on the communication complexity of distributed algebraic computation abstract we consider a situation where two processors p sub 1 and p sub 2 ar e to evaluate a collection of functions function 1 function 8 of two vector variables x y under the assumption that processor p sub 1 respectively p sub 2 has access only to the value of the variable x respectively y and the functional form of function 1 function 8 we provide some new bounds on the communication complexity the amount of information that has to be exchanged between the processors for this problem an almost optimal bound is derived for the case of one way communication when the functions function 1 function 8 are polynomials we also derive some new lower bounds for the case of two way communication which improve on earlier bounds by abelson a 80 as an application we consider the case where x and y are n x n matrices and f x y is a particular entry of the inverse of x y under certain restriction on the class of allowed communication protocols we obtain an omega n squared lower bound in contrast to the omega n lower bound obtained by applying abelson s results our results are based on certain tools from classical algebraic geometry and field extension theory

a note on the elastodynamic load transfer problem abstract this paper illustrates the solution of elastodynamic load transfer problems involving a cylindrical elastic bar partially embedded in a homogeneous isotropic elastic half space using a solution scheme based on a coupled variational boundary integral equation algorithm the present solution scheme has several advantages over conventional schemes based on the fictitious bar extended half space model when applied to solve elastodynamic load transfer problems the analysis ensures limiteddisplacement compatibility andtraction continuity along thetrue contact surface between the bar and the half space the solution scheme is based on an elastodynamic variational principle and utilizes appropriate green s function representations for the surrounding half space selected numerical results for torsional and axial impedances of the bar half space system are presented and these are compared with those obtained previously on the basis of the fictitious bar extended half space model in addition the bar displacement and the bar stress resultant profiles are presented for torsion and axial load transfer problems to portray the dependence of the load diffusion on the governing parameters of the bar half space system

some aspects of fusion in estimation theory the problem of fusing or combining various estimates to obtain a single good estimate is investigated the problem of fusion in estimation theory is addressed and several examples using common distributions in which virtually any method of fusion would be useless in approximating the random variable of interest are presented a theorem which for a very general situation shows that fusion resulting in an almost surely exact approximation is always possible is presented in particular this result addresses the situation in which the data consists of the random variable of interest corrupted by additive gaussian noise and the random variable of interest could be any second order random variable finally an example which illustrates the utility of this result is presented

dynamic quantizer design for hidden markov state estimation via multiple sensors with fusion center feedback this paper considers the state estimation of hidden markov models by sensor networks the objective is to minimize the long term average of the mean square estimation error for the underlying finite state markov chain by employing feedback from the fusion center a dynamic quantization scheme for the sensor nodes is proposed and analyzed by a stochastic control approach dynamic rate allocation is also considered when the sensor nodes generate mode dependent measurements

distributed estimators for nonlinear systems a nonlinear distributed estimation problem is solved by using reduced order local models using local models with lower dimensions than the observed process model will lessen the local processors complexities or computational loads fusion algorithms that combine local densities to construct the centralized density of a nonlinear random process are presented the local densities are generated at each measurement time and communicated to a coordinator the models used to produce these densities are reduced order valid models the validity of the local models guarantees that the coordinator reconstructs exactly the centralized density function

smoothing error dynamics and their use in the solution of smoothing and mapping problems martingale decomposition techniques are used to derive markovian models for the error in smoothed estimates of processes described by linear models driven by white noise these models together with some simple hilbert space decomposition ideas provide a simple unified framework for examining a variety of problems involving the efficient assimilation of spatial data which we refer to as mapping problems algorithms for several different mapping problems are derived a specific example of map updating for a two dimensional random field is included

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

nonlinear filtering and control of a switching diffusion with small observation noise this paper is concerned with nonlinear filtering and control of a switching diffusion coupled by an unknown markov chain two statistical estimation methods are used to track the unknown markov chain computable approximate filters are obtained based on these methods the filters are then used to construct controls for the partially observed system these controls are shown to be asymptotically optimal as the observation noise tends to zero finally an example is considered and numerical experiments are reported

distributed multisensor parameter estimation in dependent noise the problem of distributed estimation of a weak nonrandom location parameter theta in additive stationary dependent noise is addressed multisensor configurations with and without a coordinator are considered dependence in the sensor observations is described by m dependent phi mixing and p mixing models two cases of interest are addressed one in which sensor observations are dependent across time but independent across sensors and one in which sensor observations are dependent across both time and sensors numerical results on the performance evaluation of the various estimation schemes derived are presented and the relative performances of the various schemes are compared

combining and updating of local estimates and regional maps along sets of one dimensional tracks in this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates generated at different times of the same process sample path the first of these cases has applications in decentralized estimation while the second has applications in updating maps of spatially distributed random quantities given measurements along several tracks the method of solution for the second problem uses the result of the first and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields

stochastic adaptive one step ahead optimal controllers based on input matching optimal adaptive controller based on the els algorithm is established using the input matching technique the control signal is reduced to a constant weighted sum of the measurable information state vector components using a one step ahead quadratic cost function to govern the behavior of the stochastic linear systems the control effort can be estimated globally the algorithm also predicts the convergence rate with no excitation condition the closed loop system is globally stable and the input converges to the one step ahead optimal input

on the load transfer from a rigid cylindrical inclusion into an elastic half space abstract the present paper examines the problems related to the axial lateral and rotational loading of a rigid cylindrical inclusion which is embedded in bonded contact at the boundary of an isotropic elastic half space the rigid inclusion is modeled as a field of distributed forces which represent the normal and shear tractions that act on the inclusion elastic medium interface the intensities of these distributed tractions are determined by enforcing displacement compatibility conditions at discrete locations of the interface these compatibility conditions are derived from rigid body displacement modes appropriate for each loading the results derived from this numerical scheme are compared with equivalent results derived via analytical techniques which focus on the solution of the governing integral equation schemes and other approximate solution schemes the numerical results presented in the paper illustrate the manner in which the generalized stiffnesses of the embedded inclusion are influenced by its geometry and poisson s ratio of the half space region

distributed estimation in energy constrained wireless sensor networks in this paper we consider distributed estimation of a noise corrupted deterministic parameter in energy constrained wireless sensor networks from energy distortion perspective given a total energy budget allowable to be used by all sensors there exists a tradeoff between the subset of active sensors and the energy used by each active sensor in order to minimize the estimation mse to determine the optimal quantization bit rate and transmission energy of each sensor a concept of equivalent unit energy mse function is introduced based on this concept an optimal energy constrained distributed estimation algorithm for homogeneous sensor networks and a quasi optimal energy constrained distributed estimation algorithm for heterogeneous sensor networks are proposed moreover the theoretical energy distortion performance bound for distributed estimation is addressed and it is shown that the proposed algorithm is quasi optimal within a factor 2 of the theoretical lower bound simulation results also show that the proposed method can achieve a significant reduction in the estimation mse when compared with other uniform schemes finally the proposed algorithm is easy to implement in a distributed manner and it adapts well to the dynamic sensor environments

optimal control of unknown parameter systems the problem is discussed of finding a cost functional for which an adaptive control law is optimal the system under consideration is a partially observed linear stochastic system with unknown parameters it is well known that an optimal finite dimensional filter for this problem can be derived when the parameters belong to a finite set since the optimal filter involves the evaluation of a finite set of a posteriori probabilities for each of the parameter values given the observations a natural adaptive control scheme is i develop the optimal linear feedback law given each parameter ii use the a posteriori probabilities to form the weighted average convex combination of the individual control policies and iii use the weighted average as the control law a quadratic cost functional is devised for which this strategy is optimal in a general case and it is shown that the probing effect identified with dual control problems is inherent in the standard linear quadratic gaussian problem with parameter uncertainty

two time scale approximation for wonham filters this paper is concerned with approximation of wonham filters a focal point is that the underlying hidden markov chain has a large state space to reduce computational complexity a two time scale approach is developed under time scale separation the state space of the underlying markov chain is divided into a number of groups such that the chain jumps rapidly within each group and switches occasionally from one group to another such structure gives rise to a limit wonham filter that preserves the main features of the filtering process but has a much smaller dimension and therefore is easier to compute using the limit filter enables us to develop efficient approximations and useful filters for hidden markov chains the main advantage of our approach is the reduction of dimensionality

