adaptive control of linear systems with markov perturbations the stochastic model considered is a linear jump diffusion process x for which the coefficients and the jump processes depend on a markov chain z with finite state space first we study the optimal filtering and control problem for these systems with non gaussian initial conditions given noisy observations of the state x and perfect measurements of z we derive a new sufficient condition which ensures the existence and the uniqueness of the solution of the nonlinear stochastic differential equations satisfied by the output of the filter we study a quadratic control problem and show that the separation principle holds next we investigate an adaptive control problem for a state process x defined by a linear diffusion for which the coefficients depend on a markov chain the processes x and z being observed in independent white noises suboptimal estimates for the process x z and approximate control law are investigated for a large class of probability distributions of the initial state asymptotic properties of these filters and this control law are obtained upper bounds for the corresponding error are given

state estimation in stochastic hybrid systems with sparse observations in this note we study the problem of state estimation for a class of sampled measurement stochastic hybrid systems where the continuous state x satisfies a linear stochastic differential equation and noisy measurements y are taken at assigned discrete time instants the parameters of both the state and measurement equation depend on the discrete state q of a continuous time finite markov chain even in the fault detection setting we consider at most one transition for q is admissible the switch may occur between two observations whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable so that the known estimation techniques cannot be applied we derive and implement an algorithm for the estimation of the states x q and of the discrete state switching time that is convenient for both recursive update and the eventual numerical quadrature numerical simulations are illustrated

partially linear estimation with application to sparse signal recovery from measurement pairs we address the problem of estimating a random vector from two sets of measurements and such that the estimator is linear in we show that the partially linear minimum mean square error plmmse estimator does not require knowing the joint distribution of and in full but rather only its second order moments this renders it of potential interest in various applications we further show that the plmmse method is minimax optimal among all estimators that solely depend on the second order statistics of and we demonstrate our approach in the context of recovering a signal which is sparse in a unitary dictionary from noisy observations of it and of a filtered version we show that in this setting plmmse estimation has a clear computational advantage while its performance is comparable to state of the art algorithms we apply our approach both in static and in dynamic estimation applications in the former category we treat the problem of image enhancement from blurred noisy image pairs we show that plmmse estimation performs only slightly worse than state of the art algorithms while running an order of magnitude faster in the dynamic setting we provide a recursive implementation of the estimator and demonstrate its utility in tracking maneuvering targets from position and acceleration measurements

jump diffusion processes in tracking recognition advances in sensor technology permit more sophisticated tracking identification algorithms to be implemented this correspondence compares and contrasts the modeling framework employed in two recent image enhanced trackers and generalizes one of them the pme for use in target identification

approximation and decomposition of singularly perturbed stochastic hybrid systems this paper considers a singularly perturbed stochastic hybrid system whose state equations are governed by a stochastic switching process which is modelled as a nearly completely decomposable continuous time finite state markov chain approximate models for the slow mode subsystem are derived over the intervals of rapid switching and their accuracy the mean squared errors between the approximate models and the original systems is quantified aggregate models for the subsystem are obtained over a longer period the almost surely exponential stability of the subsystem is studied the behaviour of the fast subsystem which depends on the relative size of the perturbation parameters is analysed the decomposition of the overall system and the switching process together into slow and fast subsystems is investigated the results derived in the paper are shown to hold when the switching process is stationary and irreducible and each group of strongly interacting states is irreducible and time reversible fina

robust linear filtering for discrete time hybrid markov linear systems in this paper we consider the robust linear filtering of hybrid discrete time markovian jump linear systems we assume that only an output of the system is available and therefore the values of the jump parameter are not known it is desired to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the square error we consider uncertainties on the parameters of the possible modes of operation of the system a linear matrix inequalities lmi formulation is proposed to solve the problem for the case in which there are no uncertainties on the modes of operation of the system we show that the lmi formulation provides a filter with the same stationary mean square error as the one obtained from the riccati equation approach

the algorithmic complexity of bondage and reinforcement problems in bipartite graphs abstract let g v e be a graph a subset d v is a dominating set if every vertex not in d is adjacent to a vertex in d the domination number of g denoted by g is the smallest cardinality of a dominating set of g the bondage number of a nonempty graph g is the smallest number of edges whose removal from g results in a graph with domination number larger than g the reinforcement number of g is the smallest number of edges whose addition to g results in a graph with smaller domination number than g in 2012 hu and xu proved that the decision problems for the bondage the total bondage the reinforcement and the total reinforcement numbers are all np hard in general graphs in this paper we improve these results to bipartite graphs

image estimation using doubly stochastic gaussian random field models the two dimensional 2 d doubly stochastic gaussian dsg model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal here we present the optimal estimator and 2 d fixed lag smoother for this dsg model extending earlier work of ackerson and fu as the optimal estimator has an exponentially growing state space we investigate suboptimal estimators using both a tree and a decision directed method experimental results are presented

on domination problems for permutation and other graphs abstract there is an increasing interest in results on the influence of restricting np complete graph problems to special classes of perfect graphs as e g permutation graphs it was shown that several problems restricted to permutation graphs are solvable in polynomial time 2 3 4 6 7 14 16 in this paper we give 1 i an algorithm with time bound o n 2 for the weighted independent domination problem on permutation graphs which is an improvement of the o n 3 solution given in 7 2 ii a polynomial time solution for the weighted feedback vertex set problem on permutation graphs 3 iii an investigation of weighted dominating clique problems for several graph classes including an np completeness result for weakly triangulated graphs as well as polynomial time bounds

