optimal waveform selection for tracking systems investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations the authors give explicit expressions for two one step ahead optimization problems for a single target in white gaussian noise when the tracker is a conventional kalman filter these problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse in cases where target motion is restricted to one dimension closed form solutions to the local one step ahead waveform optimization problem have been obtained the optimal waveform selection algorithms in the paper may be included with conventional kalman filtering equations to form an enhanced kalman tracker simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators including multiple waveform classes the extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed

reducing conservatism in an h_ infty robust state feedback control design of t s fuzzy systems a nonmonotonic approach this paper proposes an h infty robust state feedback controller design for uncertain takagi sugeno fuzzy systems using a nonmonotonic lyapunov function in the nonmonotonic approach the monotonicity requirement of the lyapunov function is relaxed by allowing it to increase locally based on the nonmonotonic lyapunov function approach sufficient conditions for the existence of a robust state feedback h infty controller that guarantees stability and a prescribed h infty performance are given in terms of linear matrix inequalities the proposed design technique is shown to be less conservative than the existing k samples variations of the lyapunov function the effectiveness of the proposed approach is further illustrated via numerical examples

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

recursive estimation of images using non gaussian autoregressive models we consider recursive estimation of images modeled by non gaussian autoregressive ar models and corrupted by spatially white gaussian noise the goal is to find a recursive algorithm to compute a near minimum mean square error mmse estimate of each pixel of the scene using a fixed lookahead of d rows and d columns of the observations our method is based on a simple approximation that makes possible the development of a useful suboptimal nonlinear estimator the algorithm is first developed for a non gaussian ar time series and then generalized to two dimensions in the process we draw on the well known reduced update kalman filter kf technique of woods and radewan 1977 to circumvent computational load problems several examples demonstrate the non gaussian nature of residuals for ar image models and that our algorithm compares favorably with the kalman filtering techniques in such cases

tracking in clutter with strongest neighbor measurements i theoretical analysis when tracking a target in clutter a measurement may have originated from either the target clutter or some other source the measurement with the strongest intensity amplitude in the neighborhood of the predicted target measurement is known as the strongest neighbor sn measurement a simple and commonly used method for tracking in clutter is the so called strongest neighbor filter snf which uses the sn measurement at each time as if it were the true one the paper deals with tracking in clutter with the sn measurements it presents analytic results along with useful comments for the sn measurement and the snf including the a priori and a posteriori probabilities of data association events the conditional probability density functions and the covariance matrices of the sn measurement and various mean square error matrices of state prediction and state update these results provide valuable insight into the problem of tracking in clutter and theoretical foundation for the development of improved tracking algorithms for performance analysis prediction and comparison of tracking with the sn measurements and for solving some important detection tracking problems such as the optimal determination of the detection threshold and gate size

the defect of generalized fourier matrices the n n complex hadamard matrices form a real algebraic manifold cn we have cn mn t nun and following tadej and yczkowski we investigate here the computation of the enveloping tangent space t hcn thmn t thnun and notably of its dimension d h dim t hcn called undephased defect of h our main result is an explicit formula for the defect of the fourier matrix fg associated to an arbitrary finite abelian group g zn1 znr we also comment on the general question does the associated quantum permutation group see the defect with a probabilistic speculation involving diaconis shahshahani type variables

the optimal order of processing sensor information in sequential multisensor fusion algorithms we examine the order of sensor processing in the sequential multisensor probabilistic data association mspda filter for target tracking applications if two sensors of different qualities are used in the sequential mspda filter the r m s position error is generally smaller when the worse sensor is processed first this finding regarding the order of sensor processing is supported by simulations of a target tracking system and by analysis of firstthrough sixth order target process models using the modified riccati equation

finding decompositions of a class of separable states abstract we consider the class of separable states which admit a decomposition i a i b i with the b i s having independent images we give a simple intrinsic characterization of this class of states given a density matrix in this class we construct such a decomposition which can be chosen so that the a i s are distinct with unit trace and then the decomposition is unique we relate this to the facial structure of the set of separable states the states investigated include a class that corresponds under the choi jamiolkowski isomorphism to the quantum channels called quantum classical and classical quantum by holevo