distributed estimation algorithms for nonlinear systems in this paper we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information sufficient statistics for the local distributions are communicated to a coordinator who attempts to reconstruct the global centralized distribution using only the communicated statistics we obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution the results can be applied in designing distributed hypothesis testing algorithms for event driven systems

construction and applications of discrete time smoothing error models we present a unified perspective on techniques for constructing both forward and backward markovian realizations of the error process associated with discrete time fixed interval smoothing several alternative approaches are presented each of which provides additional insight and connections with other results in linear estimation theory in addition two applications of such models are described the first is a problem in the validation of an error model for a measurement system while the second concerns the problems of updating and combining smoothed estimates we also present an example of the use of our updating solution for the mapping of random fields based on several sets of data tracks

derived length of solvable groups of local diffeomorphisms let g be a solvable subgroup of the group mathrm diff mathbb c n 0 of local complex analytic diffeomorphisms analogously as for groups of matrices we bound the solvable length of g by a function of n moreover we provide the best possible bounds for connected unipotent and nilpotent groups

a torsion load transfer problem for a class of non homogeneous elastic solids abstract this paper is concerned with the axisymmetric torsion of a finite long cylindrical bar which is partially embedded in a non homogeneous transversely isotropic elastic layer underlaid by a rigid base the non homogeneity of the elastic layer is represented by both linear and non linear variations of shear moduli with depth the bar elastic layer system is decomposed to a real bar and an elastic layer with a cylindrical cavity identical to the embedded bar instead of adopting the conventional fictitious bar extended elastic medium decomposition the proposed decomposition allows the imposition of displacement compatibility and traction continuity along the true contact surface in the analysis a solution scheme based on a classical variational theorem is presented to analyse the load transfer problem the displacement and traction green s functions of the nonhomogeneous elastic layer are required in the analysis and these are derived explicitly using hankel integral transforms numerical results are presented to illustrate the effect of non homogeneity and transverse isotropy on the torque twist relationship at the top end of the bar and twist angle and torque transfer curves along the length of the bar

data fusion with minimal communication two sensors obtain data vectors x and y respectively and transmit real vectors m spl i oarr sub 1 x and m spl i oarr sub 2 y respectively to a fusion center the authors obtain tight lower bounds on the number of messages the sum of the dimensions of m spl i oarr sub 1 and m spl i oarr sub 2 that have to be transmitted for the fusion center to be able to evaluate a given function f spl i oarr x y when the function f spl i oarr is linear they show that these bounds are effectively computable certain decentralized estimation problems can be cast in the framework and are discussed in some detail in particular the authors consider the case where x and y are random variables representing noisy measurements and f spl i oarr x y e z x y where z is a random variable to be estimated furthermore it is established that a standard method for combining decentralized estimates of gaussian random variables has nearly optimal communication requirements

linear coherent decentralized estimation we consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center due to power and bandwidth limitations each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center in this context we study the linear decentralized estimation of the source vector where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages we adopt the mean squared error mse as the performance criterion when the channels between sensors and the fusion center are orthogonal it has been shown previously that the complexity of designing the optimal encoding matrices is np hard in general in this paper we study the optimal linear decentralized estimation when the multiple access channel mac is coherent for the case when the source and observations are scalars we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation simulations show that the proposed power scheduling improves the mse performance by a large margin when compared to the uniform power scheduling we also show that under a finite network power budget the asymptotic mse performance when the total number of sensors is large critically depends on the multiple access scheme for the case when the source and observations are vectors we study the optimal linear decentralized estimation under both bandwidth and power constraints we show that when the mac between sensors and the fusion center is noiseless the resulting problem has a closed form solution which is in sharp contrast to the orthogonal mac case while in the noisy mac case the problem can be efficiently solved by semidefinite programming sdp