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

brief paper a method for the estimation of infrequent abrupt changes in nonlinear systems this paper presents a framework for obtaining better performance from multiple model approaches for estimating infrequent abrupt changes in nonlinear systems by using insight into the nature of the problem and basic probability a procedure that greatly reduces the number of filters required by multiple model approaches is obtained this allows for a much longer detection horizon without increasing the computational requirements and results in improved performance over standard multiple model approaches the performance of this approach is evaluated for state parameter estimation of a heptane to toluene aromatization process the method is also shown to be robust to errors in the assumed noise statistics

effects of rotation on the dynamics of a circular cylindrical shell with application to tire vibration abstract for the purpose of understanding the effects of rotation on wave propagation within a tire s treadband the vibration of an inflated circular cylindrical shell rotating about a fixed axis has been considered here the equations of motion of the rotating shell are formulated in a fixed reference frame i e eulerian co ordinates by assuming wave like solutions for the free vibration case the natural frequencies and corresponding wave like basis functions can then be obtained a natural frequency selection procedure is introduced that can be used to associate each of the basis functions with a single natural frequency the basis functions are then superimposed to represent the forced response of the system when driven by a point harmonic force at a fixed location in the reference frame by using the procedure described here the coefficients of the basis functions can be obtained directly by solving an uncoupled ordinary differential equation finally the resulting forced responses are presented in both the spatial and wave number domains and the wave number spectrum of the rotating shell is compared with that of a stationary shell based on the results presented here it is suggested that at typical rotational speeds it may be possible to use a stationary tire analysis to predict the characteristics of a rotating tire after performing a simple kinematic compensation

a class of fast exact bayesian filters in dynamical models with jumps we address the statistical filtering problem in dynamical models with jumps when a particular application is adequately modeled by linear and gaussian probability density functions with jumps a usual method consists in approximating the optimal bayesian estimate in the sense of the minimum mean square error mmse in a linear and gaussian jump markov state space system jmss practical solutions include algorithms based on numerical approximations or on sequential monte carlo smc methods in this paper we propose a class of alternative methods which consists in building statistical models which locally similarly model the problem of interest but in which the computation of the mmse estimate can be be computed exactly without numerical nor smc approximations and at a computational cost which is linear in the number of observations

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

optimal linear mean square filter for continuous time jump linear systems we consider a class of hybrid systems which is modeled by continuous time linear systems with markovian jumps in the parameters lsmjp our aim is to derive the best linear mean square estimator for such systems the approach adopted here produces a filter which bears those desirable properties of the kalman filter a recursive scheme suitable for computer implementation which allows some offline computation that alleviates the computational burden apart from the intrinsic theoretical interest of the problem in its own right and the application oriented motivation of getting more easily implementable filters another compelling reason why the study here is pertinent has to do with the fact that the optimal nonlinear filter for our estimation problem is not computable via a finite computation the filter is infinite dimensional our filter has dimension nn with n denoting the dimension of the state vector and n the number of states of the markov chain

modal estimation in hybrid systems in hybrid systems estimation is made difficult by the nonlinear equations of state evolution several algorithms for generating an approximation to the conditional mean estimator have been proposed these are satisfactory in many cases but because of the way the observations are fused the estimate of the modal component of the state is often less good this paper proposes a novel algorithm for state estimation and compares it with some in current use

tracking multiple particles in fluorescence time lapse microscopy images via probabilistic data association tracking subcellular structures as well as viral structures displayed as particles in fluorescence microscopy images yields quantitative information on the underlying dynamical processes we have developed an approach for tracking multiple fluorescent particles based on probabilistic data association the approach combines a localization scheme that uses a bottom up strategy based on the spot enhancing filter as well as a top down strategy based on an ellipsoidal sampling scheme that uses the gaussian probability distributions computed by a kalman filter the localization scheme yields multiple measurements that are incorporated into the kalman filter via a combined innovation where the association probabilities are interpreted as weights calculated using an image likelihood to track objects in close proximity we compute the support of each image position relative to the neighboring objects of a tracked object and use this support to recalculate the weights to cope with multiple motion models we integrated the interacting multiple model algorithm the approach has been successfully applied to synthetic 2 d and 3 d images as well as to real 2 d and 3 d microscopy images and the performance has been quantified in addition the approach was successfully applied to the 2 d and 3 d image data of the recent particle tracking challenge at the ieee international symposium on biomedical imaging isbi 2012

