asymptotic stability of impulsive stochastic partial differential equations with infinite delays in this paper we study the existence and asymptotic stability in pth moment of mild solutions to nonlinear impulsive stochastic partial differential equations with infinite delay by employing a fixed point approach sufficient conditions are derived for achieving the required result these conditions do not require the monotone decreasing behaviour of the delays

coding schemes for user cooperation in low power regimes we consider the design of cooperation coding schemes for a two user multiaccess channel mac in particular we consider two block markov coding schemes namely the multiplexed coding and the superposition coding although the fully multiplexed fmp coding outperforms the superposition coding in theory it is difficult to implement with practical error correction codes we therefore introduce a partially multiplexed pmp coding scheme for code rate r 0 5 and propose a simplified superposition coding scheme the outage analysis shows that these cooperation schemes provide significant gains over the non cooperative mac in the low power regime when the bandwidth w rarr infin we then propose a pmp code design using irregular repeat accumulate ira codes the design method can be extended to build the low rate pmp codes using irregular repeat zigzag hadamard irzh codes a new class of capacity achieving low rate codes simulation results demonstrate that the block markov multiplexed coding using pmp ira codes outperforms the practical superposition coding by 2 db at 10 2 fer and it provides a 10 db gain over the noncooperative mac the multiplex coding using pmp irzh codes offers 1 db gain over the superposition coding and a 9 5 db gain over noncooperative mac at 10 2 fer moreover the pmp irzh coding performs only 0 5 db away from the outage capacity of multiplexed coding in the low power regime

optimal multiple sensor scheduling for general scalar gauss markov systems with the terminal error in this work we study finite horizon multiple sensor scheduling for general scalar gauss markov systems extending previous results where only a class of systems are considered the scheduling objective is to minimize the terminal estimation error covariance only one sensor can transmit its measurement per time instant and each sensor has limited energy through building a comparison function and solving its monotone intervals an efficient algorithm is designed to construct the optimal schedule

on controllability of linear stochastic systems we discuss several concepts of controllability for partially observable stochastic systems complete controllability approximate controllability controllability and s controllability and show that complete and approximate controllability notions are equivalent and in turn are equivalent to the controllability for linear stochastic systems controlled by gaussian processes we derive necessary and sufficient conditions for these concepts of controllability these criteria reduce to the well known rank condition

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

joint physical layer coding and network coding for bidirectional relaying we consider a communication system where two transmitters wish to exchange information through a central relay the transmitter and relay nodes exchange data over synchronized average power constrained additive white gaussian noise channels with a real input with signal to noise ratio snr of snr an upper bound on the capacity is 1 2 log 1 snr bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel we show that using lattice codes and lattice decoding we can obtain a rate of 1 2 log 1 2 snr bits per transmitter which is essentially optimal at high snr the main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs slepian wolf coding we also show that if the two transmitters use identical lattices with minimum angle decoding we can achieve the same rate of 1 2 log 1 2 snr the proposed scheme can be thought of as a joint physical layer network layer code which outperforms other recently proposed analog network coding schemes

existence results for an impulsive fractional integro differential equation with state dependent delay in this paper we have a tendency to implement different fixed point theorem banach contraction principle krasnoselskii s 18 and schaefer s 18 coupled with solution operator to analyze the existence and uniqueness results for an impulsive fractional integro differential equations ifide with state dependent delay sdd in banach spaces finally cases are offered to demonstrate the concept

locational optimization problems solved through voronoi diagrams abstract this paper reviews a class of continuous locational optimization problems where an optimal location or an optimal configuration of facilities is found in a continuum on a plane or a network that can be solved through the voronoi diagram eight types of continuous locational optimization problems are formulated and these problems are solved through the ordinary voronoi diagram the farthest point voronoi diagram the weighted voronoi diagram the network voronoi diagram the voronoi diagram with a convex distance function the line voronoi diagram and the area voronoi diagram