embedding adaptive jlqg into lq martingale control with a completely observable stochastic control matrix with jump linear quadratic gaussian jlqg control one refers to the control under a quadratic performance criterion of a linear gaussian system the coefficients of which are completely observable while they are jumping according to a finite state markov process with adaptive jlqg one refers to the more complicated situation that the finite state process is only partially observable although many practically applicable results have been developed jlqg and adaptive jlqg control are lagging behind those for linear quadratic gaussian lqg and adaptive lqg the aim of this paper is to help improve the situation by introducing an exact transformation which embeds adaptive jlqg control into lqm linear quadratic martingale control with a completely observable stochastic control matrix by lqm control the authors mean the control of a martingale driven linear system under a quadratic performance criterion with the lqm transformation the adaptive jlqg control can be studied within the framework of robust or minimax control without the need for the usual approach of averaging or approximating the adaptive jlqg dynamics to show the effectiveness of the authors transformation it is used to characterize the open loop optimal feedback olof policy for adaptive jlqg control

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

decentralized estimation in an inhomogeneous sensing environment we consider decentralized estimation of a noise corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center the sensor noises are assumed to be additive zero mean spatially uncorrelated but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment the classical best linear unbiased estimator blue linearly combines the real valued sensor observations to minimize the mean square error mse unfortunately such a scheme cannot be implemented in a practical bandwidth constrained sensor network due to its requirement to transmit real valued messages in this paper we construct a decentralized estimation scheme des where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal to noise ratio snr the resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter the proposed des is universal in the sense that each sensor compression scheme requires only the knowledge of local snr rather than the noise probability distribution functions pdf while the final fusion step is also independent of the local noise pdfs we show that the mse of the proposed des is within a constant factor of 25 8 of that achieved by the classical centralized blue estimator

ordering for estimation and optimization in energy efficient sensor networks a discretized version of a continuous optimization problem is considered for the case where data is obtained from a set of dispersed sensor nodes and the overall metric is a sum of individual metrics computed at each sensor an example of such a problem is maximum likelihood estimation based on statistically independent sensor observations by ordering transmissions from the sensor nodes a method for achieving a saving in the average number of sensor transmissions is described while the average number of sensor transmissions is reduced the approach always yields the same solution as the optimum approach where all sensor transmissions occur the approach is described first for a general optimization problem a maximum likelihood target location and velocity estimation example for a multiple node noncoherent multiple input multiple output mimo radar system is later described in particular for cases with n good quality sensors with ideal signals and sufficiently large signal to interference plus noise ratio sinr the average percentage of transmissions saved approaches 100 as the number of discrete grid points in the optimization problem q becomes significantly large in these same cases the average percentage of transmissions saved approaches q 1 q 100 as the number of sensors n in the network becomes significantly large similar savings are illustrated for general optimization or estimation problems with some sufficiently well designed sensors savings can be even larger in some cases for systems with some poor quality sensors

a topological tits alternative let k be a local eld and gln k a linear group over k we prove that either contains a relatively open solvable subgroup or it contains a relatively dense free subgroup this result has applications in dynamics riemannian foliations and pronite groups

optimal adaptive control and stabilization of families of linear systems a natural adaptive linear quadratic regulator is studied the optimal control is shown to be the best estimate given the observation of the linear quadratic control computed assuming that the true parameter were known moreover this optimal control is stabilizing the new ingredient that makes these results possible is the introduction of the concept of entropy into linear quadratic control

optimal stochastic adaptive control with quadratic index the discrete time stochastic control system with complete observation is considered with quadratic loss function when the constant coefficients of the system are unknown the parameter estimates given by the recursive least squares method are used to define the feedback gain and the adaptive control is taken to be either a linear state feedback disturbed by a sequence of random vectors with variances tending to zero or only the disturbance without the feedback term in accordance with stopping times defined on the trajectory of the system it is proved that the parameter estimates are strongly consistent and the loss function reaches its minimum i e the adaptive control is optimal

on the quasi decentralized estimation and control of linear stochastic systems abstract it is shown that the quasi decentralized estimation and control of linear stochastic systems have extremely simple and computationally very efficient solutions in the domain of nonoptimal local filters these solutions reduce both off line and on line computation requirements the optimal global estimate is obtained simply by the addition of nonoptimal local estimates

