recovering the initial state of an infinite dimensional system using observers let a be the generator of a strongly continuous semigroup t on the hilbert space x and let c be a linear operator from d a to another hilbert space y possibly unbounded with respect to x not necessarily admissible we consider the problem of estimating the initial state z 0 d a with respect to the norm of x from the output function y t ct tz 0 given for all t in a bounded interval 0 t we introduce the concepts of estimatability and backward estimatability for a c in a more general way than currently available in the literature we introduce forward and backward observers and we provide an iterative algorithm for estimating z 0 from y this algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the gramian our results lead also to a very general formulation of russell s principle i e estimatability and backward estimatability imply exact observability this general formulation of the principle does not require t to be invertible we illustrate our estimation algorithms on systems described by wave and schrodinger equations and we provide results from numerical simulations

exact results for one dimensional cellular automata with different types of updates we study two common types of time noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions we first construct the stationary states using the matrix product formalism this construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates using this connection we derive explicit relations between the densities and correlation functions for these different stationary states

feedback boundary stabilization of wave equations with interior delay in this paper we consider a boundary stabilization problem for the wave equation with interior delay we prove an exponential stability result under some lions geometric condition the proof of the main result is based on an identity with multipliers that allows us to obtain a uniform decay estimate for a suitable lyapunov functional

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

sampled data observers for semilinear damped wave equations under spatially sampled state measurements abstract sampled data observers controllers under the sampled in space and time measurements were suggested in the past for parabolic systems in the present paper for the first time a sampled data observer is constructed for a hyperbolic system governed by 1d semilinear wave equation with either viscous or boundary damping the measurements are sampled in space and time sufficient conditions for the exponential stability of the estimation error are derived by using the time delay approach to sampled data control and appropriate lyapunov krasovskii functionals the dual sampled data controller problems are formulated numerical examples including observer design for unstable damped sine gordon equation illustrate the efficiency of the method

partially asymmetric exclusion process with open boundaries exclusive diffusion on a one dimensional lattice is studied in the model particles hop stochastically in both directions but with different rates at the ends of the lattice particles are injected and removed the exact stationary probability measure is represented in the form of a matrix product as a generalization of the solution given by derrida et al j phys a 26 1493 1993 for the fully asymmetric process the phase diagram of the current on the infinite lattice is obtained analytic expressions for the current in the different phases are derived the model is equivalent to an xxz heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation

exact solution of an exclusion process with three classes of particles and vacancies we present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies using a matrix product ansatz we find exact expressions for the weights of the configurations in the stationary state the solution involves tensor products of quadratic algebras

generalized bethe ansatz solution of a one dimensional asymmetric exclusion process on a ring with blockage we present a model for a one dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthl with a single defect across which they move with probability 0 p 1 this model is equivalent to a two dimensional six vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions we solve this model with a bethe ansatz generalized to this kind of boundary condition we discuss in detail the steady state and derive exact expressions for the currentj the density profilen x and the two point density correlation function in the thermodynamic limitl the phase diagram shows three phases a low density phase a coexistence phase and a high density phase related to the low density phase by a particle hole symmetry in the low density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale on the phase transition line diverges and the currentj approaches its critical valuejc p as a power law jc j 1 2 in the coexistence phase the width of the interface between the high density region and the low density region is proportional tol1 2 if the density f 1 2 and 0 independent ofl if 1 2 the connected two point correlation function turns out to be of a scaling form with a space dependent amplitude n x1 x2 a x2 ake r withr x2 x1 and a critical exponent 0

exact controllability of a class of nonlinear distributed parameter systems using back and forth iterations we investigate the exact controllability of a nonlinear plant described by the equation x t ax t bu t bnn x t t where t 0 here a is the infinitesimal generator of a strongly cont

semilinear observation systems abstract in this paper we introduce locally lipschitz observation systems for nonlinear semigroups and show that they can be represented by an admissible nonlinear output operator defined on a suitable subspace in the semilinear case this concept fits well to the lebesgue extension known from linear system theory for semilinear systems we show robustness of exact observability near equilibria under locally small lipschitz perturbations finally we apply our results to a damped nonlinear plate equation and a semilinear thermo elastic system

temporal evolution of product shock measures in the totally asymmetric simple exclusion process with sublattice parallel update it is known that when the steady state of a one dimensional multispecies system which evolves via a random sequential updating mechanism is written in terms of a linear combination of bernoulli shock measures with random walk dynamics it can be equivalently expressed as a matrix product state in this case the quadratic algebra of the system always has a two dimensional matrix representation our investigations show that this equivalence exists at least for the systems with deterministic sublattice parallel update in this paper we consider the totally asymmetric simple exclusion process on a finite lattice with open boundaries and sublattice parallel update as an example

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal h sub 2 l sub 1 control via duality theory in this paper we consider the problem of minimizing the h sub 2 norm of the closed loop map while maintaining its l sub 1 norm at a prescribed level the problem is analyzed in the case of discrete time siso closed loop maps utilizing duality theory it is shown that the optimal solution is unique and in the nontrivial case where the l sub 1 constraint is active the optimal solution has a finite impulse response a finite step procedure is given for the construction of the exact solution this procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods finally continuity properties of the optimal solution with respect to changes in the l sub 1 constraint are established

on matrix product ground states for reaction diffusion models we discuss a new mechanism leading to a matrix product form for the stationary state of one dimensional stochastic models the corresponding algebra is quadratic and involves four different matrices for the example of a coagulation decoagulation model explicit four dimensional representations are given and exact expressions for various physical quantities are recovered we also find the general structure of n point correlation functions at the phase transition

a characterization of all solutions to the four block general distance problem all solutions to the four block general distance problem which arises in h infty optimal control are characterized the procedure is to embed the original problem in an all pass matrix which is constructed it is then shown that part of this all pass matrix acts as a generator of all solutions special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all pass transfer functions as an application necessary and sufficient conditions are found for the existence of an h infty optimal controller following that a descriptor representation of all solutions is derived

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest

a hamiltonian formulation of risk sensitive linear quadratic gaussian control we consider the optimal control problem with time homogeneous linear and in general non markov dynamics and risk sensitive criterion appeal to the extremal principle prescribed by the risk sensitive certainty equivalence principle rscep yields a symmetric equation system indicating that the extended hamiltonian formulation generalizes naturally to the risk sensitive case the conjugate variable of a hamiltonian formulation now has an interpretation in terms of forecasted process noise and the rscep in fact provides a stochastic maximum principle for which all variables have a clear interpretation and the desired measurability properties in the infinite horizon case meaningful under generalized controllability conditions optimal control is determined explicitly in terms of a canonical factorization for the case of imperfect process observation the rscep leads to coupled equation systems that can again be solved in terms of canonical factorizations in the time invariant stationary case

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

observer based boundary control of the sine gordon model energy abstract the problem of observer based boundary control of the sine gordon model energy is first posed a luenberger type observer for the sine gordon equation is analysed and explicit bounds on the system parameters ensuring the exponential decay of the estimation error are obtained with the use of this observer a speed gradient output feedback for sine gordon model energy control is proposed the achievement of the control goal is established under the assumption that system s energy does not vanish in finite time it is shown that the transient time in energy is close that the transient time in observation error i e the closed loop system has a reasonable performance it is also shown that the conditions on the observer gain sufficient for the state estimation error convergence are almost necessary in the sense that violation of these conditions makes the state estimation error transients too long

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

exact results for 2d directed animals on a strip of finite width proves a conjecture giving the exact number of directed animals of s sites with any root on a strip of finite width of a square lattice the authors also rederive more simply some previous results concerning the connective constant and particular eigenvectors of the transfer matrix

stabilization of second order evolution equations with unbounded feedback with time dependent delay we consider abstract second order evolution equations with unbounded feedback with time varying delay existence results are obtained under some realistic assumptions we prove the exponential decay under some conditions by introducing an abstract lyapunov functional our abstract framework is applied to the wave to the beam and to the plate equations with boundary delays

a maximum entropy principle for contractive interpolants abstract in this paper a maximum entropy principle is established for a class of continuous contractive m n matrix valued functions g with preassigned fourier coefficients gj j for j 0 1 the function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a hankel operator based on the prescribed matrices 0 1 a pair of seemingly new szego type formulas are obtained enroute and some applications to nevanlinna pick interpolation are indicated

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

concentration and lack of observability of waves in highly heterogeneous media we construct rapidly oscillating holder continuous coefficients for which the corresponding 1 dimensional wave equation lacks the classical observability property guaranteeing that the total energy of solutions may be bounded above by the energy localized in an open subset of the domain where the equation holds if the observation time is large enough the coefficients we build oscillate arbitrarily fast around two accumulation points this allows us to build quasi eigenfunctions for the corresponding eigenvalue problem that concentrate the energy away from the observation region as much as we wish this example may be extended to several space dimensions by separation of variables and illustrates why the well known controllability and dispersive properties for wave equations with smooth coefficients fail in the class of holder continuous coefficients in particular we show that for such coefficients no strichartz type estimate holds

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

minimum entropy static output feedback control with an h sub spl infin norm performance bound the problem of designing static output feedback controllers is considered the controller is required to minimize the closed loop entropy at s spl infin and to satisfy a prescribed h sub spl infin norm bound the design equations consist of a modified riccati equation and a lyapunov equation that are coupled via a projection these equations are solved using a homotopy algorithm the design procedure is illustrated by two examples the first one is a classical example that was solved in the literature using convex optimization techniques the second example is one of designing a gain scheduled normal acceleration loop for an air launched unmanned air vehicle

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

observer based compensators for fixed order h control this paper present a two riccati inequality approach for the design of fixed order h suboptimal controllers with an observer based structure the two riccati inequalities are only one way coupled and can be solved consecutively the fixed order controller has the structure of a fixed order estimator of the state feedback control law in the presence of the worst case disturbances it retains the observed based compensator structure of the full order central controller of the standard h design but adds a fixed order dynamic and mappings between the full order and the fixed order state spaces in the full order special case this controller recovers to the minimal entropy central controller of the standard h design

solutions to the h general distance problem which minimize an entropy integral abstract we pose and solve the problem of minimizing the entropy of an h norm bounded and stabilized closed loop solution proceeds via the equivalent error system distance problem the central member of the admissible class is shown to minimize the entropy at infinity and in that case an explicit state space formula is derived for the minimum value of the entropy links between entropy h 2 norms and h 2 optimal control are given

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

asymmetric exclusion processes with shuffled dynamics the asymmetric simple exclusion process asep with periodic boundary conditions is investigated for shuffled dynamics in this type of update in each discrete timestep the particles are updated in a random sequence such an update is important for several applications e g for certain models of pedestrian flow in two dimensions for the asep with shuffled dynamics and a related truncated process exact results are obtained for deterministic motion p 1 since the shuffled dynamics is intrinsically stochastic also this case is nontrivial for the case of stochastic motion 0 p 1 it is shown that in contrast to all other updates studied previously the asep with shuffled update does not have a product measure steady state approximative formulae for the steady state distribution and fundamental diagram are derived that are in very good agreement with simulation data

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

an entropy formula for time varying discrete time control systems the results of this paper generalize the formula for the entropy of a transfer function to time varying systems this is done through the use of some results on spectral factorizations due to arveson and properties of the cw transform which generalizes the usual cz transform for time varying systems using the formula defined it is shown that for linear fractional transformations like those that arise in time varying f control there exists a unique bounded contraction which maximizes the entropy this generalizes known results in the time invariant case possible extensions are discussed along with state space formulae

a risk sensitive maximum principle abstract a stochastic maximum principle is derived which is formally of general application and so not restricted to the diffusion case it moreover differs from the classic deterministic principle only by a modification of the hamiltonian and so requires no solution of stochastic differential equations or calculation of conditional expectations the two essential points in its construction are that one considers the family of criterion functions exponential in an additive cost function of which the conventional expected cost case is a degenerate member and that in the non lqg case appeal to large deviation theory must be valid

cellular automation models and traffic flow a cellular automaton model for the description of traffic flow is investigated it generalizes asymmetric exclusion models which have attracted a lot of interest in the past the authors calculate the so called fundamental diagram flow versus density for parallel dynamics using an improved mean field approximation which takes into account short range correlations for maximum velocity they find that the simplest of these non trivial approximations gives the exact result for higher velocities their results are in excellent agreement with numerical data

matrix product ground states for exclusion processes with parallel dynamics we show in the example of a one dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form the corresponding algebra is quadratic and involves three different matrices using this formalism we prove previous conjectures for the equal time correlation functions of the model

a risk sensitive maximum principle the case of imperfect state observation the risk sensitive maximum principle for optimal stochastic control derived by the author in an earlier work system control letters vol 15 1990 is restated this is an immediate generalization of the classic pontryagin principle to which it reduces in the deterministic case and is expressed immediately in terms of observables it is derived on the assumption that the criterion function is the exponential of an additive cost function and is exact under linear quadratic gaussian assumptions but is otherwise valid as a large deviation approximation the principle is extended to the case of imperfect state observation after preliminary establishment of a certainty equivalence principle the derivation yields as byproduct a large deviation version of the updating equation for nonlinear filtering the development is heuristic it is believed that the mathematical arguments given are the essential ones and provide a self contained treatment at this level

