finite size scaling in the driven lattice gas we present a monte carlo study of the high temperature phase of the two dimensional driven lattice gas at infinite driving field we define a finite volume correlation length verify that this definition has a good infinite volume limit independent of the lattice geometry and study its finite size scaling behavior the results for the correlation length are in good agreement with the predictions based on the field theory proposed by janssen schmittmann leung and cardy the theoretical predictions for the susceptibility and the magnetization are also well verified we show that the transverse binder parameter vanishes at the critical point in all dimensions d geqslant 2 and discuss how such result should be expected in the theory of janssen et al in spite of the existence of a dangerously irrelevant operator our results confirm the gaussian nature of the transverse excitations

long range spatial correlations for anisotropic zero range processes the spatial correlations are investigated for a homogeneous system of indistinguishable particles undergoing stochastic anisotropic hopping dynamics on the d dimensional lattice d or 2 the interaction is zero range i e the rate at which particles leave a given site only depends on the occupation number at that site a series expansion around the independent particle system is given for the equal time correlations and is shown to converge for small times t the formal t to infinity limiting expansion is analysed termwise from which a quadrupole type decay approximately r d is derived for the stationary two points function eta 0 eta r eta 0 2 this phenomenon of self organized criticality is a direct consequence of the anisotropy causing the system to violate the condition of detailed balance combined with the conservation law forcing a diffusive decay approximately t d2 of the temporal correlations

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

phase separation and coarsening in one dimensional driven diffusive systems local dynamics leading to long range hamiltonians a driven system of three species of particles diffusing on a ring is studied in detail the dynamics is local and conserves the three densities a simple argument suggesting that the model should phase separate and break the translational symmetry is given we show that for the special case where the three densities are equal the model obeys detailed balance and the steady state distribution is governed by a hamiltonian with asymmetric long range interactions this provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension the steady state of finite size systems is studied using a generalized matrix product ansatz the coarsening process leading to phase separation is studied numerically and in a mean field model the system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size the typical domain size is shown to grow logarithmically in time generalizations to a larger number of species are discussed

pole placement by parametric output feedback abstract this note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m p n where n m and p are the number of states inputs and outputs respectively the approach is based upon parametric eigenstructure assignment of linear time invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations thus the resulting analytical solution explicitly offers all remaining m p n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping minimizing the norm of the feedback matrix and robust control respectively

understanding the edge effect in tasep with mean field theoretic approaches we study a totally asymmetric simple exclusion process tasep with one defect site hopping rate q 1 near the system boundary regarding our system as a pair of uniform tasep s coupled through the defect we study various methods to match a finite tasep and an infinite one across a common boundary several approximation schemes are investigated utilizing the finite segment mean field fsmf method we set up a framework for computing the steady state current j as a function of the entry rate and q for the case where the defect is located at the entry site we obtain an analytical expression for j q which is in good agreement with monte carlo simulation results when the defect is located deeper in the bulk we refined the scheme of macdonald et al 1968 biopolymers 6 1 and find reasonably good fits to the density profiles before the defect site we discuss the strengths and limitations of each method as well as possible avenues for further studies

parametric output feedback controller design abstract a parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters the set of n closed loop system eigenvalues and a set of mr n design parameters for n state r input m output systems the free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed loop eigenvectors under the condition m r n the principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria an illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth order pilot plant evaporator model

eigenstructure assignment based robust stability conditions for uncertain systems with multiple time varying delays the problem of robust stability of dynamical systems with multiple time varying delays and structured state space uncertainties is discussed based on the fact that the dynamic response of a multivariable control system can be modified by means of eigenstructure assignment a method is presented whereby a new sufficient condition for robust stability of such uncertain time delay systems is derived the new robust stability condition is a sum of terms each of which involves the ith right eigenvector the ith left eigenvector and the real part of the ith eigenvalue and is shown to be less conservative than the earlier result reported in the control literature here each time varying delay is assumed only to be any bounded continuous non negative function and the derived robust stability condition is independent of the delay therefore our results are also applicable to systems with perturbed delays finally a numerical example is given to demonstrate the validity of the results

very simple methods for all pairs network flow analysis a very simple algorithm for the classical problem of computing the maximum network flow value between every pair of nodes in an undirected capacitated n node graph is presented as in the well known gomory hu method the method given here uses only n 1 maximum flow computations our algorithm is implemented by adding only five simple lines of code to any program that produces a minimum cut a program to produce an equivalent flow tree which is a compact representation of the flow values is obtained by adding only three simple lines of code to any program producing a minimum cut a very simple version of the gomory hu cut tree method that finds one minimum cut for every pair of nodes is also derived and it is shown that the seemingly fundamental operation of that method node contraction is not needed nor must crossing cuts be avoided as a result this version of the gomory hu method is implemented by adding less than ten simple lines of code to any program that produces a minimum cut the algor

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

totally asymmetric exclusion processes with particles of arbitrary size the steady state currents and densities of a one dimensional totally asymmetric exclusion process tasep with particles that occlude an integer number d of lattice sites are computed using various mean field approximations and monte carlo simulations taseps featuring particles of arbitrary size are relevant for modelling systems such as mrna translation vesicle locomotion along microtubules and protein sliding along dna we conjecture that the nonequilibrium steady state properties separate into low density high density and maximal current phases similar to those of the standard d 1 tasep a simple mean field approximation for steady state particle currents and densities is found to be inaccurate however we find local equilibrium particle distributions derived from a discrete tonks gas partition function yield apparently exact currents within the maximal current phase for the boundary limited phases the equilibrium tonks gas distribution cannot be used to predict currents phase boundaries or the order of the phase transitions however we employ a refined mean field approach to find apparently exact expressions for the steady state currents boundary densities and phase diagrams of the d 1 tasep extensive monte carlo simulations are performed to support our analytic mean field results

phase transitions and damage spreading in a nonequilibrium lattice gas model with mixed dynamic rules abstract phase transitions and damage spreading for a lattice gas model with mixed driven lattice gas dlg glauber dynamics are studied by means of monte carlo simulations in order to control the number of sites updated according to the nonconservative glauber dynamics a parameter p 0 1 is defined in this way for p 0 the system corresponds to the dlg model with biased kawasaki conservative dynamics while for p 1 it corresponds to the ising model with glauber dynamics the results obtained show that the introduction of nonconservative dynamics dramatically affects the behavior of the dlg model leading to the existence of ising like phase transitions from fully occupied to disordered states the short time dynamics results suggest that this transition is second order for values of p 0 1 and p 0 6 and first order for 0 1 p 0 6 on the other hand damage always spreads within the investigated temperature range and reaches a saturation value d s a t that depends on the system size the temperature and p the value of d s a t in the thermodynamic limit is estimated by performing a finite size analysis for p 0 6 the results show a change in the behavior of d s a t with temperature similar to those reported for the pure p 0 dlg model however for p 0 6 the data remind us of the ising p 1 curves in each case a damage temperature t d p can be defined as the value where either d s a t reaches a maximum or it becomes nonzero this temperature is within error bars similar to the reported values of the temperatures that characterize the mentioned phase transitions

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

eigenstructure assignment for componentwise ultimate bound minimization in discrete time linear systems this technical note presents a feedback design approach to minimise state ultimate bounds ubs in linear time invariant discrete time systems subject to non vanishing bounded disturbances a target closed loop eigenstructure is first constructed to achieve the lowest possible ubs for one or more state components of the system structural conditions on the system matrices are then derived to guarantee that the target eigenstructure can be assigned by state feedback when the required structural conditions are satisfied an eigenvector assignment procedure can be applied to simultaneously minimise multiple ubs in systems with multiple inputs the results are illustrated by a numerical example drawn from a distributed voltage control problem in inverter based microgrids

eigenvalue generalized eigenvector assignment by output feedback this note generalizes the previous results of the closed loop eigenstructure assignment via output feedback in linear multivariable systems necessary and sufficient conditions for the closed loop eigenstructure assignment by output feedback are presented some known results on entire eigenstructure assignment are deduced from this result

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

l sub 1 optimality of feedback control systems the siso discrete time case controllers that optimally reject a class of disturbances are considered the problem of determining when a stabilizing control is l sub 1 optimal for a given plant is studied for some stable weighting function this problem belongs to the class of inverse problems in optimal control introduced by kalman it is shown that for a given plant the set of all the h sub infinity optimal controllers obtained by considering all stable weighting functions with no zeros on the unit circle is actually contained in the corresponding set of l sub 1 optimal controllers it is also demonstrated that an l sub 1 optimal controller unlike an h sub infinity optimal controller can remain l sub 1 optimal for the same plant for a wide range of nontrivially different weighting functions

solution bases of multiterminal cut problems gomory and hu proved that the left n atop 2 right maxflow problems in an undirected network have at most n 1 distinct solution values we generalize their theorems in several ways an interesting special case is that the on4 2 commodity maxflow problems on an undirected network have at most left n atop 2 right distinct solution values these results follow from general theorems on the number of distinct solution values to sets of optimization problems we then show how the solutions can be compactly represented by a basis of the solution matrix a where aij 1 if solution j is feasible for problem i and aij 0 otherwise for the special case of the 2 cut problem we also show how to construct such a representation efficiently