adaptive gaussian sum filter for nonlinear bayesian estimation a nonlinear filter is developed by representing the state probability density function by a finite sum of gaussian density kernels whose mean and covariance are propagated from one time step to the next using linear system theory methods such as extended kalman filter or unscented kalman filter the novelty in the proposed method is that the weights of the gaussian kernels are updated at every time step by solving a convex optimization problem posed by requiring the gaussian sum approximation to satisfy the fokker planck kolmogorov equation for continuous time dynamical systems and the chapman kolmogorov equation for discrete time dynamical systems the numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function

linear minimum mean square filter for discrete time linear systems with markov jumps and multiplicative noises in this paper we obtain the linear minimum mean square estimator lmmse for discrete time linear systems subject to state and measurement multiplicative noises and markov jumps on the parameters it is assumed that the markov chain is not available by using geometric arguments we obtain a kalman type filter conveniently implementable in a recurrence form the stationary case is also studied and a proof for the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated markov chain is obtained it is shown that there exists a unique positive semi definite solution for the stationary riccati like filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed offline

spectral bayesian estimation for general stochastic hybrid systems abstract general stochastic hybrid systems gshs have been formulated to represent various types of uncertainties in hybrid dynamical systems in this paper we propose computational techniques for bayesian estimation of gshs in particular the fokker planck equation that describes the evolution of uncertainty distributions along gshs is solved by spectral techniques where an arbitrary form of probability density of the hybrid state is represented by a mixture of fourier series the method is based on splitting the fokker planck equation represented by an integro partial differential equation into the partial differentiation part for continuous diffusion and the integral part for discrete transition and integrating the solution of each part the propagated density function is used with a likelihood function in the bayes formula to estimate the hybrid state for given sensor measurements the unique feature of the proposed technique is that the probability density describing complete stochastic properties of the hybrid state is constructed without relying on the common gaussian assumption in contrast to other methods that compute certain expected values such as mean or variance we apply the proposed method to the estimation of two examples the bouncing ball model and the dubins vehicle model we show that the proposed technique yields propagated densities consistent with monte carlo simulations more accurate estimates over the gaussian based approach and some computational benefits over a particle filter

on applicability of the interacting multiple model approach to state estimation for systems with sojourn time dependent markov model switching in this paper the attempt at the interacting multiple model imm method extension to the state estimation problem with semi markov sojourn time dependent markov stdm system model switching is analyzed it is demonstrated that such an stdm imm approach does not properly take into account the specific character of the stdm switching in the system and it becomes a reason for the reduction of estimation accuracy for this problem it is shown that a hypotheses merging should be restricted in such a way that not only the current system model but also the sojourn time in the model should be given in hypotheses to be tested some other aspects of bayesian estimation in a switching environment are also discussed

state and mode estimation for discrete time jump markov systems in this article we compute new state and mode estimation algorithms for discrete time gauss markov models whose parameter sets switch according to a known markov law an important feature of our algorithms is that they are based upon the exact filter dynamics computed in r j elliott f dufour and d sworder ieee trans automat control 41 1996 pp 1807 1810 the fundamental and well known obstacle in estimation of jump markov systems is managing the geometrically growing history of candidate hypotheses in our scheme we address this issue by proposing an extension of an idea due to viterbi our scheme maintains a fixed number of candidate paths in a history each identified by an optimal subset of estimated mode probabilities we compute finite dimensional suboptimal filters and smoothers which estimate the hidden state process and the mode probability our smoothers are based upon a duality between forward and backward dynamics further our smoothing algorithms are general and can be configured into the standard forms of fixed point fixed lag and fixed interval smoothers a computer simulation is included to demonstrate performance

steiner trees for hereditary graph classes a treewidth perspective abstract we consider the classical problems edge steiner tree and vertex steiner tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs we show a dichotomy for the former problem restricted to h 1 h 2 free graphs and a dichotomy for the latter problem restricted to h free graphs we find that there exists an infinite family of graphs h such that vertex steiner tree is polynomial time solvable for h free graphs whereas there exist only two graphs h for which this holds for edge steiner tree assuming p np we also find that edge steiner tree is polynomial time solvable for h 1 h 2 free graphs if and only if the treewidth of the class of h 1 h 2 free graphs is bounded subject to p np to obtain the latter result we determine all pairs h 1 h 2 for which the class of h 1 h 2 free graphs has bounded treewidth

maximum likelihood estimation of transition probabilities of jump markov linear systems this paper describes an online maximum likelihood estimator for the transition probabilities associated with a jump markov linear system jmls the maximum likelihood estimator is derived using the reference probability method which exploits an hypothetical probability measure to find recursions for complex expectations expectation maximization em procedure is utilized for maximizing the likelihood function in order to avoid the exponential increase in the number of statistics of the optimal em algorithm we make interacting multiple model imm type approximations the resulting method needs the mode weights of an imm filter with n3 components where n is the number of models in the jmls the algorithm can also supply base state estimates and covariances as a by product the performance of the estimator is illustrated on two simulated examples and compared to a recently proposed alternative