output feedback control for t s fuzzy delta operator systems with time varying delays via an input output approach in this paper the problem of induced l 2 disturbance attenuation control is investigated for discrete time takagi sugeno t s fuzzy delta operator systems with time varying delays and disturbance input via an input output approach a model transformation method is utilized to approximate the time varying delay in t s fuzzy delta operator systems by applying the scaled small gain ssg theorem and lyapunov krasovskii functional approach a sufficient condition is established to guarantee that the closed loop system is asymptotically stable and has an induced l 2 disturbance attenuation performance the existence condition of the dynamic output feedback controller can be solved via convex optimization problems finally simulation results are given to demonstrate the feasibility and effectiveness of the proposed method

fault tolerant control for fuzzy switched singular systems with persistent dwell time subject to actuator fault abstract this paper investigates the problem of fault tolerant state feedback fuzzy control for discrete time nonlinear switched singular systems subject to the actuator fault the typical takagi sugeno model is utilized to process the nonlinearity of the systems for the purpose of describing the intermittent occurrence of fast and slow switching among subsystems a switching signal complying with persistent dwell time switching regularity is introduced for the first time into the analysis of nonlinear switched singular systems the primary objective is focused on constructing a fault tolerant controller which can ensure that the closed loop system is exponentially admissible with a prescribed l 2 gain performance in the presence of actuator fault by using mode dependent lyapunov function and employing an improved matrix decoupling method sufficient conditions with less conservatism for the existence of the desired controller are established and the explicit form of the controller gains is presented for explaining the effectiveness of the proposed method two illustrative examples are given finally

stability of cascaded fuzzy systems and observers a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents it is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system therefore several stability conditions have been developed for ts fuzzy systems we study a special class of nonlinear dynamic systems that can be decomposed into cascaded subsystems which are represented as ts fuzzy models we analyze the stability of the overall ts system based on the stability of the subsystems and prove that the stability of the subsystems implies the stability of the overall system the main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed thereby solving some of the feasibility problems another benefit is that by using this approach the dimension of the associated linear matrix inequality lmi problem can be reduced for naturally distributed applications such as multiagent systems the construction and tuning of a centralized observer may not be feasible therefore we also extend the cascaded approach to the observer design and use fuzzy observers to individually estimate the states of these subsystems a theoretical proof of stability and simulation examples are presented the results show that the distributed observer achieves the same performance as the centralized one while leading to increased modularity reduced complexity lower computational costs and easier tuning applications of such cascaded systems include multiagent systems distributed process control and hierarchical large scale systems

integration of bayes detection with target tracking existing detection systems generally are operated using a fixed threshold and optimized to the neyman pearson criterion an alternative is bayes detection in which the threshold varies according to the ratio of prior probabilities in a recursive target tracker such as the probabilistic data association filter pdaf such priors are available in the form of a predicted location and associated covariance however the information is not at present made available to the detector put another way in a standard detection tracking implementation information flows only one way from detector to tracker here we explore the idea of two way information flow in which the tracker instructs the detector where to look for a target and the detector returns what it has found more specifically we show that the bayesian detection threshold is lowered in the vicinity of the predicted measurement and we explain the appropriate modification to the pdaf the implementation is simple and the performance is remarkably good

on some classes of bipartite unitary operators we investigate unitary operators acting on a tensor product space with the property that the quantum channels they generate via the stinespring dilation theorem are of a particular type independently of the state of the ancilla system in the stinespring relation the types of quantum channels we consider are those of interest in quantum information theory unitary conjugations constant channels unital channels mixed unitary channels ppt channels and en tanglement breaking channels for some of the classes of bipartite unitary operators corresponding to the above types of channels we provide explicit characterizations necessary and or sufficient conditions for membership and we compute the dimension of the corresponding algebraic variety inclusions between these classes are considered and we show that for small dimensions many of these sets are identical

probabilistic data association for systems with multiple simultaneous measurements we consider the problem of estimating the state of a discrete time linear stochastic system whose observation process consists of a finite set of known linear measurement models the correspondence of the measurements with the models is unknown assuming all the measurements relate to the state we derive a recursive algorithm the multiple simultaneous measurement filter msmf which provides a fixed complexity sub optimal solution to this problem the msmf is a generalization of the discrete time kalman filter and reduces to the latter when a single measurement model applies simulations are provided that demonstrate the superior performance of the msmf over the probabilistic data association filter for tracking a single target in an environment where up to three measurements of the state are received simultaneously

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

brief paper consistency and robustness of pdaf for target tracking in cluttered environments this paper presents a simulation based investigation of the consistency of the pdaf via statistical tests of its actual errors versus the filter calculated covariances these tests confirm the goodness of the approximation done at every stage in the pdaf where a gaussian mixture is replaced by an umbrella gaussian using moment matching two versions of the pdaf are examined a parametric one that uses a poisson model for the number of clutter originated measurements and a nonparametric one that uses a diffuse prior while no new theoretical results are presented the methodology of testing filter consistency can prove to be useful in the general evaluation of filters that contain approximations

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

stability evaluation and track life of the pdaf for tracking in clutter the authors present an effective approach of a hybrid nature to the nonsimulation performance evaluation of the probabilistic data association filtering pdaf method for tracking in clutter in this approach a continuous valued covariance which is a function of a discrete valued random variable the number of validated measurements is used to characterize the tracking errors in an average sense this covariance can be calculated offline recursively from a modified riccati equation which can be obtained by replacing the measurement dependent terms in the original stochastic equation with their conditional expectations this approach has the merit that it yields a quantification of the transients of tracking divergence as well as substantially better accuracy than previous work such an approach is particularly suitable for stability evaluation of tracking filters in addition a quantitative study of the track life problem is made in which the number of validated measurements plays a central role

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

h_ infty observer design for fuzzy system with immeasurable state variables via a new lyapunov function this paper is concerned with the design of h infty observers for fuzzy system with immeasurable state variables via a new lyapunov function by decomposing the space of premise variables into crisp regions and fuzzy regions piecewise fuzzy h infty observers are established at different instants to cope with the challenges caused by the mismatch of the premise variables and exogenous disturbances based on the proposed new lyapunov functions that depend on the different regions where the premise variables are located sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the stability and desired performance of the error systems finally a simulation example is provided to show that the new design technology proposed in this paper achieves better h infty performance than the existing design methods

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

h2 guaranteed cost fuzzy control design for discrete time nonlinear systems with parameter uncertainty this paper presents a design method of h 2 guaranteed cost gc fuzzy controllers for discrete time nonlinear systems with parameter uncertainties the takagi and sugeno t s fuzzy model with parameter uncertainties is employed to represent an uncertain discrete time nonlinear system a sufficient condition for the existence of h 2 gc fuzzy controllers is presented in terms of linear matrix inequalities lmis the resulting fuzzy controllers not only guarantee that the closed loop fuzzy system is quadratically stable but also provide a guaranteed cost on the h 2 performance index furthermore an optimal h 2 gc fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an lmi optimization procedure finally it is also demonstrated through numerical simulations on the backing up control of a truck trailer that the proposed design method is effective

on bipartite unitary matrices generating subalgebra preserving quantum operations we study the structure of bipartite unitary operators which generate via the stinespring dilation theorem quantum operations preserving some given matrix algebra independently of the ancilla state we characterize completely the unitary operators preserving diagonal block diagonal and tensor product algebras some unexpected connections with the theory of quantum latin squares are explored and we introduce and study a sinkhorn like algorithm used to randomly generate quantum latin squares

on birkhoff s theorem for doubly stochastic completely positive maps of matrix algebras abstract a study is made of the extreme points of the convex set of doubly stochastic completely positive maps of the matrix algebra m n if n 2 the extreme points are precisely the unitary maps but if n 3 there are nonunitary extreme points examples of which are exhibited a tilde operation is defined on the linear maps of m n and used to give an elementary derivation of a result of kummerer and maassen

detection thresholds for tracking in clutter a connection between estimation and signal processing in the kalman bucy filter and other trackers the dependence of tracking performance upon the quality of the measurement data is well understood in terms of the measurement noise covariance matrix which specifies the uncertainty in the values of the measurement inputs the measurement noise and process noise covariances determine via the riccati equation the state estimation error covariance when the origin of the measurements is also uncertain one has the widely studied problem of data association or data correlation and tracking performance depends critically on signal processing parameters primarily the probabilities of detection and false alarm in this paper we derive a modified riccati equation that quantifies approximately the dependence of the state error covariance on these parameters we also show how to use a receiver operating characteristic roc curve in conjunction with the above relationship to determine the detection threshold in the signal processing system that provides measurements to the tracker so as to minimize tracking errors the approach presented in this paper provides a feedback mechanism from the information processing tracking subsystem to the signal processing subsystem so as to optimize the overall performance in clutter

overgroups of some classical linear groups with applications to linear preserver problems abstract the study of linear operators on a matrix space that leave invariant certain functions subsets or relations is commonly referred to as the study of linear preserver problems and has attracted the attention of many mathematicians in the last few decades dynkin in his classic paper studied maximal subgroups of the classical groups and showed how his results may be used to study preserver problems the purpose of this paper is to further exploit this very powerful approach the subgroups g of the general linear group that we deal with are not necessarily maximal for the applications that we have in mind we obtained a description of all possible overgroups of g the results are then applied to various linear preserver problems shorter alternative proofs for various existing results are given and some open questions are answered

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

variance estimation and ranking of target tracking position errors modeled using gaussian mixture distributions in this paper variance estimation and ranking methods are developed for stochastic processes modeled by gaussian mixture distributions it is shown that the variance estimate from a gaussian mixture distribution has the same properties as the variance estimate from a single gaussian distribution based on a reduced number of samples hence well known tools for variance estimation and ranking of single gaussian distributions can be applied to gaussian mixture distributions as an application example we present optimization of sensor processing order in the sequential multi target multi sensor joint probabilistic data association msjpda algorithm

defect of a unitary matrix abstract we analyze properties of a map f sending a unitary matrix u of size n into a doubly stochastic matrix b f u defined by bi j ui j 2 for any u we define its defect determined by the dimension of the image df t u u of the space t u u tangent to the manifold of unitary matrices u at u under the tangent map df corresponding to f the defect of u equal to zero for a generic unitary matrix gives an upper bound for the dimension of a smooth orbit a manifold stemming from u of inequivalent unitary matrices mapped into the same doubly stochastic matrix b f u we demonstrate several properties of the defect and prove an explicit formula for the defect of the fourier matrix fn of size n in this way we obtain an upper bound for the dimension of a smooth orbit of inequivalent unitary complex hadamard matrices stemming from fn it is equal to zero iff n is prime and coincides with the dimension of the known orbits if n is a power of a prime two constructions of these orbits are presented at the end of this work

no signalling assisted zero error capacity of quantum channels and an information theoretic interpretation of the lovasz number we study the one shot zero error classical capacity of a quantum channel assisted by quantum no signalling correlations and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one quantum no signalling correlations are viewed as two input and two output completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal both problems lead to simple semidefinite programmes sdps that depend only on the choi kraus operator space of the channel in particular we show that the zero error classical simulation cost is precisely the conditional min entropy of the choi jamiolkowski matrix of the given channel the zero error classical capacity is given by a similar looking but different sdp the asymptotic zero error classical capacity is the regularization of this sdp and in general we do not know of any simple form interestingly however for the class of classical quantum channels we show that the asymptotic capacity is given by a much simpler sdp which coincides with a semidefinite generalization of the fractional packing number suggested earlier by aram harrow this finally results in an operational interpretation of the celebrated lovasz vartheta function of a graph as the zero error classical capacity of the graph assisted by quantum no signalling correlations the first information theoretic interpretation of the lovasz number

complex obtuse random walks and their continuous time limits we study a particular class of complex valued random variables and their associated random walks complex obtuse random variables they generalize to the complex case the real valued obtuse random variables introduced in equations de structure pour des martingales vectorielles seminaire de probabilites xxviii p 256278 lecture notes in math vol 1583 springer berlin 1994 in order to understand the structure of normal martingales in mathbb r n the extension to the complex case is motivated by quantum statistical mechanics in particular for characterizing those quantum baths acting as classical noises the extension of obtuse random variables to the complex case is far from obvious and makes use of very interesting algebraical structures we show that complex obtuse random variables are characterized by a 3 tensor which admits certain symmetries we show that these symmetries are the exact 3 tensor analogue of the normal character for 2 tensors i e matrices that is a necessary and sufficient condition for being diagonalizable in some orthonormal basis we discuss the passage to the continuous time limit for these random walks and show that they converge in distribution to normal martingales in mathbb c n we show that the 3 tensor associated to these normal martingales encodes their behavior in particular the diagonalization directions of the 3 tensor indicate the directions of the space where the martingales behaves like a diffusion and those where it behaves like a poisson process we finally prove the convergence in the continuous time limit of the corresponding multiplication operators on the canonical fock space with an explicit expression in terms of the associated 3 tensor again

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller