consensus in ad hoc wsns with noisy links part i distributed estimation of deterministic signals we deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks wsns we cast the decentralized estimation problem as the solution of multiple constrained convex optimization subproblems using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation different from existing alternatives our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages thus allowing for decentralized computation even of nonlinear estimators including maximum likelihood estimators mle in nonlinear and non gaussian data models we prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal furthermore our decentralized algorithms exhibit resilience in the presence of receiver and or quantization noise in particular we introduce a decentralized scheme for least squares and best linear unbiased estimation blue and establish its convergence in the presence of communication noise our algorithms also exhibit potential for higher convergence rate with respect to existing schemes corroborating simulations demonstrate the merits of the novel distributed estimation algorithms

performance of a distributed stochastic approximation algorithm in this paper a distributed stochastic approximation algorithm is studied applications of such algorithms include decentralized estimation optimization control or computing the algorithm consists in two steps a local step where each node in a network updates a local estimate using a stochastic approximation algorithm with decreasing step size and a gossip step where a node computes a local weighted average between its estimates and those of its neighbors convergence of the estimates toward a consensus is established under weak assumptions the approach relies on two main ingredients the existence of a lyapunov function for the mean field in the agreement subspace and a contraction property of the random matrices of weights in the subspace orthogonal to the agreement subspace a second order analysis of the algorithm is also performed under the form of a central limit theorem the polyak averaged version of the algorithm is also considered

incremental stochastic subgradient algorithms for convex optimization this paper studies the effect of stochastic errors on two constrained incremental subgradient algorithms the incremental subgradient algorithms are viewed as decentralized network optimization algorithms as applied to minimize a sum of functions when each component function is known only to a particular agent of a distributed network first the standard cyclic incremental subgradient algorithm is studied in this the agents form a ring structure and pass the iterate in a cycle when there are stochastic errors in the subgradient evaluations sufficient conditions on the moments of the stochastic errors are obtained that guarantee almost sure convergence when a diminishing step size is used in addition almost sure bounds on the algorithm s performance with a constant step size are also obtained next the markov randomized incremental subgradient method is studied this is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous markov chain such a model is appropriate for mobile networks as the network topology changes across time in these networks convergence results and error bounds for the markov randomized method in the presence of stochastic errors for diminishing and constant step sizes are obtained

preference foundations for nonexpected utility a generalized and simplified technique this paper examines a tradeoff consistency technique for testing and axiomatically founding decision models the technique modifies earlier tradeoff consistency techniques by only considering indifferences not strict preferences the resulting foundations are both more general and more accessible than earlier results and they are so regarding both the technical and the intuitive axioms axiomatizations based on other bisymmetry like conditions also follow as corollaries from the results of this paper the tradeoff technique is applied to three popular theories of individual decision under uncertainty and risk i e expected utility choquet expected utility and prospect theory the conditions used are better suited for empirical measurements of utility than earlier tradeoff conditions and accordingly are easier to test

just in time control of timed event graphs update of reference input presence of uncontrollable input a linear system theory has been developed for the class of discrete event systems subject to synchronization this paper presents the just in time control of such systems when reference input is updated and or in the presence of uncontrollable input s the proposed controls are the solutions to an optimization problem under equality constraint

stability of stochastic approximation under verifiable conditions in this paper we address the problem of the stability and convergence of the stochastic approximation procedure theta n 1 theta n gamma n 1 h theta n xi n 1 the stability of such sequences theta n is known to heavily rely on the behavior of the mean field h at the boundary of the parameter set and the magnitude of the stepsizes used the conditions typically required to ensure convergence and in particular the boundedness or stability of theta n are either too difficult to check in practice or not satisfied at all this is the case even for very simple models the most popular technique for circumventing the stability problem consists of constraining theta n to a compact subset mathcal k in the parameter space this is obviously not a satisfactory solution as the choice of mathcal k is a delicate one in this paper we first prove a deterministic stability result which relies on simple conditions on the sequences xi n and gamma n we then propose and analyze an algorithm based on projections on adaptive truncation sets which ensures that the aforementioned conditions required for stability are satisfied we focus in particular on the case where xi n is a so called markov state dependent noise we establish both the stability and convergence with probability 1 w p 1 of the algorithm under a set of simple and verifiable assumptions we illustrate our results with an example related to adaptive markov chain monte carlo algorithms