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

on the approximate controllability of fractional evolution equations with compact analytic semigroup in this paper we discuss the approximate controllability of fractional evolution equations involving caputo fractional derivative the results are obtained with the help of the theory of fractional calculus semigroup theory and the schauder s fixed point theorem under the assumption that the corresponding linear system is approximately controllable finally an example is provided to illustrate the obtained results

controllability of stochastic semilinear functional differential equations in hilbert spaces in this paper approximate and exact controllability for semilinear stochastic functional differential equations in hilbert spaces is studied sufficient conditions are established for each of these types of controllability the results are obtained by using the banach fixed point theorem applications to stochastic heat equation are given

existence of solutions for nonlinear fractional stochastic differential equations abstract the fractional stochastic differential equations have wide applications in various fields of science and engineering this paper addresses the issue of existence of mild solutions for a class of fractional stochastic differential equations with impulses in hilbert spaces using fractional calculations fixed point technique stochastic analysis theory and methods adopted directly from deterministic fractional equations new set of sufficient conditions are formulated and proved for the existence of mild solutions for the fractional impulsive stochastic differential equation with infinite delay further we study the existence of solutions for fractional stochastic semilinear differential equations with nonlocal conditions examples are provided to illustrate the obtained theory

optimal capacity allocation for sampled networked systems abstract we consider the problem of estimating the states of weakly coupled linear systems from sampled measurements we assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above and that each sample requires the same amount of communication our goal is then to find an optimal allocation of the capacity to the sensors so that the time averaged estimation error is minimized we show that when the total available channel capacity is large this resource allocation problem can be recast as a strictly convex optimization problem and hence there exists a unique optimal allocation of the capacity we further investigate how this optimal allocation varies as the available capacity increases in particular we show that if the coupling among the subsystems is weak then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate and is strictly increasing if and only if the total sampling rate exceeds a certain threshold

deterministic coding capacity of networks in the low power regime the deterministic coding capacity of a network is the capacity of a network when nodes are restricted to transmitting reliable information that is asymptotically deterministic functions of the source messages this is a generalization of network coding to wireless networks the main contribution of this paper is to develop new outer bounds on the deterministic coding capacity in the low power regime mathrm snr to 0 this is accomplished by developing a technique for finding the limits of single letter bounds for mathrm snr to 0 even when these cannot be evaluated for finite snr it is shown that these outer bounds are tight in a number of cases including the butterfly network of ahlswede et al in a wireless setting

optimal sensor scheduling for multiple linear dynamical systems we consider the design of an optimal collision free sensor schedule for a number of sensors which monitor different linear dynamical systems correspondingly at each time only one of all the sensors can send its local estimate to the remote estimator a preliminary work for the two sensor scheduling case has been studied in the literature the generalization into multiple sensor scheduling case is shown to be nontrivial we first find a necessary condition of the optimal solution which can significantly reduce the feasible optimal solution space without loss of performance by modelling a finite state markov decision process mdp problem we can numerically search an asymptotic periodic schedule which is proven to be optimal some simple but effective suboptimal schedules for any systems are proposed we also find a lower bound of the optimal cost which enables us to quantify the performance gap between any suboptimal schedule and an optimal one

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

fixed point theorems for discontinuous multivalued operators on ordered spaces with applications in this paper some fixed point theorems for discontinuous multivalued operators on ordered spaces are proved these theorems improve the earlier known fixed point theorems of 1 2 the main fixed point theorems are applied to first order discontinuous differential inclusions for proving the existence of extremal solutions under certain monotonicity conditions