twenty five years after kls a celebration of non equilibrium statistical mechanics when lenz proposed a simple model for phase transitions in magnetism he couldn t have imagined that the ising model was to become a jewel in field of equilibrium statistical mechanics its role spans the spectrum from a good pedagogical example to a universality class in critical phenomena a quarter century ago katz lebowitz and spohn found a similar treasure by introducing a seemingly trivial modification to the ising lattice gas they took it into the vast realms of non equilibrium statistical mechanics an abundant variety of unexpected behavior emerged and caught many of us by surprise we present a brief review of some of the new insights garnered and some of the outstanding puzzles as well as speculate on the model s role in the future of non equilibrium statistical physics

competition between multiple totally asymmetric simple exclusion processes for a finite pool of resources using monte carlo simulations and a domain wall theory we discuss the effect of coupling several totally asymmetric simple exclusion processes taseps to a finite reservoir of particles this simple model mimics directed biological transport processes in the presence of finite resources such as protein synthesis limited by a finite pool of ribosomes if all taseps have equal length we find behavior which is analogous to a single tasep coupled to a finite pool for the more generic case of chains with different lengths several unanticipated regimes emerge a generalized domain wall theory captures our findings in good agreement with simulation results

brief paper control design with guaranteed ultimate bound for perturbed systems we present a new control design method for perturbed multiple input systems which guarantees any desired componentwise ultimate bound on the system state the method involves eigenvalue eigenvector assignment by state feedback and utilises a componentwise bound computation procedure this procedure directly takes into account both the system and perturbation structures by performing componentwise analysis thus avoiding the need for bounds on the norm of the perturbation the perturbation description adopted can accommodate numerous types of uncertainties including uncertain time delays in the feedback loop we apply the method to an example taken from the literature to illustrate its simplicity and generality

transverse fluctuations in the driven lattice gas we define a transverse correlation length suitable to discuss the finite size scaling behaviour of an out of equilibrium lattice gas whose correlation functions decay algebraically with the distance by numerical simulations we verify that this definition has a good infinite volume limit independent of the lattice geometry we study the transverse fluctuations as they can select the correct field theoretical description by means of a careful finite size scaling analysis without tunable parameters we show that they are gaussian in agreement with the predictions of the field theory proposed by janssen schmittmann leung and cardy

parametric eigenstructure assignment by output feedback control the case of multiple eigenvalues this paper deals with closed loop eigenstructure assignment by output feedback control in linear multivariable systems for the general case of multiple eigenvalues the approach is algebraic in nature and operates directly on the closed loop characteristic equation using fundamental properties of determinants and their derivatives a compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non uniqueness of the solution of the eigenvalue assignment problem some of these parameter vectors assume restricted forms while others are free a computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least square error sense an illustrative numerical example is included

on the spl lscr sub 1 norm of uncertain linear systems in this paper we present an algorithm for computing the l sub spl infin induced norm of linear systems described by time varying difference equations with uncertain system matrices the approach is based on ideas from convex analysis the convergence of the algorithm is studied and vertex type results related to the stabilization and spl lscr sub 1 control of uncertain discrete time systems are established

a possible classification of nonequilibrium steady states we propose a general classification of nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents the stationary probabilities can be represented graph theoretically as directed labelled trees closing a single loop in such a graph leads to a representation of probability currents this classification allows us to identify all choices of transition rates based on a master equation which generate the same nonequilibrium steady state we explore the implications of this freedom e g for entropy production

exact stationary distribution of an asymmetric simple exclusion process with langmuir kinetics and memory reservoirs we present exact stationary distribution of the asymmetric simple exclusion process with langmuir kinetics and its related model on a ring the distribution is expressed in simple factorized forms that is supported by detailed balance conditions satisfied in the attachment and detachment transitions using the equations we derive the density of particles the current and the variance of particle numbers in each lane the expressions for the density are well associated with the ones found in equilibrium theories moreover a simple relation between the variance of particle number and the current is proved

domain growth in a one dimensional driven diffusive system the low temperature coarsening dynamics of a one dimensional ising model with conserved magnetisation and subject to a small external driving force is studied analytically in the limit where the volume fraction mu of the minority phase is small and numerically for general mu the mean domain size l t grows as t 1 2 in all cases and the domain size distribution for domains of one sign is very well described by the form p l l propto l l 3 exp lambda mu l 2 l 2 which is exact for small mu and possibly for all mu the persistence exponent for the minority phase has the value 3 2 for mu to 0

on nonlinear state feedback controllers for persistent disturbance rejection abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant in the state feedback case there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance in the case of d 12 square and invertible we show that it is enough to have the nonlinearity on a particular substate which can be used to significantly simplify the design problem

a convex optimization approach to fixed order controller design for disturbance rejection in siso systems the problem of rejection of persistent unknown but bounded disturbances can be solved using the well known l sup 1 design approach however in spite of its success this theory suffers from the fact that the resulting controller may have arbitrarily high order even in the state feedback case in addition system performance is optimized under the assumption of zero initial conditions in this paper we propose a new approach to the problem of synthesizing fixed order controllers to optimally reject persistent disturbances the main result of the paper shows that this approach leads to a finite dimensional convex optimization problem that can be efficiently solved

field theory of critical behavior in a driven diffusive system we use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field a fixed point stable belowd c 5 is found to govern the critical behavior scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in 5 d spatial correlations are found to be very anisotropic with elongated correlations along the external field long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents

minimization of the worst case peak to peak gain via dynamic programming state feedback case considers the problem of designing a controller that minimizes the worst case peak to peak gain of a closed loop system in particular we concentrate on the case where the controller has access to the state of a linear plant and it possibly knows the maximal disturbance input amplitude we apply the principle of optimality and derive a dynamic programming formulation of the optimization problem under mild assumptions we show that at each step of the dynamic program the cost to go has the form of a gauge function and can be recursively determined through simple transformations we study both the finite horizon and the infinite horizon case under different information structures the proposed approach allows us to encompass and improve earlier results based on viability theory in particular we present a computational scheme alternative to the standard bisection algorithm or gamma iteration that allows us to compute the exact value of the worst case peak to peak gain for any finite horizon we show that the sequence of finite horizon optimal costs converges as the length of the horizon goes to infinity to the infinite horizon optimal cost the sequence of such optimal costs converges from below to the optimal performance for the infinite horizon problem we also show the existence of an optimal state feedback strategy that is globally exponentially stabilizing and derive suboptimal globally exponentially stabilizing strategies from the solutions of finite horizon problems

brief practical l2 disturbance attenuation for nonlinear systems in this work a notion of generalized l 2 gain for nonlinear systems where the gain is considered as a function of the state instead of a global constant is presented this new notion seems to be adequate to characterize the gain properties of several nonlinear systems which do not possess a uniform l 2 gain property i e the l 2 gain depends on the operating point moreover a notion of practical l 2 gain attenuation which extends the standard definition and parallels mutatae mutandis the concepts of practical stability is also proposed

distribution of structure factors and phase transitions in a driven lattice gas using monte carlo methods we study the full distribution of structure factors in the standard driven lattice gas at half filling the time evolution of the structure factors associated with the two lowest non trivial wavevectors is used to construct histograms for saturation drive at temperatures well above both are exponentially distributed but with different widths these results are well described by a continuum field theory with a dynamics which violates the usual fluctuation dissipation theorem as t is lowered one of these distributions remains essentially unaltered by contrast the other develops a maximum away from the origin while staying single peaked throughout this behaviour is an unmistakable signal for a continuous transition

dynamic programming and graph optimization problems abstract several classes of graph optimization problems which can be solved using dynamic programming are known to have more efficient tailor made algorithms this paper discusses four such classes and the underlying constraints on their subproblem interrelationships that yield these efficient algorithms these classes are also extended to handle more general cost functions

exact diffusion constant for one dimensional asymmetric exclusion models the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions is considered on a ring of size n the steady state of this system is known all configurations have equal weight which allows for easy computation of the average velocity of a particle in the steady state here an exact expression for the diffusion constant of a particle is obtained for arbitrary number of particles and system size by using a matrix formulation two limits of infinite system size n are discussed firstly when the number of particles remains finite as n to infinity the diffusion constant remains dependent on the exact number of particles due to correlations between successive collisions secondly when the density p of particles is non zero i e when the number of particles is equal to n rho as n to infinity the diffusion constant scales as n 12 the exponent 1 2 is related to the dynamic exponent z 3 2 of the kpz equation in 1 1 dimensions