convergence of approximate and incremental subgradient methods for convex optimization we present a unified convergence framework for approximate subgradient methods that covers various stepsize rules including both diminishing and nonvanishing stepsizes convergence in objective values and convergence to a neighborhood of the optimal set we discuss ways of ensuring the boundedness of the iterates and give efficiency estimates our results are extended to incremental subgradient methods for minimizing a sum of convex functions which have recently been shown to be promising for various large scale problems including those arising from lagrangian relaxation

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

from extremal trajectories to token deaths in p time event graphs in this technical note we consider the max model of p time event graphs whose behaviors are defined by lower and upper bound constraints the extremal trajectories of the system starting from an initial interval are characterized with a particular series of matrices for a given finite horizon two dual polynomial algorithms are proposed to check the existence of feasible trajectories the series of matrices are used in the determination of the maximal horizon of consistency and the calculation of the date of the first token deaths

approximate projected consensus for convex intersection computation convergence analysis and critical error angle in this paper we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets where each set corresponds to one network node instead of assuming exact convex projection that each node can compute we allow each node to compute an approximate projection with respect to its own set after receiving the approximate projection information nodes update their states by weighted averaging with the neighbors over a directed and time varying communication graph the approximate projections are related to projection angle errors which introduces state dependent disturbance in the iterative algorithm projection accuracy conditions are presented for the considered algorithm to converge the results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected in addition we show that pi 4 is a critical angle for the error of the projection approximation to ensure the boundedness finally the results are illustrated by simulations

a linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing a discrete event system is a system whose behavior can be described by means of a set of time consuming activities performed according to a prescribed ordering events correspond to starting or ending some activity an analogy between linear systems and a class of discrete event systems is developed following this analogy such discrete event systems can be viewed as linear in the sense of an appropriate algebra the periodical behavior of closed discrete event systems i e involving a set of repeatedly performed activities can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra this problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph the potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized the case of a flowshop like production process is analyzed in detail

optimal control synthesis of timed event graphs with interval model specifications the purpose of this technical note is the optimal control synthesis of a timed event graph when the state and control trajectories should follow the specifications defined by an interval model the problem is reformulated in the fixed point form and the spectral theory gives the conditions of existence of a solution

distributed parameter estimation in sensor networks nonlinear observation models and imperfect communication the paper studies distributed static parameter vector estimation in sensor networks with nonlinear observation models and noisy intersensor communication it introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation it studies two distributed estimation algorithms in separably estimable models the nu with its linear counterpart lu and the nlu their update rule combines a consensus step where each sensor updates the state by weight averaging it with its neighbors states and an innovation step where each sensor processes its local current observation this makes the three algorithms of the consensus innovations type very different from traditional consensus this paper proves consistency all sensors reach consensus almost surely and converge to the true parameter value efficiency and asymptotic unbiasedness for lu and nu it proves asymptotic normality and provides convergence rate guarantees the three algorithms are characterized by appropriately chosen decaying weight sequences algorithms lu and nu are analyzed in the framework of stochastic approximation theory algorithm nlu exhibits mixed time scale behavior and biased perturbations and its analysis requires a different approach that is developed in this paper

on feedback invariance properties for systems over a principal ideal domain simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the a b invariance property and the a bf invariance or feedback invariance property for systems over a ring this equivalence is no longer true and many results of the geometric control theory cannot be extended we present new algorithmically checkable characterizations of the a bf invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem

a simple behavioral characterization of subjective expected utility subjective expected utility is the most widely used model to represent preferences under uncertainty when objective probabilities of events may not be known this paper presents a new behavioral characterization preference axiomatization of subjective expected utility the latter is derived from a behavioral assumption of cardinal independence also known as standard sequence invariance this axiom requires that a standard sequence of outcomes equally spaced in terms of utility is independent of the conditional event this axiom is a weaker version of the trade off consistency condition of wakker wakker pp 1984 cardinal coordinate independence for expected utility j math psych 28 110 117 the main representation theorem is derived both in the connected topology approach and the algebraic approach when step continuity is replaced with solvability and archimedean axioms

randomized optimal consensus of multi agent systems in this paper we formulate and solve a randomized optimal consensus problem for multi agent systems with stochastically time varying interconnection topology the considered multi agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min z r email protected i 1 nf i z in which the optimal solution set of objective function f i can only be observed by agent i itself at each time step simply determined by a bernoulli trial each agent independently and randomly chooses either taking an average among its neighbor set or projecting onto the optimal solution set of its own optimization component both directed and bidirectional communication graphs are studied connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions the convergence analysis is carried out using convex analysis we compare the randomized algorithm with the deterministic one via a numerical example the results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade off between following its neighbors or sticking to its own opinion at each time step

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

incremental subgradient methods for nondifferentiable optimization we consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions this type of minimization arises in a dual context from lagrangian relaxation of the coupling constraints of large scale separable problems the idea is to perform the subgradient iteration incrementally by sequentially taking steps along the subgradients of the component functions with intermediate adjustment of the variables after processing each component function this incremental approach has been very successful in solving large differentiable least squares problems such as those arising in the training of neural networks and it has resulted in a much better practical rate of convergence than the steepest descent method in this paper we establish the convergence properties of a number of variants of incremental subgradient methods including some that are stochastic based on the analysis and computational experiments the methods appear very promising and effective for important classes of large problems a particularly interesting discovery is that by randomizing the order of selection of component functions for iteration the convergence rate is substantially improved

optimistic optimization for model predictive control of max plus linear systems model predictive control for max plus linear discrete event systems usually leads to a nonsmooth nonconvex optimization problem with real valued variables which may be hard to solve efficiently an alternative approach is to transform the given problem into a mixed integer linear programming problem however the computational complexity of current mixed integer linear programming algorithms increases in the worst case exponentially as a function of the prediction horizon the focus of this paper is on making optimistic optimization suited to solve the given problem optimistic optimization is a class of algorithms that can find an approximation of the global optimum for general nonlinear optimization a key advantage of optimistic optimization is that one can specify the computational budget in advance and guarantee bounds on the suboptimality with respect to the global optimum we prove that optimistic optimization can be applied for the given problem by developing a dedicated semi metric and by proving it satisfies the necessary requirements for optimistic optimization moreover we show that the complexity of optimistic optimization is exponential in the control horizon instead of the prediction horizon hence using optimistic optimization is more efficient when the control horizon is small and the prediction horizon is large

gradient convergence in gradient methods with errors we consider the gradient method x t 1 x t g t s t w t where s t is a descent direction of a function f rn to re and w t is a deterministic or stochastic error we assume that gr f is lipschitz continuous that the stepsize g t diminishes to 0 and that s t and w t satisfy standard conditions we show that either f x t to infty or f x t converges to a finite value and gr f x t to0 with probability 1 in the stochastic case and in doing so we remove various boundedness conditions that are assumed in existing results such as boundedness from below of f boundedness of gr f x t or boundedness of xt

stochastic gradient push for strongly convex functions on time varying directed graphs we investigate the convergence rate of the recently proposed subgradient push method for distributed optimization over time varying directed graphs the subgradient push method can be implemented in a distributed way without requiring knowledge of either the number of agents or the graph sequence each node is only required to know its out degree at each time our main result is a convergence rate of o ln t t for strongly convex functions with lipschitz gradients even if only stochastic gradient samples are available this is asymptotically faster than the o ln t sqrt t rate previously known for general convex functions

asymptotic properties of distributed and communication stochastic approximation algorithms the asymptotic properties of extensions of the type of distributed or decentralized stochastic approximation proposed in 1 are developed such algorithms have numerous potential applications in decentralized estimation detection and adaptive control or in decentralized monte carlo simulation for system optimization where they can exploit the possibilities of parallel processing the structure involves several isolated processors recursive algorithms that communicate to each other asynchronously and at random intervals the asymptotic small gain properties are derived the communication intervals need not be strictly bounded and they and the system noise can depend on the communicating system state state space constraints are also handled in many applications the dynamical terms are merely indicator functions or have other types of discontinuities the typical such case is also treated as is the case where there is noise in the communication the linear stochastic differential equation

probability weighting and l moments abstract several popular generalizations of expected utility theory cumulative prospect theory rank dependent utility and yaari s dual model allow for non linear transformation of de cumulative probabilities this paper shows an unexpected connection between probability weighting and the statistical theory of l moments specifically cubic probability weighting results in a linear tradeoff between the expected value the first l moment gini 1912 mean difference statistic the second l moment also known as l scale and the third l moment measuring skewness inverse s shaped probability weighting function crossing the 45 line at a probability 0 5 reflects an aversion to the dispersion of outcomes and an attraction to positively skewed distributions

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

convergence and asymptotic agreement in distributed decision problems we consider a distributed team decision problem in which different agents obtain from the environment different stochastic measurements possibly at different random times related to the same uncertain random vector each agent has the same objective function and prior probability distribution we assume that each agent can compute an optimal tentative decision based upon his own observation and that these tentative decisions are communicated and received possibly at random times by a subset of other agents conditions for asymptotic convergence of each agent s decison sequence and asymptotic agreement of all agents decisions are derived

stability and performance limits of adaptive primal dual networks this paper studies distributed primal dual strategies for adaptation and learning over networks from streaming data two first order methods are considered based on the arrow hurwicz ah and augmented lagrangian al techniques several revealing results are discovered in relation to the performance and stability of these strategies when employed over adaptive networks the conclusions establish that the advantages that these methods exhibit for deterministic optimization problems do not necessarily carry over to stochastic optimization problems it is found that they have narrower stability ranges and worse steady state mean square error performance than primal methods of the consensus and diffusion type it is also found that the ah technique can become unstable under a partial observation model while the other techniques are able to recover the unknown under this scenario a method to enhance the performance of al strategies is proposed by tying the selection of the step size to their regularization parameter it is shown that this method allows the al algorithm to approach the performance of consensus and diffusion strategies but that it remains less stable than these other strategies

duality between invariant spaces for max plus linear discrete event systems we extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max plus or tropical semiring we establish a duality theorem relating both notions which we use to construct dynamic observers these are useful in situations in which some of the system coefficients may vary within certain intervals the results are illustrated by an application to a manufacturing system

max plus a b invariant spaces and control of timed discrete event systems the concept of a b invariant subspace or controlled invariant of a linear dynamical system is extended to linear systems over the max plus semiring although this extension presents several difficulties which are similar to those encountered in the same kind of extension to linear dynamical systems over rings it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings sufficient conditions are given for computing the maximal a b invariant subspace contained in a given space and the existence of linear state feedbacks is discussed an application to the study of transportation networks which evolve according to a timetable is considered

a solution to the problem of a b invariance for series the aim of this article is to study a standard problem of control theory the a b invariance problem which amounts to computing a maximal element x subject to conditions of the form ax 6 x b and x 6 k we give a solution to the problem in the framework of formal series over particular complete idempotent semirings over nite idempotent semirings we show that under the assumption that b and k are recognizable series the maximal solution exists and is also recognizable we obtain a similar result for the in nite tropical semiring with additional hypothesis that the series a is a language but the notion of recognizable series has to be extended to the weaker notion of pseudo recognizable series c 2002 elsevier science b v all rights reserved

distributed linear parameter estimation asymptotically efficient adaptive strategies this paper considers the problem of distributed adaptive linear parameter estimation in multiagent inference networks local sensing model information is only partially available at the agents and interagent communication is assumed to be unpredictable the paper develops a generic mixed time scale stochastic procedure consisting of simultaneous distributed learning and estimation in which the agents adaptively assess their relative observation quality over time and fuse the innovations accordingly under rather weak assumptions on the statistical model and the interagent communication it is shown that by properly tuning the consensus potential with respect to the innovation potential the asymptotic information rate loss incurred in the learning process may be made negligible as such it is shown that the agent estimates are asymptotically efficient in that their asymptotic covariance coincides with that of a centralized estimator the inverse of the centralized fisher information rate for gaussian

asynchronous stochastic approximations the asymptotic behavior of a distributed asynchronous stochastic approximation scheme is analyzed in terms of a limiting nonautonomous differential equation the relation between the latter and the relative values of suitably rescaled relative frequencies of updates of different components is underscored

a convergent incremental gradient method with a constant step size an incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented the method requires a single gradient evaluation per iteration and uses a constant step size for the case that the gradient is bounded and lipschitz continuous we show that the method visits infinitely often regions in which the gradient is small under certain unimodality assumptions global convergence is established in the quadratic case a global linear rate of convergence is shown the method is applied to distributed optimization problems arising in wireless sensor networks and numerical experiments compare the new method with other incremental gradient methods

the equation a x b y over max for the two sided homogeneous linear equation system a x b y over max with no infinite rows or columns in a or b an algorithm is presented which converges to a finite solution from any finite starting point whenever a finite solution exists if the finite elements of a b are all integers convergence is in a finite number of steps for which a precise bound can be calculated if moreover one of a b has only finite elements the algorithm is thus pseudopolynomial in complexity

duality and interval analysis over idempotent semirings abstract in this paper semirings with an idempotent addition are considered these algebraic structures are endowed with a partial order this allows to consider residuated maps to solve systems of inequalities a x b see 3 the purpose of this paper is to consider a dual product denoted and the dual residuation of matrices in order to solve the following inequality a x x b x sufficient conditions ensuring the existence of a non linear projector in the solution set are proposed the results are extended to semirings of intervals such as they were introduced in 25

observer based controllers for max plus linear systems max plus algebra is a suitable algebraic setting to model discrete event systems involving synchronization and delay phenomena which are often found in transportation networks communications systems and manufacturing systems one way of controlling this kind of systems consists in choosing the dates of input events in order to achieve the desired performances e g to obtain output events in order to respect given dates this kind of control is optimal according to a just in time criterion if the input event dates are delayed as much as possible while ensuring the output events to occur before a desired reference date this paper presents the observer based controller for max plus linear systems where only estimations of system states are available for the controller as in the classical sense this is a state feedback control problem which is solved in two steps first an observer computes an estimation of the state by using the input and the output measurements then this estimated state is used to compute the state feedback control action as a main result it is shown that the optimal solution of this observer based control problem leads to a greater control input than the one obtained with the output feedback strategy a high throughput screening example in drug discovery illustrates this main result by showing that the scheduling obtained from the observer based controller is better than the scheduling obtained from the output feedback controller

convergence of adaptive and interacting markov chain monte carlo algorithms adaptive and interacting markov chain monte carlo algorithms mcmc have been recently introduced in the literature these novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions motivated by some recently introduced algorithms such as the adaptive metropolis algorithm and the interacting tempering algorithm we develop a general methodological and theoretical framework to establish both the convergence of the marginal distribution and a strong law of large numbers this framework weakens the conditions introduced in the pioneering paper by roberts and rosenthal j appl probab 44 2007 458 475 it also covers the case when the target distribution is sampled by using markov transition kernels with a stationary distribution that differs from

on the steady state control of timed event graphs with firing date constraints two algorithms for solving a specific class of steady state control problems for timed event graphs are presented in the first asymptotic convergence to the desired set is guaranteed the second algorithm which builds on from the recent developments in the spectral theory of min max functions guarantees lyapunov stability since the distance between the actual state and the desired set never increases simulation results show the efficiency of the proposed approach in a problem of moderate complexity

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

a parallel decomposition method for nonconvex stochastic multi agent optimization problems this paper considers the problem of minimizing the expected value of a possibly nonconvex cost function parameterized by a random vector variable when the expectation cannot be computed accurately e g because the statistics of the random variables are unknown and or the computational complexity is prohibitive classical stochastic gradient methods for solving this problem may suffer from slow convergence in this paper we propose a stochastic parallel successive convex approximation based best response algorithm for general nonconvex stochastic sum utility optimization problems which arise naturally in the design of multi agent networks the proposed novel decomposition approach enables all users to update their optimization variables in parallel by solving a sequence of strongly convex subproblems one for each user almost sure convergence to stationary points is proved we then customize the algorithmic framework to solve the stochastic sum rate maximization problem over single input single output siso frequency selective interference channels multiple input multiple output mimo interference channels and mimo multiple access channels numerical results corroborate that the proposed algorithms can converge faster than state of the art stochastic gradient schemes while achieving the same or better sum rates

distributed multi agent optimization subject to nonidentical constraints and communication delays in this paper we study a distributed optimization problem using a subgradient projection algorithm for multi agent systems subject to nonidentical constraints and communication delays under local communication here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions each of which is known to only one agent first we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs instead the agents optimize a weighted sum of the local objective functions then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length furthermore we consider the case of communication delays where the delays are mutually independent it is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded finally numerical examples are included to show the obtained theoretical results

the disturbance decoupling problem for systems over a ring up to now the use of geometric methods in the study of disturbance decoupling problems ddps for systems over a ring has provided only necessary conditions for the existence of solutions in this paper we study such problems considering separately the case in which only static feedback solutions are allowed and the one in which dynamic feedback solutions are admitted in the first case we give a complete geometric characterization of the solvability conditions of such problems for injective systems with coefficients in a commutative ring practical procedures for testing the solvability conditions and for constructing solutions if any exist are given in the case of systems with coefficients in a principal ideal domain pid in the second case we give a complete geometric characterization of the solvability conditions for systems with coefficients in a pid

hilbert valued perturbed subgradient algorithms we propose a hilbert valued perturbed subgradient algorithm with stochastic noises and we provide a convergence proof for this algorithm under classical assumptions on the descent direction and new assumptions on the stochastic noises instead of requiring the stochastic noises to correspond to martingale increments we only require these noises to be asymptotically so furthermore the variance of these noises is allowed to grow infinitely under the control of a decreasing sequence linked with the subgradient stepsizes this algorithm can be used to solve stochastic closed loop control problems without any a priori discretization of the uncertainty such as linear decision rules or tree representations it can also be used as a way to perform stochastic dynamic programming without state space discretization or a priori functional bases i e approximate dynamic programming both problems arise frequently for example in power systems scheduling or option pricing this article focuses on the theorical foundations of the algorithm and gives references to detailed practical experimentations

distributed consensus algorithms in sensor networks quantized data and random link failures the paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures to achieve consensus dither small noise is added to the sensor states before quantization when the quantizer range is unbounded countable number of quantizer levels stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable we show that the mean squared error mse can be made arbitrarily small by tuning the link weight sequence at a cost of the convergence rate of the algorithm to study dithered consensus with random links when the range of the quantizer is bounded we establish uniform boundedness of the sample paths of the unbounded quantizer this requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer this is accomplished by splitting the state vector of the quantizer in two components one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace the proofs use maximal inequalities for submartingale and supermartingale sequences from these we derive probability bounds on the excursions of the two subsequences from which probability bounds on the excursions of the quantizer state vector follow the paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels the size of the quantization steps the desired probability of saturation and the desired level of accuracy away from consensus finally the paper illustrates the quantizer design with a numerical study

distributed and recursive parameter estimation in parametrized linear state space models we consider a network of sensors deployed to sense a spatio temporal field and infer parameters of interest about the field we are interested in the case where each sensor s observation sequence is modeled as a state space process that is perturbed by random noise and the models across sensors are parametrized by the same parameter vector the sensors collaborate to estimate this parameter from their measurements and to this end we propose a distributed and recursive estimation algorithm which we refer to as the incremental recursive prediction error algorithm this algorithm has the distributed property of incremental gradient algorithms and the on line property of recursive prediction error algorithms

unbounded utility for savage s foundations of statistics and other models a general procedure for extending finite dimensional additive like representations for binary relations to infinite dimensional integral like representations is developed by means of a condition called truncation continuity the restriction of boundedness of utility met throughout the literature can now be dispensed with and for instance normal distributions or any other distribution with finite first moment can be incorporated classical representation results of expected utility such as savage 1954 von neumann and morgenstern 1944 anscombe and aumann 1963 de finetti 1937 and many others can now be extended the results are generalized to schmeidler s 1989 approach with nonadditive measures and choquet integrals and quiggin s 1982 rank dependent utility the different approaches have been brought together in this paper to bring to the fore the unity in the extension process

the minkowski theorem for max plus convex sets abstract we establish the following max plus analogue of minkowski s theorem any point of a compact max plus convex subset of r n can be written as the max plus convex combination of at most n 1 of the extreme points of this subset we establish related results for closed max plus cones and closed unbounded max plus convex sets in particular we show that a closed max plus convex set can be decomposed as a max plus sum of its recession cone and of the max plus convex hull of its extreme points

the tropical analogue of polar cones we study the max plus or tropical analogue of the notion of polar the polar of a cone represents the set of linear inequalities satisfied by its elements we establish an analogue of the bipolar theorem which characterizes all the inequalities satisfied by the elements of a tropical convex cone we derive this characterization from a new separation theorem we also establish variants of these results concerning systems of linear equalities

incremental proximal methods for large scale convex optimization we consider the minimization of a sum sum i 1 mf i x consisting of a large number of convex component functions f i for this problem incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective we propose new incremental methods consisting of proximal iterations applied to single components as well as combinations of gradient subgradient and proximal iterations we provide a convergence and rate of convergence analysis of a variety of such methods including some that involve randomization in the selection of components we also discuss applications in a few contexts including signal processing and inference machine learning

extremal solutions of inequations over lattices with applications to supervisory control we study the existence and computation of extremal solutions of a system of inequations defined over lattices using the knaster tarski fixed point theorem we obtain sufficient conditions for the existence of supremal as well as infimal solution of a given system of inequations iterative techniques are presented for the computation of the extremal solutions whenever they exist and conditions under which the termination occurs in a single iteration are provided these results are then applied for obtaining extremal solutions of various inequations that arise in computation of maximally permissive supervisors in control of logical discrete event systems dess first studied by ramadge and wonham thus our work presents a unifying approach for computation of supervisors in a variety of situations

success and failure of adaptation diffusion algorithms with decaying step size in multiagent networks this paper investigates the problem of distributed stochastic approximation in multiagent systems the algorithm under study consists of two steps a local stochastic approximation step and a diffusion step which drives the network to a consensus the diffusion step uses row stochastic matrices to weight the network exchanges as opposed to previous works exchange matrices are not supposed to be doubly stochastic and may also depend on the past estimate we prove that nondoubly stochastic matrices generally influence the limit points of the algorithm nevertheless the limit points are not affected by the choice of the matrices provided that the latter are doubly stochastic in expectation this conclusion legitimates the use of broadcast like diffusion protocols which are easier to implement next by means of a central limit theorem we prove that doubly stochastic protocols perform asymptotically as well as centralized algorithms and we quantify the degradation caused by the use of nondoubly stochastic matrices throughout this paper a special emphasis is put on the special case of distributed nonconvex optimization as an illustration of our results

max plus control design for temporal constraints meeting in timed event graphs the aim of the presented work is the control of timed event graph to meet tight temporal constraints the problem of temporal constraints is formulated in terms of control of linear max plus models first the synthesis of a control law that ensures the satisfaction of a single constraint for a single input system is presented then the single input multi constraints problem is tackled and finally the method is extended to the multi inputs multi constraints problem the proposed method is illustrated on the example of a simple production process

choice based elicitation and decomposition of decision weights for gains and losses under uncertainty this paper reports the results of an experimental parameter free elicitation and decomposition of decision weights under uncertainty assuming cumulative prospect theory utility functions were elicited for gains and losses at an individual level using the tradeoff method subsequently decision weights were elicited through certainty equivalents of uncertain two outcome prospects furthermore decision weights were decomposed using observable choice instead of invoking other empirical primitives as in previous experimental studies the choice based elicitation of decision weights allows for a quantitative study of their characteristics and also allows among other things for the examination of the sign dependence hypothesis for observed choice under uncertainty our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice based subjective probabilities we also find evidence for sign dependence of decision weights

an integrated control strategy to solve the disturbance decoupling problem for max plus linear systems with applications to a high throughput screening system this paper presents the new investigations on the disturbance decoupling problem ddp for the geometric control of max plus linear systems the classical ddp concept in the geometric control theory means that the controlled outputs will not be changed by any disturbances in practical manufacturing systems solving for the ddp would require further delays on the output parts than the existing delays caused by the system breakdown the new proposed modified disturbance decoupling problem mddp in this paper ensures that the controlled output signals will not be delayed more than the existing delays caused by the disturbances in order to achieve the just in time optimal control furthermore this paper presents the integration of output feedback and open loop control strategies to solve for the mddp as well as for the ddp if these controls can only solve for the mddp but not for the ddp an evaluation principle is established to compare the distance between two output signals generated by controls solving for the mddp and ddp respectively this distance can be interpreted as the number of tokens or firings that are needed in order for the controls to solve for the ddp moreover another alternative approach is finding a new disturbance mapping in order to guarantee the solvability of the ddp by the same optimal control for the mddp the main results of this paper are illustrated by using a timed event graph model of a high throughput screening system in drug discovery

decentralized parameter estimation by consensus based stochastic approximation in this paper an algorithm for decentralized multi agent estimation of parameters in linear discrete time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy an analysis of the asymptotic properties of the proposed algorithm is presented taking into account both the multi agent network structure and the probabilities of getting local measurements and implementing exchange of inter agent messages in the case of non vanishing gains in the stochastic approximation algorithms an asymptotic estimation error covariance matrix bound is defined as the solution of a lyapunov like matrix equation in the case of asymptotically vanishing gains the mean square convergence is proved and the rate of convergence estimated in the discussion the problem of additive communication noise is treated in a methodologically consistent way it is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence some simulation results illustrate the obtained theoretical results

on max plus linear dynamical system theory a class of timed discrete event systems can be modeled by using timed event graphs a class of timed petri nets that can have its firing dynamic described by using an algebra called max plus algebra for this kind of systems it may be desirable to enforce some timing constraints in steady state in this paper this problem is called a max plus regulation problem in this context we show a necessary condition for solving these regulation problems and in addition that this condition is sufficient for a large class of problems the obtained controller is a simple linear static state feedback and can be computed using efficient pseudo polynomial algorithms simulation results will illustrate the applicability of the proposed methodology

diffusion strategies outperform consensus strategies for distributed estimation over adaptive networks adaptive networks consist of a collection of nodes with adaptation and learning abilities the nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner in this work we compare the mean square performance of two main strategies for distributed estimation over networks consensus strategies and diffusion strategies the analysis in the paper confirms that under constant step sizes diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network diffusion networks are shown to converge faster and reach lower mean square deviation than consensus networks and their mean square stability is insensitive to the choice of the combination weights in contrast and surprisingly it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own when this occurs cooperation over the network leads to a catastrophic failure of the estimation task this phenomenon does not occur for diffusion networks we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology simulation results support the theoretical findings

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

paper a new approach to the analysis of discrete event dynamic systems we present a new time domain approach to the study of discrete event dynamical systems deds typified by queueing networks and production systems a general state space representation is developed and perturbation analysis is carried out observation of a single sample realization of such a system can be used to predict behavior over other sample realizations when some parameter is perturbed without having to make additional observations conditions under which this is always possible are investigated and explicit results for some special cases are included