state estimation for discrete time markov jump linear systems with time correlated and mode dependent measurement noise abstract the state estimation problem for discrete time markov jump linear systems corrupted by time correlated and mode dependent measurement noise is considered where the time correlated and mode dependent measurement noise is described via a discrete time stochastic system with markov parameter and kronecker delta function by defining the measurement noise in this manner both time correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise a novel distributed measurement differencing method is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper the first algorithm is optimal in the sense of minimum mean square error which can exactly compute the minimum mean square error estimate of system state the second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some gaussian hypotheses the two proposed algorithms are recursive and the proposed suboptimal algorithm has a time independent complexity the performance of the proposed suboptimal algorithm is illustrated using computer simulations

improper complex valued multiple model adaptive estimation motivated by the problem of estimating the discrete and continuous states of an improper complex valued stochastic hybrid system the paper proposes a class of widely linear augmented multiple model adaptive estimation algorithms referred to as the c mmae we show that for an improper complex valued signal pseudo covariance of the innovation sequence is not zero and therefore carries useful statistical information regarding the unknown behaviour mode of the hybrid system a new bayesian law is therefore derived as a function of the pseudo covariance of the innovation sequence and used to compute the probability that a hypothesized model is in effect at a certain time we show that the c mmae which uses the new bayesian law and utilizes the complete second order statistical characterization of the complex valued innovation sequence convergences faster than its counterpart which only uses the conventional covariance of the innovation sequence in order to simplify the computational complexity we develop two circularized versions of the c mmae using a preprocessing step referred to as the circularizing filter cf the cf is incorporated to convert the improper observations innovations into the proper ones in order to reduce the computational complexity of the hypothesis testing step finally an interacting version of the c mmae referred to as c imm is developed for improper complex valued systems with markovian switching coefficients simulation results indicate that the proposed hybrid estimators provide improved performance and convergence properties over their traditional counterparts

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

brief paper risk sensitive filtering for jump markov linear systems in this paper a risk sensitive multiple model filtering algorithm is derived using the reference probability methods first the approximation of the interacting multiple model imm algorithm is identified in the reference probability domain then the same type of approximation is used to derive the finite dimensional risk sensitive filtering algorithm the derived algorithm reduces to the imm filter when the risk sensitive parameter goes to zero and reduces to the risk sensitive filter for linear gauss markov systems when the number of models is unity the algorithm performs better in a simulated uncertain parameter scenario than the imm filter

a new multiple model filter with switch time conditions the interacting multiple model filter has long been the method of choice for performing target tracking using multiple motion models the filter finds a suboptimal solution to a problem which has the implicit assumption that immediate model shifts have the highest probability when the sampling rate of the underlying continuous process is high compared to the target dynamics this is not a reasonable assumption instead changes in dynamics persist for some time in this paper we propose an alternative switching model which forces the dynamic models to persist for at least a model specific time the model is semi markov in nature with a sojourn time probability mass function which is zero for a model specific number of time steps and then follows a geometrical distribution through this assumption a less complex problem in terms of model hypotheses arises and to that problem we derive a state estimation algorithm that is close to optimal when the model assumptions are valid three other semi markov based multiple model filters are discussed and compared to in a qualitative sense we also derive a new aircraft motion model for start and termination of turns finally the proposed filter is evaluated on a benchmark scenario for tracking and the results show a performance increase compared to the interacting multiple model imm filter for the trajectories considered

on the in plane vibrations of rotating rings the general problem of the in plane vibrations of a rotating ring is investigated the potential and kinetic energy functionals including the effects of extensional and shear deformation and of rotatory inertia respectively are derived the governing differential equations for the inextensional case are derived by using hamilton s principal and shown to have additional terms not present in previous works numerical studies which show the importance of these additional terms are presented

semitotal domination new hardness results and a polynomial time algorithm for graphs of bounded mim width abstract a semitotal dominating set of a graph g with no isolated vertex is a dominating set d of g such that every vertex in d is within distance two of another vertex in d the minimum size t 2 g of a semitotal dominating set of g is squeezed between the domination number g and the total domination number t g semitotal dominating set is the problem of finding given a graph g a semitotal dominating set of g of size t 2 g in this paper we continue the systematic study on the computational complexity of this problem when restricted to special graph classes in particular we show that it is solvable in polynomial time for the class of graphs of bounded mim width by a reduction to total dominating set and we provide several approximation lower bounds for subclasses of subcubic graphs moreover we obtain complexity dichotomies in monogenic classes for the decision versions of semitotal dominating set and total dominating set finally we show that it is np complete to recognise the graphs such that t 2 g t g and those such that g t 2 g even if restricted to be planar and with maximum degree at most 4 and we provide forbidden induced subgraph characterisations for the graphs hereditarily satisfying either of these two equalities

algorithm and hardness results on neighborhood total domination in graphs abstract a set d v of a graph g v e is called a neighborhood total dominating set of g if d is a dominating set and the subgraph of g induced by the open neighborhood of d has no isolated vertex given a graph g min ntds is the problem of finding a neighborhood total dominating set of g of minimum cardinality the decision version of min ntds is known to be np complete for bipartite graphs and chordal graphs in this paper we extend this np completeness result to undirected path graphs chordal bipartite graphs and planar graphs we also present a linear time algorithm for computing a minimum neighborhood total dominating set in proper interval graphs we show that for a given graph g v e min ntds cannot be approximated within a factor of 1 e log v unless np dtime v o log log v and can be approximated within a factor of o log where is the maximum degree of the graph g finally we show that min ntds is apx complete for graphs of degree at most 3

response of rotating rings to harmonic and periodic loading and comparison with the inverted problem abstract the harmonic and periodic forced vibrations of rotating rings are derived and investigated the modal expansion technique yields the forced solution which is characterized by four generalized co ordinates associated with each n circumferential wave number the inextensional assumption is presumed when flexural vibration is the only important component to reduce the order of the system the closed form solutions to the harmonic load cases once concentrated once distributed are demonstrated and interpreted the approach is then extended to periodic loads where fourier sine and cosine series is applied examples depict the numerical responses to all the cases being derived the solutions of a stationary ring subjected to traveling loads are also solved for comparison their difference is investigated and interpreted from various viewpoints

on contact induced standing waves in rotating tires experiment and theory an experimental and theoretical study of standing waves in a rotating tire is presented a test set up for studying small balloon tires is described experimental observations of standing waves arising after a critical speed transition are presented including measurements of the spatial structure of the standing waves a simple model for the tire is developed which has a single degree of freedom at each radial location steady state solutions at any rotation speed are governed by a non linear boundary value problem which is studied in detail appropriate boundary conditions are obtained using asymptotic arguments and then used in numerical solutions the analysis is shown to agree well with the experimental observations based on the analysis a method for suppressing the standing waves is proposed and confirmed experimentally

flexural vibration of a thin rotating ring abstract flexural vibration of a thin rotating ring has been investigated experimentally and from some theoretical points of view the frequencies of forward and backward flexural traveling waves were measured by using strain gages the range of rotational speeds of the ring was such as to include frequencies comparable with that of the fundamental flexural mode of a non rotating ring and the stability of flexural vibration was examined with consideration of the effects of the centrifugal and coriolis forces it was ascertained that for all the flexural modes of the rotating ring no instability phenomenon exists in the sense that the natural frequencies of the rotating ring never become zero over the whole range of rotational speed in the light of the experimental results previous theories for a rotating ring or a circular cylindrical shell and the author s theory for a ring are examined and some differences among them discussed

adaptive joint detection and estimation in mimo systems a hybrid systems approach an adaptive receiver based on hybrid system theory is developed for a multiuser multiple input multiple output mimo fading code division multiple access cdma system the basic idea is to treat the transmitted symbols and channel gains as unknown states discrete and continuous within a hybrid systems framework the bayesian inference based state estimation is derived using multiple model theory resulting in an optimal joint sequence estimator which is shown to be intractable in its computational complexity a suboptimal receiver imm sic is then derived based on the well known interacting multiple model imm algorithm and successive interference cancellation sic scheme this paper shows the specific approximations made to the probability densities of the optimal receiver in deriving the imm sic receiver with complexity linear in number of users this receiver design is well suited for online recursive processing of space time coded cdma system where the decoding stage is incorporated within the multiple model framework

exact hybrid filters in discrete time using the reference probability method and the change of measure in discrete time the state estimator problem is considered for linear systems observed in gaussian noise when the coefficients are functions of a noisily observed finite state markov chain the methods are new and finite dimensional filters are obtained however the number of statistics increases in time a numerical comparison of this filter with the interactive multiple model algorithm introduced by blom and bar shalom 1988 is given

brief paper a convex optimization approach to filtering in jump linear systems with state dependent transitions we introduce a new methodology to construct a gaussian mixture approximation to the true filter density in hybrid markovian switching systems we relax the assumption that the mode transition process is a markov chain and allow it to depend on the actual and unobservable state of the system the main feature of the method is that the gaussian densities used in the approximation are selected as the solution of a convex programming problem which trades off sparsity of the solution with goodness of fit a meaningful example shows that the proposed method can outperform the widely used interacting multiple model imm filter and gpb2 in terms of accuracy at the expenses of an increase in computational time

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

an image based filter for discrete time markovian jump linear systems abstract a discrete time filtering problem for hybrid systems is studied in which the state process is observed in white noise and the random jump process called the mode or the regime is observed by a point process the optimal state and mode estimator when only the mode measurements are used is studied some properties of this filter are then established apart from their theoretical interest these results have an interesting practical implication for the design of image based tracking systems since they lead to an easily implementable suboptimal algorithm two illustrative examples are given to show the performance of the proposed approach

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

on the bayesian cramer rao bound for markovian switching systems we propose a numerical algorithm to evaluate the bayesian cramer rao bound bcrb for multiple model filtering problems it is assumed that the individual models have additive gaussian noise and that the measurement model is linear the algorithm is also given in a recursive form making it applicable for sequences of arbitrary length previous attempts to calculate the bcrb for multiple model filtering problems are based on rough approximations which usually make them simple to calculate in this paper we propose an algorithm which is based on monte carlo sampling and which is hence more computationally demanding but yields accurate approximations of the bcrb an important observation from the simulations is that the bcrb is more overoptimistic than previously suggested bounds which we motivate using theoretical results

consensus based distributed multiple model ukf for jump markov nonlinear systems this note studies the problem of distributed estimation for jump markov nonlinear systems jmnlss in a not fully connected sensor network based on the consensus theory a distributed unscented kalman filter ukf is first derived for nonlinear systems without jumping parameters and then it is extended to develop a distributed multiple model ukf for jmnlss the proposed filtering algorithm is illustrated via a simulation example involving tracking a maneuvering target

conditional densities for continuous time nonlinear hybrid systems with applications to fault detection continuous time nonlinear stochastic differential state and measurement equations all of which have coefficients capable of abrupt changes at a random time are considered finite state jump markov chains are used to model the changes conditional probability densities which are essential in obtaining filtered estimates for these hybrid systems are then derived they are governed by a coupled system of stochastic partial differential equations when the q matrix of the markov chain is either lower or upper diagonal it is shown that the system of conditional density equations is finite dimensional computable these findings are then applied to a fault detection problem to compute state estimates that include the failure time

response of modulated doublet modes to travelling wave excitation the forced vibration of a rotationally periodic structure when subjected to travelling wave excitation is discussed with emphasis placed on the steady state response of doublet modes having either repeated or split frequencies such vibration modes have spatially modulated shapes defined by 1 the number of nodal diameters present in the limiting case of axisymmetry and 2 certain additional fourier harmonics which contaminate and distort their appearances the natural frequency and mode structure of a model periodic structure is discussed in the context of an otherwise axisymmetric disk having evenly spaced sector shaped line distributions of stiffness and inertia through perturbation analysis the contamination wavenumbers present in a doublet having repeated frequency are shown to comprise two subsets the members of which have sine and cosine coefficients of the same or of differing signs for each wavenumber in the mode shape s fourier expansion the structure of the wavenumber content is explored further with respect to the response of repeated and split doublets to a harmonic travelling wave excitation the individual fourier components comprising a modulated doublet can respond and propagate in the same direction as the excitation or opposite to it depending on the wavenumber of the excitation and the subset to which the contamination wavenumber belongs the response of the split frequency doublets and the circumstances under which travelling or standing wave responses or a blend of the two can occur in the structure s reference frame are also examined in the context of the model periodic structure the qualitative character of the response the forward or backward propagation direction of each mode s constituent wavenumber components and the phase speeds of those components are discussed in illustrative case studies

concurrent particle filtering and data association using game theory for tracking multiple maneuvering targets we propose a particle filtering technique to track multiple maneuvering targets in the presence of clutter we treat data association and state estimation which are the two important sub problems in tracking as separate problems we develop a game theoretic framework to solve the data association in which we model each tracker as a player and the set of measurements as strategies we develop utility functions for each player and then use a regret based learning algorithm to find the equilibrium of this game the game theoretic approach allows us to associate measurements to all the targets simultaneously further in contrast to the traditional monte carlo data association algorithms that use samples of the association vector obtained from a proposal distribution our method finds the association in a deterministic fashion we then use monte carlo sampling on the reduced dimensional state of each target independently and thereby mitigate the curse of dimensionality problem that is known to occur in particle filtering we provide a number of numerical results to demonstrate the performance of our proposed filtering algorithm

sub trans and supercritical variable magnitude travelling loads on cylindrical rings abstract the problem of time dependent variable magnitude travelling loads in a closed symmetric structure is considered this includes the circumferential propagation in viscoelastically supported cylindrical rings which can rotate about their axes the main emphasis of the work is to establish the effects of time dependent load variability on the response characteristics when travelling velocities are in the sub trans and supercritical speed ranges this will enable the doppler like interactions among the propagating bending and in plane waves at the various travelling load speed ranges to be evaluated as an example simulation the model is tuned to define the dynamic response characteristics of tires rolling on bumpy surfaces this enables the sub trans and the supercritical response characteristics to be evaluated

boundary classes for graph problems involving non local properties abstract we continue the study of boundary classes for np hard problems and focus on seven np hard graph problems involving non local properties hamiltonian cycle hamiltonian cycle through specified edge hamiltonian path feedback vertex set connected vertex cover connected dominating set and graph vc con dimension our main result is the determination of the first boundary class for feedback vertex set we also determine boundary classes for hamiltonian cycle through specified edge and hamiltonian path and give some insights on the structure of some boundary classes for the remaining problems

on hybrid state estimation for stochastic hybrid systems this paper considers the state estimation problem for the general continuous time stochastic hybrid system shs which has various applications defined on the hybrid state space the shs has the interacting discrete dynamics and continuous dynamics subject to various uncertainties the hybrid state estimation problem is to estimate both the continuous state and the discrete state of the shs with the information given by a continuous time observation process in this paper the hybrid state estimation problem is mathematically formulated and the corresponding filtering equations that are stochastic partial differential equations are derived to describe the evolution of the hybrid state estimates conditioned on the observation history a numerical algorithm based on a finite difference approach is proposed to solve the filtering equations a markov chain mc is constructed on the descretized hybrid state space to approximate the infinitesimal generator of the shs and then hybrid state estimation for the shs is reduced to estimating the state of the mc it is proved that the state estimation results of the mc converge to the solution to the filtering equations as the constructed mc converges to the shs an illustrative example of aircraft tracking is used to demonstrate the performance of the proposed algorithm