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

discrete time h controllers satisfying a minimum entropy criterion a discrete time minimum entropy h control problem is solved and state space formulae are derived the solution is obtained from first principles and so avoids the reformulation of the problem to a continuous time problem via a bilinear transformation

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

duality relations for asymmetric exclusion processes we derive duality relations for a class ofu q su 2 symmetric stochastic processes including among others the asymmetric exclusion process in one dimension like the known duality relations for symmetric hopping processes these relations express certainm point correlation functions inn particle systems n m in terms of sums of correlation functions of the same system but with onlym particles for the totally asymmetric case we obtain exact expressions for some boundary density correlation functions the dynamical exponent for these correlators isz 2 which is different from the dynamical exponent for bulk density correlations which is known to bez 3 2

new stability and exact observability conditions for semilinear wave equations the problem of estimating the initial state of 1 d wave equations with globally lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers and deriving the upper bound for exact observability time in terms of linear matrix inequalities lmis fridman 2013 in the present paper we generalize this result to n d wave equations on a hypercube this extension includes new lmi based exponential stability conditions for n d wave equations as well as an upper bound on the minimum exact observability time in terms of lmis for 1 d wave equations with locally lipschitz nonlinearities we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements the efficiency of the results is illustrated by numerical examples

product measures and dynamics for solid on solid interfaces a two species asymmetric exclusion process is considered with general transition rates subject only to the constraint of charge conservation conditions for the existence of a stationary product measure are found in both the cases of odd even parallel dynamics and continuous time dynamics the results are then applied to a one dimensional restricted solid on solid model considered as a model of driven interfacial growth showing a nontrivial dependence of the stationary measure on the external driving field the dependence of the growth velocity on the slope of the interface is given and interface shapes in finite volume with opposite boundary conditions are investigated numerically

state space formulae for all the stabilizing discrete controllers that satisfy an h norm bound part 1 main results and the full information problem given a linear discrete time system necessary and sufficient conditions for the existence of a linear or nonlinear controller which satisfies a specified closed loop h norm bound are stated in terms of the solutions to two uncoupled algebraic discrete riccati equations of the order of the system state space formulae for all the stabilizing controllers some of the order of the system which satisfy an achievable bound are also given in this first part of the paper new growth and convergence properties of the solution to a time varying discrete riccati equation are used to derive the necessary and sufficient conditions for the existence of a solution in the full information case these properties generalize those of the corresponding discrete riccati equation related to the lqr problem in the second part of the paper a non standard estimation problem is posed and solved this problem arises as a novel reinterpretation of the h norm objective its solution can be used to reduce a partial informa

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

finitely correlated states on quantum spin chains we study a construction that yields a class of translation invariant states on quantum spin chains characterized by the property that the correlations across any bond can be modeled on a finite dimensional vector space these states can be considered as generalized valence bond states and they are dense in the set of all translation invariant states we develop a complete theory of the ergodic decomposition of such states including the decomposition into periodic neel ordered states the ergodic components have exponential decay of correlations all states considered can be obtained as local functions of states of a special kind so called purely generated states which are shown to be ground states for suitably chosen finite range vbs interactions we show that all these generalized vbs models have a spectral gap our theory does not require symmetry of the state with respect to a local gauge group in particular we illustrate our results with a one parameter family of examples which are not isotropic except for one special case this isotropic model coincides with the one dimensional antiferromagnet recently studied by affleck kennedy lieb and tasaki

an lmi approach to stability analysis of coupled parabolic systems we analyze the exponential stability of a class of distributed parameter systems the system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients we approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis using a quadratic lyapunov function we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities

time dependent correlation functions in a one dimensional asymmetric exclusion process we study a one dimensional anisotropic exclusion process describing particles injected at the origin moving to the right on a chain of l sites and being removed at the right boundary we construct the steady state and compute the density profile exact expressions for all equal time n point density correlation functions and the time dependent two point function in the steady state as functions of the injection and absorption rates we determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