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

recurrent orbits of subgroups of local complex analytic diffeomorphisms we show recurrent phenomena for orbits of groups of local complex analytic diffeomorphisms that have a certain subgroup or image by a morphism of groups that is non virtually solvable in particular we prove that a non virtually solvable subgroup of local biholomorphisms has always recurrent orbits i e there exists an orbit contained in its set of limit points

universal decentralized estimation in a bandwidth constrained sensor network consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval u u each sensor collects one noise corrupted sample performs a local estimation and transmits a message to the fusion center while the latter combines the received messages to produce a final estimate this correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one bit message such a binary message constraint is well motivated by the bandwidth limitation of the communication links fusion center and by the limited power budget of local sensors in the absence of bandwidth constraint and assuming the noises are bounded to the interval u u additive independent but otherwise unknown the classical estimation theory suggests that a total of o u2 epsi2 sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error mse it is shown in this correspondence that the same remains true even with the binary message constraint furthermore the optimal decentralized estimation scheme suggests allocating 1 2 of the sensors to estimate the first bit of the unknown parameter 1 4 of the sensors to estimate the second bit and so on

constrained decentralized estimation over noisy channels for sensor networks decentralized estimation of a noise corrupted source parameter by a bandwidth constrained sensor network feeding through a noisy channel a fusion center is considered the sensors due to bandwidth constraints provide binary representatives of a noise corrupted source parameter recently proposed decentralized distributed estimation and power scheduling methods do no consider errors occurring during the transmission of binary observations from the sensors to fusion center in this paper we extend the decentralized estimation model to the case where imperfect transmission channels are considered the proposed estimator which operates on additive channel noise corrupted versions of quantized noisy sensor observations is approached from maximum likelihood ml perspective the resulting ml estimate is a root in the region of interest roi of a derivative polynomial function we analyze the natural logarithm of the polynomial within the roi showing that the function is log concave thereby indicating that numerical methods such as newton s algorithm can be utilized to obtain the optimal solution due to complexity and implementation issues associated with the numerical methods we derive and analyze simpler suboptimal solutions i e the two stage and mean estimators the two stage estimator first estimates the binary observations from noisy fusion center observations utilizing a threshold operation followed by an estimate of the source parameter the optimal threshold is the maximum a posteriori map detector for binary detection and minimizes the probability of binary observation estimation error optimal threshold expressions for commonly utilized light gaussian and heavy tailed cauchy channel noise models are derived the mean estimator simply averages the noisy fusion center observations the output variances of means of the proposed suboptimal estimators are derived in addition a computational complexity analysis is presented comparing the proposed ml optimal and suboptimal two stage and mean estimators numerical examples evaluating and comparing the performance of proposed ml two stage and mean estimators are also presented

distributing the kalman filter for large scale systems this paper presents a distributed kalman filter to estimate the state of a sparsely connected large scale n dimensional dynamical system monitored by a network of n sensors local kalman filters are implemented on nl dimensional subsystems nl lt n obtained by spatially decomposing the large scale system the distributed kalman filter is optimal under an lth order gauss markov approximation to the centralized filter we quantify the information loss due to this lth order approximation by the divergence which decreases as l increases the order of the approximation l leads to a bound on the dimension of the subsystems hence providing a criterion for subsystem selection the approximated centralized riccati and lyapunov equations are computed iteratively with only local communication and low order computation by a distributed iterate collapse inversion dici algorithm we fuse the observations that are common among the local kalman filters using bipartite fusion graphs and consensus averaging algorithms the proposed algorithm achieves full distribution of the kalman filter nowhere in the network storage communication or computation of n dimensional vectors and matrices is required only nl lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors in other words knowledge of the state is itself distributed

optimal adaptive lqg control for systems with finite state process parameters the situation where a totally observed process y t is generated by a stochastic differential equation whose parameters evolve on a finite set 1 n according to a stochastic differential equation is considered the optimal control law is sought with respect to quadratic loss functions on y t and the control u t the auxiliary p d e technique of hijab 6 is used together with a nonlinear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxiliary p d e and strong solutions to the system s d e under the given control inputs