control of discrete time hybrid stochastic systems a realistic stochastic control problem for hybrid systems with markovian jump parameters can have switching parameters in both the state and the measurement equations furthermore both the base and jump states in general are not perfectly observed there are only two existing controllers for this problem both with complexity exponentially increasing with time the authors present another control algorithm for stochastic systems with markovian jump parameters this algorithm is derived through the use of stochastic dynamic programming and is designed to be used for realistic stochastic control problems i e with noisy state observations this scheme has fixed computational requirements at each stage and a natural parallel implementation simulation results are used to compare the algorithm with previous schemes

discrete time estimation of a markov chain with marked point process observations application to markovian jump filtering in this paper various discrete time estimation problems are studied for a finite and homogeneous markov chain observed by a marked point process these problems which could have significant applications in target tracking manufacturing or communication theory have never been studied in the literature the quantities to be estimated are the state the number of jumps and the occupation times the identification of the chain transition matrix is also addressed via an expectation maximization procedure solutions in the sense of the conditional distribution are obtained by a change of probability measure and are shown to have convenient recursive forms the efficiency of this new approach for sensor modeling is illustrated by the study of a linear markovian jump filtering problem where in addition to a classical state observation a mode markov point process observation is assumed a numerical example is given

novel extended viterbi based multiple model algorithms for state estimation of discrete time systems with markov jump parameters this paper considers a state estimation problem for discrete time systems with markov switching parameters for this the generalized pseudo bayesian second order extended viterbi gpb2 ev and the interacting multiple model extended viterbi imm ev algorithms are presented the derivations of these new algorithms rely on a nontrival incorporation of some functional mechanisms of a new extended viterbi algorithm into the gpb2 and the imm methods for hypothesis reductions in order to improve computational efficiency and or estimation performance the imm ev and the gpb2 ev algorithm and the imm and the gpb2 algorithm have some common components but their schemes for the calculation of weights and for the combination of the inputs and outputs are different indeed the imm ev and the gpb2 ev algorithm spans the continuum from hard decision methods with merged hypothesis tree style to the imm and the gpb2 algorithm inclusive the proposed algorithms are well suited to state estimation problems in maneuvering target tracking simulations demonstrate that an imm ev algorithm can be an improvement to the imm the gpb2 and the variable structure multiple model with likely model set methods for tracking a target undergoing various types of maneuvers at some unknown times

algorithmic aspects of upper paired domination in graphs abstract a set d of vertices in a graph g is a paired dominating set of g if every vertex of g is adjacent to a vertex in d and the subgraph induced by d contains a perfect matching not necessarily as an induced subgraph a paired dominating set of g is minimal if no proper subset of it is a paired dominating set of g the upper paired domination number of g denoted by pr g is the maximum cardinality of a minimal paired dominating set of g in upper pds it is required to compute a minimal paired dominating set with cardinality pr g for a given graph g in this paper we show that upper pds cannot be approximated within a factor of n 1 e for any e 0 unless p np and upper pds is apx complete for bipartite graphs of maximum degree 4 on the positive side we show that upper pds can be approximated within o factor for graphs with maximum degree we also show that upper pds is solvable in polynomial time for threshold graphs chain graphs and proper interval graphs

algorithmic aspects of semitotal domination in graphs abstract for a graph g v e a set d v is called a semitotal dominating set of g if d is a dominating set of g and every vertex in d is within distance 2 of another vertex of d the minimum semitotal domination problem is to find a semitotal dominating set of minimum cardinality given a graph g and a positive integer k the semitotal domination decision problem is to decide whether g has a semitotal dominating set of cardinality at most k the semitotal domination decision problem is known to be np complete for general graphs in this paper we show that the semitotal domination decision problem remains np complete for planar graphs split graphs and chordal bipartite graphs we give a polynomial time algorithm to solve the minimum semitotal domination problem in interval graphs we show that the minimum semitotal domination problem in a graph with maximum degree admits an approximation algorithm that achieves the approximation ratio of 2 3 ln 1 showing that the problem is in the class log apx we also show that the minimum semitotal domination problem cannot be approximated within 1 ln v for any 0 unless np dtime v o log log v finally we prove that the minimum semitotal domination problem is apx complete for bipartite graphs with maximum degree 4

image enhanced multiple model tracking we consider tracking algorithms for manoeuvring targets when the observations include extra information on the current operating mode of the target obtained from an image sensor the target is modelled as a markov jump linear system and the image based observations form a discrete time point process we derive the optimal minimum mean square error filtered estimate which intrinsically fuses the image based and primary observations this optimal filter is computationally prohibitive but provides the basis for a clear understanding of various suboptimal approaches we propose the image enhanced imm filter as a practical alternative which retains many desirable properties of the optimal filter and outperforms existing image enhanced tracking algorithms over a broad range of operating scenarios

control of nonlinear systems with markovian parameter changes the control of hybrid systems in which a totally observed state process is generated by a nonlinear stochastic differential equation whose parameters are functions of a random jump process called the plant regime is considered regime transitions typically represent target maneuvers in a tracking system the control task is split between a jump detection and identification jdi filter and a discrete adaption or reconfiguration a design that takes into account the errors of the jdi device and the plant nonlinearities to produce a near optimal passively adaptive control law with an easily implemented affine structure is presented

parametric instability of a circular ring subjected to moving springs this work investigates parametric instabilities of in plane bending vibrations of a thin elastic ring subject to forces from discrete rotating springs of arbitrary number spacing and orientation several configurations are examined including systems with symmetric and asymmetric circumferential spring spacing and systems with and without fixed springs the method of multiple scales is applied to analytically identify principal and combination instability boundaries as closed form expressions two different numerical approaches are used to verify the analytical results the effects of different system parameters on the instability boundaries are studied analytically the bending stiffness of the ring the number of springs and their stiffness location orientation and rotation speed for several cases well defined properties for the occurrence or suppression of instabilities are obtained as simple relations in the system parameters

the np completeness of steiner tree and dominating set for chordal bipartite graphs we show that the problems steiner tree dominating set and connected dominating set are np complete for chordal bipartite graphs

the in plane free vibration of an elastically supported thin ring rotating at high speeds revisited abstract the in plane free vibration of a rotating thin ring is revisited in this paper a new model is proposed which accounts for the elastic foundation and the through thickness variation of the radial stress the emphasis is placed on a proper consideration of the geometrical nonlinearity which is essential for the consistent modelling of the ring stiffening resulting from the radial expansion caused by rotation the in plane stability of a thin ring rotating at relatively high speeds is analysed thoroughly it is shown that the ring can become unstable should the rotational speed exceed a critical value this result is new as in most known to the authors previous studies the stability problem is either not considered or it is stated that the in plane vibration of a rotating ring is stable in the studies which did address the instability the conclusions and the employed models are prone to criticism a parametric study is conducted to illustrate the effects of the ring properties on the in plane stability finally modes which appear as stationary displacement patterns of the ring to an observer in the space fixed reference system are investigated it is shown that the stationary patterns can occur prior to the onset of the instability for certain ring parameters

exact bayesian filter and joint imm coupled pda tracking of maneuvering targets from possibly missing and false measurements this paper represents the problem of tracking multiple maneuvering targets from possibly missing and false measurements as one of filtering for a jump linear descriptor system with stochastic i i d coefficients this particular representation serves as an instrument in the characterization of the exact bayesian filter subsequently novel finite dimensional filter algorithms are developed through introducing approximations to the exact bayesian solution one filter approximation assumes conditionally gaussian density of the joint target state given the joint target maneuver mode and the algorithm is referred to as joint imm coupled pda jimmcpda the specialty of this filter algorithm is that both the imm step and the pda step are performed jointly over the modes and states of all targets subsequently the cpda track coalescence avoiding hypothesis pruning approach of blom bloem 2000 probabilistic data association avoiding track coalescence ieee transactions of automatic control 45 247 259 is extended to bring the joint target modes into account the resulting filter algorithm is referred to as track coalescence avoiding joint imm coupled pda the two novel algorithms are compared to immjpda and immpda through monte carlo simulations

robust m ary detection filters and smoothers for continuous time jump markov systems in this paper we consider a dynamic m ary detection problem when markov chains are observed through a wiener process these systems are fully specified by a candidate set of parameters whose elements are a rate matrix for the markov chain and a parameter for the observation model further we suppose these parameter sets can switch according to the state of an unobserved markov chain and thereby produce an observation process generated by time varying jump stochastic parameter sets given such an observation process and a specified collection of models we estimate the probabilities of each model parameter set explaining the observation by defining a new augmented state process then applying the method of reference probability we compute matrix valued dynamics whose solutions estimate joint probabilities for all combinations of candidate model parameter sets and values taken by the indirectly observed state process these matrix valued dynamics satisfy a stochastic integral equation with a wiener process integrator using the gauge transformation techniques introduced by clark and a pointwise matrix product we compute robust matrix valued dynamics for the joint probabilities on the augmented state space in these new dynamics the observation wiener process appears as a parameter matrix in a linear ordinary differential equation rather than an integrator in a stochastic integral equation it is shown that these robust dynamics when discretised enjoy a deterministic upper bound which ensures nonnegative probabilities for any observation sample path in contrast no such upper bounds can be computed for taylor expansion approximations such as the euler maryauana and milstein schemes finally by exploiting a duality between causal and anticausal robust detector dynamics we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations a computer simulation demonstrating performance is included

a decidability result for the dominating set problem we study the following question given a finite collection of graphs g 1 g k is the dominating set problem polynomial time solvable in the class of g 1 g k free graphs in this paper we prove the existence of an efficient algorithm that answers this question for k 2