulus of continuity result is presented for the limit the singular concentration set of the limit cannot be a compact union of closed geodesics and measured geodesic laminations

an exponentially increasing semiclassical spectral form factor for a class of chaotic systems the spectral form factor k tau plays a crucial role in the understanding of the statistical properties of quantal energy spectra of strongly chaotic systems in terms of periodic orbits it allows the semiclassical computation of those statistics that are bilinear in the spectral density d e like the spectral rigidity delta 3 l and the number variance sigma 2 l since berry s 1985 1991 work on the semiclassical approximation of the spectral rigidity in terms of periodic orbits it is generally assumed that the periodic orbit expression for the spectral form factor universally obeys k tau 1 for tau 1 we show that for a wide class of strongly chaotic systems including billiards with neumann boundary conditions and the motion on some riemann surfaces the asymptotic behaviour of the semiclassical spectral form factor k tau depends very sensitively on the averaging employed a gaussian averaging is preferable from a theoretical as well as from a numerical point of view to for example a rectangular averaging however we show in this paper that the gaussian averaging leads in some cases to an asymptotic behaviour like k tau approximately ec tau where c 0 depends only on the energy e at which the statistic is considered

robust control of uncertain multi inventory systems via linear matrix inequality we consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes we address the problem of e stabilising the inventory since this implies some reduction of the inventory costs the main results are certain conditions under which e stabilisability is possible through a saturated linear state feedback control all the results are based on a linear matrix inequalities approach and on some recent techniques for the modelling and analysis of polytopic systems with saturations numerical simulations are provided

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

optimal estimation in udp like networked control systems with intermittent inputs stability analysis and suboptimal filter design we investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator most existing results for this setup are concerned with the design of controller while the optimal estimation and its performance evaluation have been rarely treated in this paper we show that unlike many other cases such as intermittent observations or tcp like systems the system state follows a gaussian mixture distribution with exponentially increasing terms which leads to a gaussian sum filter based optimal estimation we develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices it is revealed that the stability is independent of the packet loss rate and is not affected by the lack of acknowledgment a suboptimal filtering algorithm with improved computational efficiency is then developed numerical examples and simulations are employed to illustrate the theoretical results

a new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

exact theory for the quantum eigenstates of a strongly chaotic system we present an exact theory for the quantum eigenstates of a strongly chaotic system which consists of a point particle sliding freely on a two dimensional compact surface of constant negative curvature the main result is a general sum rule which relates an almost arbitrarily smoothed sum over the quantum wavefunctions to a sum over the lengths of the classical orbits as an example we apply this formula to the gaussian smoothed sum over wavefunctions the question of scars as imprints of individual closed orbits is discussed and the connection with bogomolny s semiclassical theory is explicitly worked out the investigation of the amplitude distribution p reveals that the higher excited wavefunctions behave as gaussian random waves

energy level statistics of the hadamard gutzwiller ensemble abstract the statistical properties of the quantal energy levels of the hadamard gutzwiller ensemble whose classical members belong to the class of systems with hard chaos are investigated based on a sample of 4500 energy levels it is shown that the short range statistics as nearest neighbour spacing distributions are governed by the goe predictions of random matrix theory which was first surmised by wigner and by landau and smorodinsky for nuclear level statistics this result strengthens the hypothesis that quantum systems with chaotic classical counterpart display level repulsion as predicted by random matrix theory however the level statistics describing correlations over greater level distances deviate from the goe predictions which is explained as a simple consequrnce of the fact that the spectral rigidity 3 l introduced by dyson and mehta saturates non universally at a finite value for l in complete agreement with the semiclassical theory developed by berry

descriptor recursive estimation for multiple sensors with different delay rates in this article the problem of recursive estimation is studied for a class of descriptor systems measured by multiple sensors with different delay rates the delay phenomenon occurs in a random way and the delay rate for each sensor is characterised by an individual binary switching sequence obeying a conditional probability distribution the original descriptor system is transformed into two non descriptor stochastic subsystems with autocorrelated and cross correlated noises by using the singular value decomposition and the state augmentation applying an innovation analysis approach and the orthogonal projection theorem recursive estimators including filter predictor and smoother are first derived for each subsystem and the process noise then based on the newly obtained recursive state estimators and process noise estimators the recursive filter predictor and smoother are obtained for the original descriptor system measured by multiple sensors with different delay rates a numerical simulation ex

local stabilization of discrete time linear systems with saturating controls an lmi based approach deals with the problem of local stabilization of linear discrete time systems subject to control saturation a linear matrix inequalities based framework is proposed in order to compute a saturating state feedback that stabilizes the system with respect to a given set of admissible initial states and in addition guarantees some dynamical performances when the system operates in the zone of linear behavior i e when the controls are not saturated