sensitivity minimization in an h norm parametrization of all suboptimal solutions a number of problems in the control of linear feedback systems can be reduced to the following we are given three stable rational matrix functions k of sizes p 1 x q 1 p 1 x q 2 and p 2 x q 1 respectively and seek a stable rational q 2 x p 2 matrix function s so as to minimize k s we assume that p 1 q 2 p 2 q 1 and that and have maximal rank q 2 and p 2 respectively on the j axis given a tolerance level sufficiently large we obtain a linear fractional map g f 0 11 g 0 12 0 13 0 21 g 0 22 0 23 1 such that f k s with s stable and f if and only if g is a stable q 2 x p 2 matrix function with g 1 the computation of 0 0 ij 1 i 2 1 j 3 reduces to solving a pair of symmetric wiener hopf factorization problems for the special case where i q2 0 t i p2 0 and k not necessarily stable to which the general case can be reduced we provide explicit state space formulae for 0 in terms of a state space realization of k and the

matrix product eigenstates for one dimensional stochastic models and quantum spin chains we show that all zero energy eigenstates of an arbitrary m state quantum spin chain hamiltonian with nearest neighbour interaction in the bulk and single site boundary terms which can also describe the dynamics of stochastic models can be written as matrix product states this means that the weights in these states can be expressed as expectation values in a fock representation of an algebra generated by 2m operators fulfilling quadratic relations which are defined by the hamiltonian

discounted linear exponential quadratic gaussian control in this note we describe a recursive formulation of discounted costs for a linear quadratic exponential gaussian linear regulator problem which implies time invariant linear decision rules in the infinite horizon case time invariance in the discounted case is attained by surrendering state separability of the risk adjusted costs

risk sensitive estimation and a differential game a large deviation result is employed to solve the state estimation problem of a continuous time gauss markov system with an exponential cost the exponential cost is the expected value of an exponential function of the state estimation error a scalar spl theta appearing in the cost termed as the risk factor determines the penalty on the higher order moments of the error in contrast to the minimum variance estimate penalty on large deviations of the estimation error is possible

finite size scaling and universality for the totally asymmetric simple exclusion process the applicability of the concepts of finite size scaling and universality to nonequilibrium phase transitions is considered in the framework of the one dimensional totally asymmetric simple exclusion process with open boundaries in the thermodynamic limit there are boundary induced transitions both of the first and second order between steady state phases of the model we derive finite size scaling expressions for the current near the continuous phase transition and for the local density near the first order transition under different stochastic dynamics and compare them to establish the existence of universal functions next we study numerically the finite size behavior of the lee yang zeros of the normalization factor for the different steady state probabilities

an analysis of the pole zero cancellations in h optimal control problems of the first kind the aim of this paper is to study the pole zero cancellations which occur in a class of h infty optimal control problems which may be embedded in the configuration of fig 1 h infty control problems are said to be of the first kind if both p 12 s and p 21 s are square but not necessarily of the same size it is primarily this class of problems which will concern us here a general bound on the mcmillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies bf mathcal r s infty leqq rho rho need not be optimal in the l infty norm sense is derived as illustrated in fig 1 bf mathcal r s is the transfer function relating y 1 s to u 1 s if the mcmillan degree of p s in fig 1 is n we show that in the single loop siso case the corresponding unique h infty optimal controller never requires more than n 1 states in the multivariable case there is a continuum of optimal controllers whose mcmil

generalized determinant solution of the discrete time totally asymmetric exclusion process and zero range process we consider the discrete time evolution of a finite number of particles obeying the totally asymmetric exclusion process with backward ordered update on an infinite chain our first result is a determinant expression for the conditional probability of finding the particles at given initial and final positions provided that they start and finish simultaneously the expression has the same form as the one obtained by schutz j stat phys 88 427 1997 for the continuous time process next we prove that under some sufficient conditions the determinant expression can be generalized to the case when the particles start and finish at their own times the latter result is used to solve a nonstationary zero range process on a finite chain with open boundaries

deterministic exclusion process with a stochastic defect matrix product ground states we study a one dimensional anisotropic exclusion model describing particles moving deterministically on a ring with a single defect across which they move with probability 0 q 1 we show that the stationary state of this model can be represented as a matrix product state

exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics a one dimensional driven lattice gas with disorder in the particle hopping probabilities is considered it has previously been shown that in the version of the model with random sequential updating a phase transition occurs from a low density inhomogeneous phase to a high density congested phase here the steady states for both parallel fully synchronous updating and ordered sequential updating are solved exactly the phase transition is shown to persist in both cases with the critical densities being higher than that for random sequential dynamics the steady state velocities are related to the fugacity of a bose system suggesting a principle of minimization of velocity a generalization of the dynamics to the case where the hopping probabilities depend on the number of empty sites in front of the particles is also solved exactly in the case of parallel updating the models have natural interpretations as simplistic descriptions of traffic flow the relation to more sophisticated traffic flow models is discussed

sampled data observers for 1 d parabolic pdes with non local outputs abstract the present work provides a systematic approach for the design of sampled data observers to a wide class of 1 d parabolic pdes with non local outputs the studied class of parabolic pdes allows the presence of globally lipschitz nonlinear and non local terms in the pde two different sampled data observers are presented one with an inter sample predictor for the unavailable continuous measurement signal and one without an inter sample predictor explicit conditions on the upper diameter of the uncertain sampling schedule for both designs are derived for exponential convergence of the observer error to zero in the absence of measurement noise and modeling errors moreover explicit estimates of the convergence rate can be deduced based on the knowledge of the upper diameter of the sampling schedule when measurement noise and or modeling errors are present input to output stability ios estimates of the observer error hold for both designs with respect to noise and modeling errors the main results are illustrated by two examples which show how the proposed methodology can be extended to other cases e g boundary point measurements

n species stochastic models with boundaries and quadratic algebras stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product ansatz the matrices are representations of some quadratic algebras the algebras and the types of representations considered depend on the boundary conditions in the language of quantum chains we obtain the ground state of n state quantum chains with free boundary conditions or with non diagonal boundary terms at one or both ends in contrast to problems involving the bethe ansatz we do not have a general framework for arbitrary n which when specialized gives the known results for n 2 in fact the n 2 and n 2 cases appear to be very different

one dimensional partially asymmetric simple exclusion process with open boundaries orthogonal polynomials approach the stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered the so called matrix product ansatz is employed this enables us to construct the stationary state in the form of the product of the matrices d and e noticing the fact that the matrix c d e for the model is related to certain q orthogonal polynomials the model is analysed for a wide range of parameters the current and the correlation length are evaluated in the thermodynamic limit it turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case

selection of a single uniquely specifiable h controller in the chain scattering framework this paper studies the notion of central h controllers in the chain scattering framework since in the chain scattering framework the h control problem is equivalent to a factorisation problem that yields non unique factors it is important to somehow pin down these factors so that the resulting central controller is uniquely defined and corresponds to the central and minimum entropy controller frequently discussed in the literature in so doing we devise a procedure for the selection of a single uniquely specifiable h controller in the chain scattering framework the chain scattering framework is important because it has a distinct advantage over state space based methods for some applications in that it poses and solves the h control problem entirely in an operator theoretic setting thereby allowing us to contemplate direct changes of the frequency domain symbols rather than changes in the corresponding state space matrices

brief paper on the geometric and dynamic structures of the h2 optimal and h central controllers in this paper the geometric structure of observer based controllers is investigated in order to characterize the controllable and unobservable subspaces of the h 2 optimal and the h central controllers it is shown that the controllable and unobservable subspaces of the h 2 optimal and the h central controllers can be characterized by the kernel and image subspaces of the solutions of two lyapunov equations under this characterization the connection between the geometric subspaces and the dynamic behavior of the plant and those of the h 2 optimal and h controllers is derived it is also shown that the h 2 optimal and the h central controllers inherit a certain part of the given plant dynamics in the geometric sense a numerical example is also given for illustration

observers and initial state recovering for a class of hyperbolic systems via lyapunov method a b s t r a c t recently the problem of estimating the initial state of some linear infinite dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers ramdani tucsnak and weiss 2010 in the present paper we introduce a direct lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval we first design forward observers and derive linear matrix inequalities lmis for the exponential stability of the estimation errors further we obtain simple finite dimensional conditions in terms of lmis for an upper bound t on the minimal time that guarantees the convergence of the sequence of forward and backward observers on 0 t for the initial state recovering this t represents also an upper bound on the observability time for observation times bigger than t these lmis give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the lyapunov functions in our approach t is found as the minimal dwelling time for the switched exponentially stable forward and backward estimation error systems with the different lyapunov functions liberzon 2003 the efficiency of the results is illustrated by numerical examples 2013 elsevier ltd all rights reserved

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

some general features of matrix product states in stochastic systems we will prove certain general relations in the matrix product ansatz mpa for one dimensional stochastic systems which are true in both random and sequential updates we will derive general mpa expressions for the currents and current correlators and find the conditions in the mpa formalism under which the correlators are site independent or completely vanishing

minimax control under a bound on the partial covariance sequence of the disturbance a discrete time linear siso plant that is acted on by a stochastic disturbance is considered it is assumed that a restriction on the partial covariance sequence of the disturbance is given the cost function is a maximum of the closed loop system output variance over the class of disturbances the problem is to find the optimal linear stabilizing regulator the transfer function of the optimal closed loop system is constructed in explicit form it is shown that the minimax regulator is intermediate between the h and h2 optimal regulators as a result of the problem solution generalizations of the caratheodory fejer and nevanlinna pick theorems are obtained

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

exact shock profile for the asep with sublattice parallel update we analytically study the one dimensional asymmetric simple exclusion process with open boundaries under sublattice parallel updating scheme we investigate the stationary state properties of this model conditioned on finding a given particle number in the system recent numerical investigations have shown that the model possesses three different phases in this case using a matrix product method we calculate both the exact canonical partition function and also density profiles of the particles in each phase application of the yang lee theory reveals that the model undergoes two second order phase transitions at critical points these results confirm the correctness of our previous numerical studies

linear estimation in krein spaces ii applications we have shown that several interesting problems in h sup spl infin filtering quadratic game theory and risk sensitive control and estimation follow as special cases of the krein space linear estimation theory developed in part i we show that all these problems can be cast into the problem of calculating the stationary point of certain second order forms and that by considering the appropriate state space models and error gramians we can use the krein space estimation theory to calculate the stationary points and study their properties the approach discussed here allows for interesting generalizations such as finite memory adaptive filtering with varying sliding patterns

multi species asymmetric exclusion process in ordered sequential update a multi species generalization of the asymmetric simple exclusion process is studied with ordered sequential and sub lattice parallel updating schemes in this model particles hop with their own specific probabilities to their rightmost empty site and fast particles overtake slow ones with a definite probability using the matrix product ansatz technique we obtain the relevant algebra and study the uncorrelated stationary state of the model both for an open system and on a ring a complete comparison between the physical results in these updates and those of random sequential introduced in karimipour v 1999 a multi species asep and its relation to traffic flow phys rev e 59 205 and karimipour v 1998 a multi species asep steady state and correlation functions on a periodic lattice preprint cond mat 9809193 is made

synchronous asymmetric exclusion processes for a fully synchronous asymmetric exclusion process with open or closed boundaries only partial analytic results are known owing to the appearance of strong short range correlations which invalidate simple mean field approximations here we present a new method for calculating basic properties of nonequilibrium steady states and calculate densities fluxes travel times spatial and temporal correlation functions phase diagrams profiles and widths of boundary layers and interfaces between phases in coexistence as well as their microstructures this paper is based on two new elements i a microscopic characterization of order parameters and local configurations in the relevant phases based on the microdynamics of the model and ii an improved mean field approximation which neglects certain four point and higher order correlation functions it is conjectured that the density profiles obtained here are exact up to terms that are exponentially small in the system size

relations between maximum entropy h control and combined h lqg control abstract the maximum entropy h control problem and a combined h lqg control problem are presented in a unified way and shown to be equivalent in the case of a full order controller and equalized h lqg weights the result links two separate approaches which have distinctly different methods of solution only two decoupled algebraic riccati equations are needed to state the controller maximum value of the entropy and minimum value of the auxiliary cost

siso controller design to minimize a positive combination of the l 1 and the h 2 norms abstract we consider the problem of minimizing a given positive linear combination of the l1 norm and the square of the h 2 norm of the closed loop over all internally stabilizing controllers the problem is analysed for the discrete time siso linear time invariant case it is shown that a unique optimal solution always exists and can be obtained by solving a finite dimensional convex optimization problem with an a priori determined dimension it is also established that the solution is continuous with respect to changes in the coefficients of the linear combination