on the use of binary programming for sensor scheduling in this paper we propose two myopic sensor scheduling algorithms for target tracking scenarios in which there is a tradeoff between tracking performance and sensor usage costs specifically we consider the problem of activating the lowest cost combination of at most l sensors that maintains a desired squared error accuracy in the target s position estimate for sensors that provide position information only we develop a binary 0 1 mixed integer programming formulation for the scheduling problem and solve it using a linear programming relaxation based branch and bound technique for sensors that provide both position and velocity information we pose the scheduling problem as a binary convex programming problem and solve it using the outer approximation algorithm we apply our scheduling procedures in a network of sensors where the sensor usage costs correspond to network energy consumption our simulation results demonstrate that scheduling using binary programming allows us to obtain optimal solutions to scheduling involving up to 50 70 sensors typically in the order of seconds

controllability of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in this work the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in a banach space has been established by using the theory of fractional calculus fixed point technique and also we introduced a new concept called a u resolvent family as an application that illustrates the abstract results an example is given

optimal periodic scheduling of sensor networks a branch and bound approach abstract a periodic scheduling problem for sensor networks with communication constraints is considered for state estimation the solvability of the problem is first discussed and a necessary and sufficient condition is presented based on the notion of periodic detectability since the calculation of the average prediction error variance requires the computation of the symmetric periodic positive semidefinite stabilizing spps solutions to the periodic riccati equations a moving approximate cost function is proposed which gradually converges to the exact cost function also it is shown that the upper bound of the approximation error is independent of the spps solutions and converges to zero exponentially based on these results a branch and bound based algorithm is proposed to compute the optimal periodic schedule and the idea is to iteratively trim the set of schedules that are potentially robust optimal with respect to the approximation error if the optimal schedule is unique the algorithm solves the periodic scheduling problem by exploring a finite number of nodes moreover given an arbitrary nonzero suboptimality specification the algorithm results in a suboptimal schedule set containing all the optimal schedules at a manageable computation effort a numerical example is presented to illustrate the proposed results

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

approximate controllability of a multi valued fractional impulsive stochastic partial integro differential equation with infinite delay in this paper the approximate controllability of a new class of multi valued fractional impulsive stochastic partial integro differential equations with infinite delay in hilbert spaces is studied firstly by using stochastic analysis analytic resolvent operator fractional powers of closed operators and a fixed point theorem for multi valued maps we prove an existence result of mild solutions for the control systems under the mixed lipschitz and caratheodory conditions secondly we discuss a new set of sufficient conditions for the approximate controllability of the systems the results are obtained under the assumption that the associated linear system is approximately controllable finally an example is provided to illustrate the proposed theory

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

curvature properties of the algebraic riccati equation abstract we prove that the solution to the algebraic ricatti equation are is concave with respect to a nonnegative definite symmetric state weighting matrix q when the input weighting matrix r r t 0 we also prove that the solution to the are is concave with respect to a positive definite diagonal input weighting matrix r when q q t 0

optimal sensor scheduling in nonlinear filtering of diffusion processes the nonlinear filtering problem of a vector diffusion process is considered when several noisy vector observations with possibly different dimension of their range space are available at each time any number of these observations or sensors can be used in the signal processing performed by the nonlinear filter the problem considered is the optimal selection of a schedule of these sensors from the available set so as to optimally estimate a function of the state at the final time optimality is measured by a combined performance measure that allocates penalties for errors in estimation for switching between sensor schedules and for running a sensor the solution is obtained in the form of a system of quasi variational inequalities in the space of solutions of certain zakai equations

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

on a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage in this note we consider the following problem suppose a set of sensors is jointly trying to estimate a process one sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors what is the sensor schedule that results in the minimum error covariance we describe a stochastic sensor selection strategy that is easy to implement and is computationally tractable the problem described above comes up in many domains out of which we discuss two in the sensor selection problem there are multiple sensors that cannot operate simultaneously e g sonars in the same frequency band thus measurements need to be scheduled in the sensor coverage problem a geographical area needs to be covered by mobile sensors each with limited range thus from every position the sensors obtain a different view point of the area and the sensors need to optimize their trajectories the algorithm is applied to these problems and illustrated through simple examples

existence of solutions for semi linear abstract differential equations with not instantaneous impulses in this paper using the theory of analytic semigroup and fractional power of closed operators we study the existence of solutions for a class of semi linear abstract impulsive differential equations with not instantaneous impulses some applications involving partial differential equations with impulses are presented

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

existence and controllability results for second order impulsive stochastic evolution systems with state dependent delay in this paper we discuss a kind of impulsive second order stochastic evolution systems with state dependent delay in a real separable hilbert space the results concerning the existence and controllability of mild solutions have been addressed by means of the fixed point techniques some sufficient conditions are formulated as well as an application involving partial differential equation with impulses is presented

optimization of observations a stochastic control approach we study a stochastic control problem for the optimization of observations in a partially observable stochastic system using a method of discontinuous time transformation we associate with the original problem with unbounded controls a problem that has bounded controls this latter problem allows us to construct nearly optimal nonanticipative lipschitz markov controls with finite observation power for the original problem since the controlled observation equation may degenerate we also derive a corresponding filtering result and show a separation property of the optimal controls

analytic feedback control and the algebraic riccati equation the central result of this correspondence is lemma 1 1 which states that the stabilizing solution p to the algebraic riccati equation in a b c depends analytically on a b c in the remainder of the correspondence various control and system theoretic ramifications of the analyticity lemma are considered an important consequence of lemma 1 1 is that any smooth state feedback control law for a finite dimensional plant may be implemented using dynamic input output compensators whose transfer functions depend smoothly on the plant transfer function

minimax estimation with intermittent observations this paper considers a problem of minimax or h state estimation with intermittent observations in this setting the disturbance in the dynamical system and the sensor noise are controlled by adversaries and the estimator receives the sensor measurements only sporadically with the availability governed by an independent and identically distributed bernoulli process we cast this problem within the framework of stochastic zero sum dynamic games we first obtain a corresponding stochastic minimax state estimator smse and an associated generalized stochastic riccati equation gsre whose evolutions depend on two parameters one that governs the random measurement arrivals and another one that quantifies the level of h disturbance attenuation we then analyze the asymptotic behavior of the sequence generated by the gsre in the expectation sense and its weak convergence specifically we obtain threshold type conditions above which the sequence generated by the gsre can be bounded both below and above in the expectation sense moreover we show that under some conditions the norm of the sequence generated by the gsre converges weakly to a unique stationary distribution finally we prove that when the disturbance attenuation parameter goes to infinity our asymptotic results are equivalent to the corresponding results from the literature on kalman filtering with intermittent observations we provide simulations to illustrate the results

simulation based optimal sensor scheduling with application to observer trajectory planning the sensor scheduling problem can be formulated as a controlled hidden markov model and this paper solves the problem when the state observation and action spaces are continuous this general case is important as it is the natural framework for many applications the aim is to minimise the variance of the estimation error of the hidden state w r t the action sequence we present a novel simulation based method that uses a stochastic gradient algorithm to find optimal actions

approximate optimal periodic scheduling of multiple sensors with constraints a constrained periodic multiple sensor scheduling problem is considered in this paper for each sensor constraints on dwell time and activation times are imposed at each time instant only one sensor can update its measurement with the estimator and the objective is to minimize the average state estimation error an approximation framework is proposed to calculate the objective function which transforms the original scheduling problem into an approximate optimal scheduling problem aosp an upper bound on the approximation error is presented to evaluate the performance of the framework to solve the aosp a necessary condition is first proposed on the optimal schedules when no constraints on activation times exist a dynamic programming based algorithm is devised to identify the optimal schedule with polynomial computational complexity when activation time constraints exist we show that the aosps can be solved by solving traveling salesman problems examples are provided to illustrate the proposed results

controllability of semilinear control systems dominated by the linear part while various equivalent conditions for controllability have been obtained in the case of linear control systems controllability problems of semilinear control systems usually require some complicated and limited assumptions in this paper we show the approximate controllability of an abstract semilinear control system under the assumption which has a simple form and can be easily checked in many examples

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments