control of singularly perturbed hybrid stochastic systems we study a class of optimal stochastic control problems involving two different time scales the fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process under a fundamental ergodicity property for a class of infinitesimal control systems associated with the fast mode we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system both the finite and infinite discounted horizon cases are considered we show how an approximate optimal control law can be constructed from the solution of the limit control problem in the particular case where the infinitesimal control systems possess the so called turnpike property i e characterized by the existence of global attractors the limit control problem can be given an interpretation related to a decomposition approach

effects of distributed transmission speeds on propagating activity in neural populations motivated by experimental evidence a distribution of axonal transmission speeds is introduced into a standard field model of neural populations the resulting field dynamics is analytically studied by a systematic investigation of the stability and bifurcations of equilibrium solutions using a perturbation approach the effect of distributed speeds on bifurcations of equilibria are determined for general connectivity and speed distributions in addition a nonlinear analysis of traveling fronts is given it is shown that the variance of the speed distribution affects the frequency of bifurcating periodic solutions and the phase speed of traveling waves moreover a new effect is discovered where the introduction of axonal speed distributions leads to the maximization of the traveling front speed doi 10 1103 physreve 73 021906 pacs numbers 87 18 hf 02 60 nm 87 19 la the measured activity of the neural system indicates that the spatiotemporal dynamics of the brain is intimately related to the various brain functions and cognition as examples we mention the space time instabilities during several types of hallucinations 1 and epileptic seizures 2 hence the study of the dynamics of neural models is important for understanding neural and cognitive processes in recent years several models of coupled neurons have attracted much attention including networks involving spatial structures 3 8 describing a continuous synaptically coupled neural field extended in space the dynamics of these fields is governed by

modeling distributed axonal delays in mean field brain dynamics the range of conduction delays between connected neuronal populations is often modeled as a single discrete delay assumed to be an effective value averaging over all fiber velocities this paper shows the effects of distributed delays on signal propagation a distribution acts as a linear filter imposing an upper frequency cutoff that is inversely proportional to the delay width distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean field model of the cortex and thalamus to illustrate their effects on the electroencephalogram eeg the power spectrum is acutely sensitive to the width of the thalamocortical delay distribution and more so than the corticothalamic distribution because all input signals must travel along the thalamocortical pathway this imposes a cutoff frequency above which the spectrum is overly damped the positions of spectral peaks in the resting eeg depend primarily on the distribution mean with only weak dependences on distribution width increasing distribution width increases the stability of fixed point solutions a single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width provided that other model parameters are moderately adjusted a pair of discrete delays together having the same mean variance and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment delay distributions with large fractional widths are well approximated by low order differential equations

approximation and decomposition of singularly perturbed stochastic hybrid systems this paper considers a singularly perturbed stochastic hybrid system whose state equations are governed by a stochastic switching process which is modelled as a nearly completely decomposable continuous time finite state markov chain approximate models for the slow mode subsystem are derived over the intervals of rapid switching and their accuracy the mean squared errors between the approximate models and the original systems is quantified aggregate models for the subsystem are obtained over a longer period the almost surely exponential stability of the subsystem is studied the behaviour of the fast subsystem which depends on the relative size of the perturbation parameters is analysed the decomposition of the overall system and the switching process together into slow and fast subsystems is investigated the results derived in the paper are shown to hold when the switching process is stationary and irreducible and each group of strongly interacting states is irreducible and time reversible fina

exponential bounds for discrete time singularly perturbed markov chains abstract this paper develops exponential type upper bounds for scaled occupation measures of singularly perturbed markov chains in discrete time by considering two time scale in the markov chains asymptotic analysis is carried out the cases of the fast changing transition probability matrix is irreducible and that are divisible into l ergodic classes are examined first the upper bounds of a sequence of scaled occupation measures are derived then extensions to markov chains involving transient states and or nonhomogeneous transition probabilities are dealt with the results enable us to further our understanding of the underlying markov chains and related dynamic systems which is essential for solving many control and optimization problems

aggregation of the policy iteration method for nearly completely decomposable markov chains a steady state optimal control problem is considered for nearly completely decomposable markov chains in order to apply the policy iteration method of r a howard dynamic programming and markov processes cambridge ma mit press 1960 a high dimensional ill conditioned system of algebraic equations must be solved in the value determination step although algorithms exist for aggregation of the steady state probability distribution problem they only provide methods for computing the cost not the dual variables using a singular perturbation approach an aggregation method for the value determination equation is developed the aggregation method is developed in three steps first a class of similarity transformations that transform the system into a singularly perturbed form is developed second an aggregation method to compute the steady state probability distribution is derived third this aggregation method is applied to the value determination step of howard s method 1960

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed

cooperative dynamics in a network of stochastic elements with delayed feedback networks of globally coupled noise activated bistable elements with connection time delays are considered the dynamics of these systems is studied numerically using a langevin description and analytically using 1 a gaussian approximation as well as 2 a dichotomous model the system demonstrates ordering phase transitions and multistability that is for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function other observed dynamical phenomena include coherence resonance and in the case of nonuniform coupling strengths amplitude death and chaos furthermore an increase of the stability of the trivial equilibrium with increasing nonuniformity of the time delays is observed

can distributed delays perfectly stabilize dynamical networks department of physics kyoto university sakyo ku kyoto 606 8502 japan dated february 2 2008 signal transmission delays tend to destabilize dynamical networks leading to oscillation but theirdispersion contributes oppositely toward stabilization we analyze an integro di erential equationthat describes the collective dynamics of a neural network with distributed signal delays with thegamma distributed delays less dispersed than exponential distribution the system exhibits reentrantphenomena in which the stability is once lost but then recovered as the mean delay is increased with delays dispersed more highly than exponential the system never destabilizes

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

analysis and comparison of multiple delay schemes for controlling unstable fixed points of discrete maps we investigate theoretically the stabilization of a fixed point of a discrete one dimensional nonlinear map by applying small perturbations to an accessible system parameter or variable the size of the perturbations is determined in real time using feedback schemes incorporating only the dynamical state of the system and its state at previous iterates without making a comparison to a reference state in particular we compare and contrast two algorithms extended time delay autosynchronization which uses an infinite series of past iterates with weights that decay by a factor of r with each time step and n time delay autosynchronization which uses an average of n past iterates with equal weights the range of feedback parameters that successfully stabilize the fixed point and the robustness of the schemes to noise are determined it is found that the domain of control for the two schemes is similar for appropriately matched values of r and n and that n time delay autosynchronization tends to be less sensitive to noise s1063 651x 98 02706 8

a two factor stochastic production model with two time scales a two factor production model where one factor is characterized by a continuous state variable and corresponds to the fast mode via a controlled diffusion process whereas the second factor is characterized by a discrete variable and corresponds to the slow mode via a controlled jump process

subsystems time scales and multimodeling through a couple of naive examples the control theorists are invited to re examine the role of modeling in the study of large scale dynamic systems instead of assuming the existence of n diagonally dominant blocks it is possible to justify one strongly coupled slow core and n weakly coupled fast subsystems this structure is exhibited with a physically meaningful choice of state variables the controls are introduced following the recent concept of multimodeling

reduced complexity estimation for large scale hidden markov models in this paper we address the problem of reduced complexity estimation of general large scale hidden markov models hmms with underlying nearly completely decomposable discrete time markov chains and finite state outputs an algorithm is presented that computes o spl epsi where spl epsi is the related weak coupling parameter approximations to the aggregate and full order filtered estimates with substantial computational savings these savings are shown to be quite large when the chains have blocks with small individual dimensions some simulation studies are presented to demonstrate the performance of the algorithm

steady state stabilization due to random delays in maps with self feedback loops and in globally delayed coupled maps we study the stability of the fixed point solution of an array of mutually coupled logistic maps focusing on the influence of the delay times ij of the interaction between the ith and jth maps two of us recently reported phys rev lett 94 134102 2005 that if ij are random enough the array synchronizes in a spatially homogeneous steady state here we study this behavior by comparing the dynamics of a map of an array of n delayed coupled maps with the dynamics of a map with n self feedback delayed loops if n is sufficiently large the dynamics of a map of the array is similar to the dynamics of a map with self feedback loops with the same delay times several delayed loops stabilize the fixed point when the delays are not the same however the distribution of delays plays a key role if the delays are all odd a periodic orbit and not the fixed point is stabilized we present a linear stability analysis and apply some mathematical theorems that explain the numerical results

markov property for a function of a markov chain a linear algebra approach abstract in this paper we address whether a probabilistic function of a finite homogeneous markov chain still enjoys a markov type property we propose a complete answer to this question using a linear algebra approach at the core of our approach is the concept of invariance of a set under a matrix in that sense the framework of this paper is related to the so called geometric approach in control theory for linear dynamical systems this allows us to derive a collection of new results under generic assumptions on the original markov chain in particular we obtain a new criterion for a function of a markov chain to be a homogeneous markov chain we provide a deterministic polynomial time algorithm for checking this criterion moreover a non standard notion of observability for a linear system will be used this allows one to show that the set of all stochastic matrices for which our criterion holds is nowhere dense in the set of stochastic matrices

applications of the method of partial inverses to convex programming decomposition a primal dual decomposition method is presented to solve the separable convex programming problem convergence to a solution and lagrange multiplier vector occurs from an arbitrary starting point the method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction in the nonseparable case it specializes to a known method the proximal method of multipliers conditions are provided which guarantee linear convergence

two time scale controlled markov chains a decomposition and parallel processing approach this correspondence deals with a class of ergodic control problems for systems described by markov chains with strong and weak interactions these systems are composed of a set of subchains that are weakly coupled using results already available in the literature one formulates a limit control problem the solution of which can be obtained via an associated nondifferentiable convex programming ndcp problem the technique used to solve the ndcp problem is the analytic center cutting plane method accpm which implements a dialogue between on one hand a master program computing the analytical center of a localization set containing the solution and on the other hand an oracle proposing cutting planes that reduce the size of the localization set at each main iteration the interesting aspect of this implementation comes from two characteristics i the oracle proposes cutting planes by solving reduced sized markov decision problems mdp via a linear program lp or a policy iteration method ii several cutting planes can be proposed simultaneously through a parallel implementation on processors the correspondence concentrates on these two aspects and shows on a large scale mdp obtained from the numerical approximation ldquoa la kushner dupuisrdquo of a singularly perturbed hybrid stochastic control problem the important computational speed up obtained

a real schur form method for modeling singularly perturbed systems a method is presented for modeling a two time scale system in the singularly perturbed form the method uses an ordered real schur decomposition which can be efficiently computed using standard subroutines from eispack three results are given first it is shown that any two time scale system can be modeled in the singularly perturbed form by a transformation into an ordered real schur form followed by balancing second under some conditions on the ordered real schur decomposition a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables third necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables

paper on coherency based decomposition algorithms a new algorithm of coherency based decomposition is presented and applied contrary to avramovic and coworkers algorithm it does not necessarily imply in practice the knowledge of the eigenvalues and eigenvectors of the system or an a priori knowledge of the number of coherent areas as long as two classes of dynamics slow and fast exist its applicability to the case of a 48 machine system is demonstrated

optimizing zero forcing precoders for mimo broadcast systems in this paper we develop optimization techniques for linear zero forcing zf multiple input multiple output mimo broadcast bc precoders a computationally efficient technique based on qr update algorithms for implementing this optimization is then proposed the application of the proposed zf precoders and decoders to systems with both large and small numbers of users is considered the proposed optimization technique is also shown to perform very well in conjunction with nonlinear tomlinson harashima precoding both coded and uncoded performances are considered

reduced complexity filtering for partially observed nearly completely decomposable markov chains this paper provides a systematic method of obtaining reduced complexity approximations to aggregate filters for a class of partially observed nearly completely decomposable markov chains it is also shown why an aggregate filter adapted from courtois 1977 aggregation scheme has the same order of approximation as achieved by the algorithm proposed in this paper this algorithm can also be used systematically to obtain reduced complexity approximations to the full order fitter as opposed to algorithms adapted from other aggregation schemes however the computational savings in computing the full order filters are substantial only when the large scale markov chain has a large number of weakly interacting blocks or superstates with small individual dimensions some simulations are carried out to compare the performance of our algorithm with algorithms adapted from various other aggregation schemes on the basis of an average approximation error criterion in aggregate slow filtering these studies indicate that the algorithms adapted from other aggregation schemes may become ad hoc under certain circumstances the algorithm proposed in this paper however always yields reduced complexity filters with a guaranteed order of approximation by appropriately exploiting the special structures of the system matrices

complexity reduction in fixed lag smoothing for hidden markov models we investigate approximate smoothing schemes for a class of hidden markov models hmms namely hmms with underlying markov chains that are nearly completely decomposable the objective is to obtain substantial computational savings our algorithm can not only be used to obtain aggregate smoothed estimates but can be used also to obtain systematically approximate full order smoothed estimates with computational savings and rigorous performance guarantees unlike many of the aggregation methods proposed earlier

high dimensional chaotic behavior in systems with time delayed feedback abstract the nature of high dimensional chaos exhibited by a class of delay differential equation is investigated by various methods this delay differential equation models systems with time delayed feedback such as nonlinear optical resonators we first describe briefly the bifurcation phenomena exhibited by the system with an increase in a control parameter representing the energy flow rate periodic states bi multi furcate themselves successively forming a hierarchy of multistable periodic states with increasing complexities finally each branch of multistable periodic states makes transition to chaos the possibility of applying such a multistability as a memory device for complicated information is discussed in the chaotic regime each of the bifurcated states in turn merge successively into fewer sets of states with larger attractor dimensions and finally a single developed chaos with a very large attractor dimension is formed lyapunov analysis is introduced to study the high dimensional chaotic states the lyapunov vectors as well as lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above characteristics of developed chaos are investigated by high pass filtered time series hfts the intermittency characteristics of the hfts changes markedly at a certain frequency the lyapunov analysis reveals that this frequency corresponds to a characteristic lyapunov mode number this characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense

generalized channel inversion methods for multiuser mimo systems block diagonalization bd is a well known precoding method in multiuser multi input multi output mimo broadcast channels this scheme can be considered as a extension of the zero forcing zf channel inversion to the case where each receiver is equipped with multiple antennas one of the limitation of the bd is that the sum rate does not grow linearly with the number of users and transmit antennas at low and medium signal to noise ratio regime since the complete suppression of multi user interference is achieved at the expense of noise enhancement also it performs poorly under imperfect channel state information in this paper we propose a generalized minimum mean squared error mmse channel inversion algorithm for users with multiple antennas to overcome the drawbacks of the bd for multiuser mimo systems we first introduce a generalized zf channel inversion algorithm as a new approach of the conventional bd applying this idea to the mmse channel inversion for identifying orthonormal basis vectors of the precoder and employing the mmse criterion for finding its combining matrix the proposed scheme increases the signal to interference plus noise ratio at each user s receiver simulation results confirm that the proposed scheme exhibits a linear growth of the sum rate as opposed to the bd scheme for block fading channels with four transmit antennas the proposed scheme provides a 3 db gain over the conventional bd scheme at 1 frame error rate also we present a modified precoding method for systems with channel estimation errors and show that the proposed algorithm is robust to channel estimation errors

singularly perturbed markov chains with two small parameters a matched asymptotic expansion this work is concerned with asymptotic properties of solutions to forward equations for singularly perturbed markov chains with two small parameters it is motivated by the model of a cost minimizing firm involving production planning and capacity expansion and a two level hierarchical decomposition our effort focuses on obtaining asymptotic expansions of the solutions to the forward equation different from previous work on singularly perturbed markov chains the inner expansion terms are constructed by solving certain partial differential equations the methods of undetermined coefficients are used the error bound is obtained

paper optimal control of markov chains admitting strong and weak interactions this paper is devoted to the study of an optimal control problem for a markov chain with generator b ea where e is a small parameter it is shown that an approximate solution can be calculated by a policy improvement algorithm involving computations relative to an aggregated problem the dimension of which is given by n the number of ergodic sets for the b matrix together with a family of decentralized problems the dimensions of which are given by the number of elements in each ergodic set for the b matrix

zero forcing methods for downlink spatial multiplexing in multiuser mimo channels the use of space division multiple access sdma in the downlink of a multiuser multiple input multiple output mimo wireless communications network can provide a substantial gain in system throughput the challenge in such multiuser systems is designing transmit vectors while considering the co channel interference of other users typical optimization problems of interest include the capacity problem maximizing the sum information rate subject to a power constraint or the power control problem minimizing transmitted power such that a certain quality of service metric for each user is met neither of these problems possess closed form solutions for the general multiuser mimo channel but the imposition of certain constraints can lead to closed form solutions this paper presents two such constrained solutions the first referred to as block diagonalization is a generalization of channel inversion when there are multiple antennas at each receiver it is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high snr the second known as successive optimization is an alternative method for solving the power minimization problem one user at a time and it yields superior results in some e g low snr situations both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined in order to accommodate more general scenarios we also propose a framework for coordinated transmitter receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas while the proposed algorithms are suboptimal they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity

zero forcing precoding and generalized inverses we consider the problem of linear zero forcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra special attention is given to a specific generalized inverse known as the pseudo inverse we begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo inverse are optimal among the generalized inverses in this setting then we proceed to examine individual per antenna power constraints in this case the pseudo inverse is not necessarily the optimal inverse in fact finding the optimal matrix is nontrivial and depends on the specific performance measure we address two common criteria fairness and throughput and show that the optimal generalized inverses may be found using standard convex optimization methods we demonstrate the improved performance offered by our approach using computer simulations

asymptotic optimization of a nonlinear hybrid system governed by a markov decision process we consider in this paper a continuous time stochastic hybrid control system with finite time horizon the objective is to minimize a nonlinear function of the state trajectory the state evolves according to a nonlinear dynamics the parameters of the dynamics of the system may change at discrete times l epsilon l 0 1 according to a controlled markov chain which has finite state and action spaces under the assumption that epsilon is a small parameter we justify an averaging procedure allowing us to establish that our problem can be approximated by the solution of some deterministic optimal control problem

solving large scale sparse semidefinite programs for combinatorial optimization we present a dual scaling interior point algorithm and show how it exploits the structure and sparsity of some large scale problems we solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints we report the first computational results of interior point algorithms for approximating maximum cut semidefinite programs with dimension up to 3 000

a stochastic multiscale model for electricity generation capacity expansion abstract long term planning for electric power systems or capacity expansion has traditionally been modeled using simplified models or heuristics to approximate the short term dynamics however current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics we present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of markov processes in continuous time we show that the uncertainties that exist in many energy planning problems in particular load demand uncertainty and uncertainties in generation availability can be captured with a multiscale model we then use a dimensionality reduction technique which is valid if the scale separation present in the model is large enough to derive a computationally tractable model we show that both wind data and electricity demand data do exhibit sufficient scale separation a numerical example using real data and a finite difference approximation of the hamilton jacobi bellman equation is used to illustrate the proposed method we compare the results of our approximate model with those of the exact model we also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models

a method to calculate steady state distributions of large markov chains by aggregating states this paper develops an efficient iterative algorithm to calculate the steady state distribution of nearly all irreducible discrete time markov chains computational experiences suggest that for large markovian systems more than 130 states the proposed algorithm can be ten times faster than standard gaussian elimination in finding solutions to an accuracy of 0 1 the proposed algorithm is developed in three stages first we develop a very efficient algorithm for determining steady state distributions of a restricted class of markovian systems a second result establishes a relationship between a general irreducible markovian system and a system in the restricted class of markovian systems finally we combine the two results to produce an efficient iterative algorithm to solve markov systems the paper concludes with a discussion of the observed performance of the algorithm

estimating axon conduction velocity in vivo from microstructural mri the conduction velocity cv of action potentials along axons is a key neurophysiological property central to neural communication the ability to estimate cv in humans in vivo from non invasive mri methods would therefore represent a significant advance in neuroscience however there are two major challenges that this paper aims to address 1 much of the complexity of the neurophysiology of action potentials cannot be captured with currently available mri techniques therefore we seek to establish the variability in cv that can be captured when predicting cv purely from parameters that have been reported to be estimatable from mri inner axon diameter ad and g ratio 2 errors inherent in existing mri based biophysical models of tissue will propagate through to estimates of cv the extent to which is currently unknown issue 1 is investigated by performing a sensitivity analysis on a comprehensive model of axon electrophysiology and determining the relative sensitivity to various morphological and electrical parameters the investigations suggest that 85 of the variance in cv is accounted for by variation in ad and g ratio the observed dependency of cv on ad and g ratio is well characterised by the previously reported model by rushton issue 2 is investigated through simulation of diffusion and relaxometry mri data for a range of axon morphologies applying models of restricted diffusion and relaxation processes to derive estimates of axon volume fraction avf ad and g ratio and estimating cv from the derived parameters the results show that errors in the avf have the biggest detrimental impact on estimates of cv particularly for sparse fibre populations avf 0 3 for our equipment set up and acquisition protocol cv estimates are most accurate below 5 error where avf is above 0 3 g ratio is between 0 6 and 0 85 and ad is high above 4 m cv estimates are robust to errors in g ratio estimation but are highly sensitive to errors in ad estimation particularly where ads are small we additionally show cv estimates in human corpus callosum in a small number of subjects in conclusion we demonstrate accurate cv estimates are possible in regions of the brain where ad is sufficiently large problems with estimating ads for smaller axons presents a problem for estimating cv across the whole cns and should be the focus of further study

synchronization of discrete dynamical networks with non delayed and delayed coupling in this paper synchronization of discrete dynamical networks with both non delayed and delayed couplings are studied firstly a class of complex networks with invariable topology structure are considered secondly a class of complex networks with variable topology structure are discussed based on lyapunov function method and linear matrix inequalities the sufficient conditions for asymptotically local synchronization of the above two classes of networks are presented respectively finally numerical examples are provided to verify our results

effects of axonal time delay on synchronization and wave formation in sparsely coupled neuronal oscillators we investigate the effects of axonal time delay when the neuronal oscillators are coupled by sparse and random connections using phase reduced models with general coupling functions we show that a small fraction of connections with time delay can destabilize synchronous states and induce near regular wave states an order parameter is introduced to characterize those states we analyze the systems using mean field type approximation

a unified view of aggregation and coherency in networks and markov chains abstract this paper presents a unified treatment of aggregability lumpability coherency reversibility partial balance and similar properties appearing in different fields including power systems and queueing theory a coherency condition well known in power systems implies the existence of a finite state filter for markov chains while aggregability and coherency yield a new condition for decentralized computation of the invariant measure

stabilization of a steady state in network oscillators by using diffusive connections with two long time delays the present study shows that diffusive connections with two long time delays can induce the stabilization of a steady state in network oscillators a linear stability analysis shows that if the two delay times retain a proportional relation with a certain bias the stabilization can be achieved independent of the delay times furthermore a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed the procedure has the following two advantages one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology our analytical results are applied to the well known double scroll circuit model on a small world network

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

asymptotic expansions of solutions of integro differential equations for transition densities of singularly perturbed switching diffusions rapid switchings this work develops asymptotic expansions for solutions of integro differential equations arising from transition densities of singularly perturbed switching diffusion processes the underlying processes have two components namely the switching component and the diffusion component processes with rapid switchings are examined here under suitable conditions it is proved that the asymptotic expansion is uniformly valid in the domain of interest

markov decision processes with slow scale periodic decisions we consider a class of discrete time dynamic decision making models which we refer to as periodically time inhomogeneous markov decision processes ptmdps in these models the decision making horizon can be partitioned into intervals calledslow scale cycles ofn 1 epochs the transition law and reward function are time homogeneous over the firstn epochs of each slow scale cycle but distinct at the final epoch the motivation for such models is in applications where decisions of different nature are taken at different time scales i e many low level decisions are made between less frequent high level ones for the ptmdp model we consider the problem of optimizing the expected discounted reward when rewards devalue by a discount factor at the beginning of each slow scale cycle whenn is large initially stationary policies i s p s are natural candidates for optimal policies similar to turnpike policies an initially stationary policy uses the same decision rule for some large number of epochs in each slow scale cycle followed by a relatively short planning horizon of time varying decision rules in this paper we characterize the form of the optimal value as a function ofn establish conditions ensuring the existence of near optimal i s p s and characterize their structure our analysis deals separately with the cases where the time homogeneous part of the system has state dependent and state independent optimal average reward as we illustrate the results in these two distinct cases are qualitatively different

optimal kullback leibler aggregation via spectral theory of markov chains this paper is concerned with model reduction for complex markov chain models the kullback leibler divergence rate is employed as a metric to measure the difference between the markov model and its approximation for a certain relaxation of the bi partition model reduction problem the solution is shown to be characterized by an associated eigenvalue problem the form of the eigenvalue problem is closely related to the markov spectral theory for model reduction this result is the basis of a heuristic proposed for the m ary partition problem resulting in a practical recursive algorithm the results are illustrated with examples

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

stochastic dynamic job shops and hierarchical production planning this paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products the concept of a dynamic job shop is introduced by interpreting the system as a directed graph and the structure of the system dynamics is characterized for its use in the asymptotic analysis the optimal control problem for the system is a state constrained problem since the number of parts in any buffer between any two machines must remain nonnegative a limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities as the rate of change in machine states approaches infinity the value function of the original problem is shown to converge to that of the limiting problem and the convergence rate is obtained furthermore near optimal controls for the original problem are constructed from near optimal controls of the limiting problem and an error estimate is obtained on the near optimality of the constructed controls

population dynamics of spiking neurons fast transients asynchronous states and locking an integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate and fire type is discussed it is analytically shown that transients from a state of incoherent firing can be immediate the stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived the response of a population of noisy integrate and fire neurons to an input current of small amplitude is calculated and characterized by a linear filter l the stability of perfectly synchronized locked solutions is analyzed

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods