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

the filtering problem for continuous time linear systems with markovian switching coefficients abstract the stochastic model under consideration is a markovian jump process with finite state space feeding the parameters of a linear diffusion process x the processes y and z observe linearly and separately x and in independent white noises some properties of the finite optimal filter for the x and processes given the history of measurements z are investigated apart from their theoretical interest these results have an interesting practical bearing on the general filtering problem by providing a natural finite suboptimal solution preliminary experimental results show the effectiveness of our approach to estimate the state trajectory even with a relatively low signal to noise ratio on the measurement processes

some applications of an implicit duality theorem to connections of structures of special types including dirac and reciprocal structures abstract in this paper we present some applications of an implicit duality theorem which was originally a folklore result on ideal transformers in electrical network theory we show among other things that results on reciprocal networks due to tellegen proc inst radio engrs 14 1953 265 and dirac structures due to van der schaft in j w polderman h l trentelman eds from intelligent control to behavioural systems university of groningen press follow as a consequence these results have the form interconnection of structures of a particular kind yields a structure of the same kind also discussed is the question given smaller structures of a given kind and a desired structure of the same kind can the former be interconnected to yield the latter we also indicate the range of possible generalizations of this result

filters for estimating markov modulated poisson processes and image based tracking we present algorithms for state and parameter estimation of markov modulated poisson processes mmpp we first derive finite dimensional innovations and zakai filters for various statistics of a mmpp using these filters a filter based expectation maximization algorithm is derived for computing maximum likelihood parameter estimates finally we present an application of the techniques in image based tracking by estimating the state of a markovian jump linear system

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

a subspace approach to linear dynamical systems abstract in this paper we present an approach to linear dynamical systems which combines the positive features of two well known formulations namely standard state space theory see for e g wonham 1978 9 and behavioural systems theory see polderman and willems 1997 4 our development is also geometric in the tradition of wonham and others but instead of using explicit linear maps we work with linear relations implicitly which amounts to working with subspaces one of our primary motivations is computational efficiency all our computations can be performed on the system as it is without elimination of variables and further unlike the behaviourists who manipulate matrices with polynomial entries we work only with real matrices using our formulation we derive the standard vector space results on controlled and conditioned invariant subspaces of linear dynamical systems duality which is a distinctive feature of state space theory but not of the behavioural view point comes out naturally in our approach too through the use of the adjoint we illustrate our ideas for an important class of dynamical systems viz electrical networks the theory proposed in this paper gives a unified description of both the standard linear dynamical systems and the linear singular systems or the linear descriptor systems see for e g f gantmacher 1959 1 and lewis 1986 2 therefore the algorithms described for the invariant spaces in this paper are also applicable to linear singular systems

exact finite dimensional filters for maximum likelihood parameter estimation of continuous time linear gaussian systems in this paper we derive a new class of finite dimensional filters for integrals and stochastic integrals of moments of the state for continuous time linear gaussian systems apart from being of significant mathematical interest these new filters can be used with the expectation maximization em algorithm to yield maximum likelihood estimates of the model parameters

on the notion of generalized minor in topological network theory and matroids abstract in this paper we consider a linking operation between matroids defined as m s p m s m s p m s p where m s p and m s are matroids on sets s p and s respectively this operation can be seen as a generalization of the minor operations on matroids in the sense that we can speak of a minor of a matroid on s p relative to another matroid on s this is analogous to a similar idea for vector spaces which is useful in topological network theory we show some interesting properties for this linking operation these include 1 an implicit duality theorem which says that the dual of the generalized minor of m s p relative to m s is same as the generalized minor of m s p relative to m s 2 attaching two matroids along a common independent set such that the resulting matroid contains the two matroids as restrictions 3 a topological transformation result where given two matroids on the same underlying set we build a matroid on a bigger set such that the two matroids can be obtained as minors of the larger matroid analogy between topological network theory and matroids leads us to a construction of self dual matroids starting from smaller and simpler self dual matroids we use the implicit duality result to show that if m s p and m s are self duals then m s p m s is also a self dual matroid finally we show that this linking idea can be directly extended to polymatroid rank functions

a detector based approach for the h_ 2 control of markov jump linear systems with partial information in this paper we study the h 2 control for discrete time markov jump linear systems mjls with partial information we consider the case in which we do not have access to the markov jump parameter but instead there is a detector that emits signals which provides information on this parameter a salient feature of our formulation is that it encompasses for instance the cases with perfect information no information and cluster observations of the markov parameter which were previously analyzed in the markov jump control literature the goal is to derive a feedback linear control using the information provided by the detector in order to stochastically stabilize the closed loop system we present two lyapunov like equations for the stochastic stability of the system in addition we show that a linear matrix inequalities lmi formulation can be obtained in order to design a stochastically stabilizing feedback control in the sequel we deal with the h 2 control problem and we show that again an lmi optimization problem can be formulated in order to design a stochastically stabilizing feedback control with guaranteed h 2 cost we also present two special cases one of them always satisfied for the limit case in which the detector provides perfect information on the markov parameter and the bernoulli jump case under which lmi conditions become necessary and sufficient for the stochastic stabilizability of the system and the lmi optimization problems provide the optimal h 2 cost for the bernoulli jump case we show that our formulation generalizes previous ones the case with convex polytopic uncertainty on the parameters of the system and on the transition probability matrix is also considered the paper is concluded with some numerical examples

exact filters for doubly stochastic ar models with conditionally poisson observations the authors derive exact filters for the state of a doubly stochastic auto regressive ar process with parameters which vary according to a nonlinear function of a gauss markov process the observations consist of a discrete time poisson process with rate a positive function of the gauss markov process the dimension of the sufficient statistic increases linearly with the number of observed events

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

bayesian analysis for the poly weibull distribution abstract in this article bayesian analysis for a poly weibull distribution using informative priors is discussed this distribution typically arises when the data is the minimum of several weibull failure times from competing risks to perform the bayesian computations simulation using the gibbs sampler is suggested this can be used to find posterior moments the marginal posterior probability density function and the predictive risk or reliability

on an infinite dimensional perturbed riccati differential equation arising in stochastic control existence and uniqueness of solutions for a class of infinite dimensional perturbed riccati differential equations in a certain banach space is our main concern in this paper besides the interest in its own right this class arises in control problems involving linear systems with countably infinite markov jump parameters

a hierarchical approach to regional flood frequency analysis a hierarchical approach to regional flood frequency estimation is described where higher order parameters controlling the skewness of annual maximum floods are determined from larger regions than are used for determining parameters controlling the coefficient of variation procedures based on two component extreme value and generalized extreme value distributions are developed and it is shown that dividing a region into subregions to estimate some parameters can lead to more precise quantile estimates the practical problem of defining the optimum number of subregions is discussed

robust kalman filtering for discrete time markovian jump systems with parameter uncertainty in this paper we examine the problem of robust kalman filtering for a class of linear uncertain discrete time systems with markovian jump parameters the underlying system is subjected to norm bounded time varying uncertainties in the state and measurement equations first stochastic quadratic stability of the system is studied then a linear state estimator is constructed such that the estimation error covariance is guaranteed to lie within certain bound for all admissible uncertainties the solution is given in terms of two coupled algebraic riccati equations

a hierarchical and empirical bayes approach for the regional pearson type iii distribution regional information has proved to be particularly valuable for estimating the higher order parameters of flood series distributions this has suggested the use of a hierarchical approach for regional curve fitting in which higher order moment ratios such as the coefficient of skewness and the coefficient of kurtosis are estimated over larger areas than lower order moment ratios such as the coefficient of variation this philosophy is applied here for the pearson type iii distribution and is combined with an empirical bayes approach for the estimation of the scale parameter this work is specifically aimed at estimating flood frequencies and quantiles at sites with short record lengths some simulation experiments are reported for an evaluation of the performance of the method and an application on a set of 59 ontarian flood series having long record length plus two example stations with short record length is described for illustrative purposes

two component extreme value distribution for flood frequency analysis theoretical considerations supported by statistical analysis of 39 annual flood series afs of italian basins suggest that the two component extreme value tcev distribution can be assumed as a parent flood distribution i e one closely representative of the real flood experience this distribution belongs to the family of distributions of the annual maximum of a compound poisson process which is a solid theoretical basis for afs analysis however the two parameter distribution of this family obtained on the assumption of identically distributed floods does not account for the high variability of both observed skewness and largest order statistics so that a significant number of observed floods qualify as outliers under this distribution the more general tcev distribution assumes individual floods to arise from a mixture of two exponential components its four parameters can be estimated by the maximum likelihood method a regionalized tcev distribution with parameters representative of a set of 39 italian afs s was shown to closely reproduce the observed distribution of skewness and that of the largest order statistic

nonlinear filtering for systems with random structure this note studies the nonlinear filtering problem for a linear system with random structure governed by a finite state markov process a characterization of the optimal mean square filter is derived and some suboptimal filter approximations are presented

stochastic stability of ito differential equations with semi markovian jump parameters in this note the problem of stochastic stability for linear systems with jump parameters being semi markovian rather than full markovian is further investigated in particular the system under consideration is described by ito type nonlinear stochastic differential equations with phase type semi markovian jump parameters stochastic stability conditions are presented

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

robust flood frequency models the concept of a robust model is briefly explored in the context of flood frequency analysis two necessary properties of a robust model are advanced namely resistance and efficiency strategies for seeking more robust models are discussed because of its versatility the five parameter wakeby distribution can credibly be considered a parent flood distribution four regionalized wakeby parents are employed in simulation studies to search for robust models these parents were shown by houghton to be representative of u s flood experience in the sense that certain raw flood data characteristics could be reproduced a limited range of sampling experiments were undertaken the results suggest that of the site specific estimators considered the two parameter log normal maximum likelihood estimator is most resistant with gumbel estimators employing either maximum likelihood or probability weighted moments displaying comparable resistance several estimators which utilize regional flood information were compared included were empirical bayes estimators which are structurally similar to james stein rules and regionalized estimators based on the flood index method these estimators exhibited substantial improvements in aggregate risk performance over their site specific counterparts particularly for short record lengths regionalized estimators appear to be preferable for short record lengths while estimators which combine both site and regional flood information are preferable for longer record lengths when such estimation procedures are considered other distributional models such as log pearson type iii and wakeby become practical alternatives to the two parameter log normal model

exact finite dimensional filters for doubly stochastic auto regressive processes in this paper we derive exact finite dimensional recursive filters for a class of doubly stochastic auto regressive ar models we assume that the parameters of the doubly stochastic ar process vary according to a nonlinear polynomial function of a gaussian state space process apart from being of mathematical interest these finite dimensional filters have potential applications in time series analysis and image enhanced tracking of maneuvering targets

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

brief optimal filtering of doubly stochastic auto regressive processes in this paper exact finite dimensional filters are derived for a class of doubly stochastic auto regressive models the parameters of the doubly stochastic auto regressive process vary according to a nonlinear function of a gauss markov process we develop a difference equation for the evolution of an unnormalized conditional density related to the state of the doubly stochastic auto regressive process we then give a characterization of the general solution followed by examples for which the state of the filter is determined by a finite number of sufficient statistics these new finite dimensional filters build upon the discrete time kalman filter

the performance of the two component extreme value distribution in regional flood frequency analysis the performance of the regional two component extreme value tcev estimation procedure in estimating both dimensionless regional frequency curves showing the t year flood as a multiple of the mean annual flood and site curves incorporating local and regional information was assessed using computer simulation experiments it was found that the tcev procedure produces estimates of both dimensionless regional curves and scaled site quantiles that are relatively unbiased but very variable when data are drawn from tcev or wakeby parents although estimates are very biased when data follow a gev distribution the tcev procedure is robust in the sense that its worst efforts are less bad than those of the alternatives considered but performance declines significantly as sample sizes reduce

a 2 sprt based approach to multiple model hypothesis testing for multi distribution detection this paper presents an approach to multiple model hypothesis testing mmht based on 2 sprt 2 mmsrpt for detecting unknown events that may have multiple possible distributions the sequential probability ratio test sprt based mmht method mmsprt is promising because of its efficiency and theoretical validity however it may suffer from sprt s lack of an upper bound on its stopping time especially in the mis specified case the proposed 2 mmsprt algorithm not only copes with this problem but also is in a setting that can provide efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints specifically we prove the theoretical validity of 2 sprt for the problem of testing hypotheses with multivariate normal densities moreover we present a technique of forced independence and identical distribution i i d to map the non i i d likelihood ratio sequence to an i i d one which enables us to apply the sprt and 2 sprt effectively to the dynamic case under the linear gaussian assumption with a non identical distribution also 2 mmsprt s detection efficiency under some assumptions approximations is verified performance of 2 mmsprt is evaluated for signal detection and model set selection problems in several scenarios simulation results demonstrate the detection efficiency of the proposed 2 mmsprt compared with the mmsprt and some traditional tests

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

optimal control of jump linear gaussian systems this paper investigates the problem of controlling a discrete time linear system with jump parameters a review of the literature is presented as well as a development of the application of dynamic programming to this class of control problems dynamic programming has been applied by many researchers and it was observed that no closed form analytical solution could be constructed because of the dual aspects of the controller the main contribution of the present work is an algorithm suitable for computer implementation for the optimal dual control the construction of the algorithm is based on transforming the dynamic programming relations into a space of sufficient statistics and using a finite dimensional optimization procedure to obtain the optimal control as a function of the statistics this is achieved by first developing a suitable recursive realization of a filter which generates the sufficient statistics for the problem and then embedding this filter into the dynamic programming equations

kalman filtering for linear systems with coefficients driven by a hidden markov jump process abstract we present an explicit algorithm for the solution of the nonlinear filtering problem concerning a linear partially observed diffusion type model where the coefficients are driven by a hidden markov jump process of which one can observe the occurrence of a jump the recursive filter is of a branching type with its finite dimension growing for each jump of the hidden markov process

discrete time point process filter for mode estimation a discrete time model of an image based observation channel using point processes is presented in the context of target tracking improvement a multidimensional point process filter was developed to effectively estimate the actual mode of the target in the presence of the clutter the structure and updating properties of the filter have been studied the sample behavior and the robustness with respect to modeling parameters are illustrated by simulation examples

on the decomposition of vector spaces abstract this paper attempts to put the notion of network decomposition into multiports in electrical network theory on a rigorous mathematical footing this is done by first defining the notion of decomposition for vector spaces the given vector space v defined on s is expressed as v a i p i v p s where v a i p i are defined on a i p i with a i s and v p is defined on p i the following questions are examined when can given v a i p i be coupled to make up a specified v s when is the decomposition minimal i e when is p minimum a i being specified and what are its characteristic properties how to build a minimal decomposition can a minimal decomposition be built preserving certain matroid properties going from the original to the decomposition such as decomposing a graph into graphs can one recover the matroid of the original vector space knowing the matroids of the decomposition it is shown that operations on the original vector space such as contraction restriction and dualization can be performed indirectly by using the same operation on the decomposition finally applications which in fact gave rise to the theory to network analysis are described