the adaptive lqg problem part i this paper is concerned with a rigorous study of the dual control problem of fel dbaum i e the lqg optimal control problem in the presence of bayesian parameter uncertainty the solution of this problem involves two parts one relating to filtering and one to control although we establish our filtering result in complete generality in the last section most of the paper concentrates on the finite parameter case to ease the exposition the control result that we establish is incomplete in the sense that the smoothness of the optimal cost function is assumed rather than proved nevertheless our results and methods are such that we arrive at a new proof of the classical separation theorem showing that the well known lqg feedback law is optimal within the widest possible class of admissible controls as this new proof avoids all talk of dependence of the sigma algebra on the control weak solutions measure transformation techniques etc we feel that this result will help to clarify what is involved in the classical separation theorem

torsion of a long cylindrical elastic bar partially embedded in a layered elastic half space abstract this is a study of the axially symmetric torsion of a long elastic cylindrical bar which is embedded in a layered elastic half space the stress singularity factor at the embedded end of the bar is estimated by an existing method and its effects on the solution are investigated such effects are found to be not so significant especially for long bars and when the main concern is only on the torque twist angle relationship even for rather short bars the results given by this study agree well with those by an existing method which is more rigorous but restrictive only to the case of an infinitely rigid bar

on the longitudinal harmonic motion of an elastic bar embedded in an elastic half space abstract the present study is concerned with the motion of a long cylindrical elastic bar which is partially embedded in a homogeneous elastic half space and subjected to a harmonic axial load initially green s functions corresponding to axisymmetric harmonic ring loads are derived and presented explicitly it is found that the direct extension of elastostatic solution schemes to solve elastodynamic problems may lead to erroneous solutions due to the inability of these algorithms to properly account for inertia effects some discrepancies in existing solutions with respect to the inertia component of the bar are shown an efficient solution scheme based on lagrange s equation of motion and a discretization technique is presented to solve the title problem numerical results are presented to illustrate the influence of bar flexibility mass density geometry and frequency of excitation on the axial impedance of the system

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

on dense free subgroups of lie groups abstract we give a method for constructing dense and free subgroups in real lie groups in particular we show that any dense subgroup of a connected semisimple real lie group g contains a free group on two generators which is still dense in g and that any finitely generated dense subgroup in a connected non solvable lie group h contains a dense free subgroup of rank 2 dim h this answers a question of carriere and ghys and it gives an elementary proof to a conjecture of connes and sullivan on amenable actions which was first proved by zimmer

distributed estimation constraints on the choice of the local models the following estimation problem is considered a coordinator must reconstruct the global probability density of a nonlinear random process conditioned on the noise corrupted observation history the coordinator can only access the local probability density produced by local processing of the observation history using a local model different from the process model it is shown that if the local model satisfies an algebraic constraint the coordinator can reconstruct the same conditional density of the state process as the one obtained if the observations were processed using the coordinator process model it is assumed that the random process is a nonlinear stochastic differential equation driven by a brownian motion and the observation process is corrupted by additive brownian motion which is identically modeled by the coordinator and the local processor

on a partially observable lqg problem for systems with markovian jumping parameters in this paper a variant of the lqg problem for systems with markovian jumping parameters is studied it is assumed that the system is partially observable in the sense that we do not have access to the jumping parameter via nonlinear filtering the problem is recast as one with complete information it is then shown that a certain averaged control is an optimal policy vis a vis a modified quadratic cost apart from its intrinsic theoretical interest this result has an important bearing on a number of different analyses related with the original quadratic cost

hybrid modelling of semi infinite media abstract an accurate and efficient hybrid formulation based on lagrange s equations of motion is presented to solve geometrically axisymmetric problems associated with layered semi infinite media under arbitrary loading a near field region containing all inhomogeneities is modelled using conventional finite elements the contribution of the exterior semi infinite domain to the equations of motion is represented by a surface integral defined over the finite element boundary the integrand of this integral involves a matrix relationship between harmonics of nodal displacements and tractions at the finite element boundary a boundary traction displacement relationship for the exterior domain is established in terms of traction and displacement green s functions for a uniform undisturbed half space the present formulation guarantees a symmetric stiffness matrix for the entire system therefore both direct and indirect versions of the boundary integral equation method can be used the accuracy of the hybrid modelling algorithm is confirmed by solving a few elastostatic and elastodynamic boundary value problems for which analytical solutions can be derived