a rule for quantizing chaos the authors find a real function delta e whose zeros approximate the quantum energy levels of a system with chaotic classical trajectories delta e is a finite sum over combinations of classical periodic orbits it is obtained from gutzwiller s infinite and divergent sum 1982 representing the spectral density in terms of periodic orbits by means of a resummation conjectured by analogy with a derivation of the riemann siegel formula for the riemann zeros they assess the practicality of the quantization condition

optimal linear state estimation over a packet dropping network using linear temporal coding we consider the problem of linear minimum mean square error estimation for a discrete time system over a packet dropping network in order to improve the estimation performance different from the standard approach of sending the current measurement data we choose sending a linear combination of the current measurement and the measurement collected at the previous time a method called linear temporal coding we assume the packet arrival sequence is unknown and the noise contained in the packet may come from sensor or communication channel in an effort to cope with colored noise caused by measurement combination after comparing with the classic state augmentation approach and measurement differencing approach we derive a recursive estimation algorithm by means of orthogonal projection principle and innovation sequence approach our algorithm consists of two parts smooth and estimate for large measurement noise case numerical example shows the benefit of using linear temporal coding strategy compared with directly sending the current data on the contrary when communication noise plays the dominating role for scalar system we prove there is no benefit to choose this scheme

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

on the periodic orbits of a strongly chaotic system abstract a point particle sliding freely on a two dimensional surface of constant negative curvature hadamard gutzwiller model exemplifies the simplest chaotic hamiltonian system exploiting the close connection between hyperbolic geometry and the group su 1 1 1 we construct an algorithm symboliv dynamics which generates the periodic orbits of the system for the simplest compact riemann surface having as its fundamental group the octagon group we present an enumeration of more than 206 million periodic orbits for the length of the n th primitive periodic orbit we find a simple expression in terms of algebraic numbers of the form m 2 n m n n are governed by a particular beatty sequence which reveals a strange arithmetical structure of chaos knowledge of the length spectrum is crucial for quantization via the selberg trace formula periodic orbit theory which in turn is expected to unravel the mystery of quantum chaos

adaptive kalman filtering in networked systems with random sensor delays multiple packet dropouts and missing measurements in this paper adaptive filtering schemes are proposed for state estimation in sensor networks and or networked control systems with mixed uncertainties of random measurement delays packet dropouts and missing measurements that is all three uncertainties in the measurement have certain probability of occurrence in the network the filter gains can be derived by solving a set of recursive discrete time riccati equations examples are presented to demonstrate the applicability and performances of the proposed schemes

on tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty we present efficiently verifiable sufficient conditions for the validity of specific np hard semi infinite systems of linear matrix inequalities lmis arising from lmis with uncertain data and demonstrate that these conditions are tight up to an absolute constant factor in particular we prove that given an n times n interval matrix cal u rho a mid a ij a ij leq rho c ij one can build a computable lower bound accurate within the factor pi over 2 on the supremum of those rho for which all instances of cal u rho share a common quadratic lyapunov function we then obtain a similar result for the problem of quadratic lyapunov stability synthesis finally we apply our techniques to the problem of maximizing a homogeneous polynomial of degree 3 over the unit cube

a robust optimization approach to dynamic pricing and inventory control with no backorders in this paper we present a robust optimization formulation for dealing with demand uncertainty in a dynamic pricing and inventory control problem for a make to stock manufacturing system we consider a multi product capacitated dynamic setting we introduce a demand based fluid model where the demand is a linear function of the price the inventory cost is linear the production cost is an increasing strictly convex function of the production rate and all coefficients are time dependent a key part of the model is that no backorders are allowed we show that the robust formulation is of the same order of complexity as the nominal problem and demonstrate how to adapt the nominal deterministic solution algorithm to the robust problem

optimal linear state estimator with multiple packet dropouts this technical note is concerned with the optimal linear estimation problem in the presence of multiple packet dropouts in both sensor to controller and controller to actuator channels the considered stochastic packet dropouts are independent and bernoulli distributed based on a linear packet dropout model with stochastic parameters a linear minimum variance lmv filter is proposed using the orthogonality principle a sufficient condition for convergence of the steady state lmv filter under a dc controller output is also given simulation results show the effectiveness of the proposed filter

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator

crossing the entropy barrier of dynamical zeta functions dynamical zeta functions are an important tool to quantize chaotic dynamical systems the basic quantization rules require the computation of the zeta functions on the real energy axis where their euler product representations running over the classical periodic orbits usually do not converge due to the existence of the so called entropy barrier determined by the topological entropy of the classical system we show that the convergence properties of the dynamical zeta functions rewritten as dirichlet series are governed not only by the well known topological and metric entropy but depend crucially on subtle statistical properties of the maslov indices and of the multiplicities of the periodic orbits that are measured by a new parameter for which we introduce the notion of a third entropy if and only if the third entropy is nonvanishing one can cross the entropy barrier if it exceeds a certain value one can even compute the zeta function in the physical region by means of a convergent dirichlet series a simple statistical model is presented which allows to compute the third entropy four examples of chaotic systems are studied in detail to test the model numerically