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

triangulations tilings and certain block triangular matrices for a convex polygonp withn sides a partitioning ofp inton 2 nonoverlapping triangles each of whose vertices is a vertex ofp is called a triangulation or tiling and each triangle is a tile each tile has a given cost associated with it which may differ one from another this paper considers the problem of finding a tiling ofp such that the sum of the costs of the tiles used is a minimum and explores the curiosity that an abstract formulation of it can be cast as a linear program further the special structure of the linear program permits a recursive o n 3 algorithm

exact solutions for kpz type growth processes random matrices and equilibrium shapes of crystals abstract three models from statistical physics can be analyzed by employing space time determinantal processes 1 crystal facets in particular the statistical properties of the facet edge and equivalently tilings of the plane 2 one dimensional growth processes in the kardar parisi zhang universality class and directed last passage percolation 3 random matrices multi matrix models and dyson s brownian motion we explain the method and survey results of physical interest

pattern recognition using asymmetric attractor neural networks the asymmetric attractor neural networks designed by the monte carlo mc adaptation rule are shown to be promising candidates for pattern recognition in such a neural network with relatively low symmetry when the members of a set of template patterns are stored as fixed point attractors their attraction basins are shown to be isolated islands embedded in a chaotic sea the sizes of these islands can be controlled by a single parameter we show that these properties can be used for effective pattern recognition and rejection in our method the pattern to be identified is attracted to a template pattern or a chaotic attractor if the difference between the pattern to be identified and the template pattern is smaller than a predescribed threshold the pattern is attracted to the template pattern automatically and thus is identified as belonging to this template pattern otherwise it wanders in a chaotic attractor for ever and thus is rejected as an unknown pattern the maximum sizes of these islands allowed by this kind of neural networks are determined by a modified mc adaptation rule which are shown to be able to dramatically enlarge the sizes of the islands we illustrate the use of our method for pattern recognition and rejection with an example of recognizing a set of chinese characters

output feedback eigenstructure assignment using a new reduced orthogonality condition this paper presents a new method of output feedback eigenstructure assignment a new reduced orthogonality condition is derived which is less restrictive on the design degrees of freedom than others in the literature from this a novel general formulation for the gain matrix is admitted which utilizes a two stage design process in the first stage a subset of desired eigenvectors is assigned either left or right in the second stage a dual set is assigned which adheres to the necessary and sufficient conditions for output feedback eigenstructure assignment proved earlier in the paper a numerical example is presented to illustrate the whole procedure

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

an efficient parallel dynamic programming algorithm abstract antonio tsai and huang proposed a scheme in 1991 to parallelize the standard dynamic programming approach to solve combinatorial multistage problems however their dynamic programming approach is restricted to those multistage problems where the decision made at each stage depends only on decisions made in the stage immediately preceding it for many interesting problems the decision at each stage depends on the decisions made at all the previous stages and therefore their approach doesn t apply the matrix chain multiplication problem longest common subsequence problem and optimal polygon triangulation problem are some examples of such problems we also present techniques for parallelizing the dynamic programming solution to such problems the parallel algorithm we develop for a pram has complexity n employing n 2 processors since the traditional sequential algorithm for such problems is n 3 our parallel algorithm is an optimal parallel algorithm based on this traditional algorithm we also describe the results of our experiments that are in conformity with our theoretical complexity results we also compare and contrast our result with results obtained by earlier researchers and show that our parallel algorithm has optimal efficiency of 100 with respect to the traditional dynamic programming algorithm

i 1 optimal control of multivariable systems with output norm constraints in this paper we consider the l1 optimal control problem for general rational plants it is shown that for plants with no poles or zeros on the unit circle an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs exactly or approximately optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed loop transfer function no assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators it is shown that constrained problems in which a set of outputs is regulated subject to l norm constraints on another set of outputs can be solved using a slight modification of the same algorithm

multistage parametric eigenstructure assignment by output feedback control this paper develops an efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output feedback control the sets of closed loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages this allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions the number of effective free parameters beyond eigenvalue assignment is determined and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced numerical examples are included to demonstrate the design procedure

some necessary and sufficient conditions for eigenstructure assignment abstract some necessary and sufficient conditions for closed loop eigenstructure assignment by output feedback in time invariant linear multivariable control systems are presented a simple condition on a square matrix necessary and sufficient for it to be the closed loop plant matrix of a given system with some output feedback is the basis of the paper some known results on entire eigenstructure assignment are deduced from this the concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors

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

quadratic characterization and use of output stabilizable subspaces this note treats the problem of stabilization of linear systems by static output feedback using the concept of c a b invariant subspaces the work provides a new characterization of output stabilizable c a b invariant subspaces through two coupled quadratic stabilization conditions an equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by static output feedback an algorithm is provided and numerical examples are reported to illustrate the approach

persistent disturbance rejection via static state feedback in contrast with spl hscr sub spl infin and spl hscr sub 2 control theories the problem of persistent disturbance rejection l sup 1 optimal control leads to dynamic controllers even when the states of the plant are available for feedback using viability theory shamma showed 1993 in a nonconstructive way that in the state feedback case the same performance achieved by any dynamic linear time invariant controller can be achieved using memoryless nonlinear state feedback in this paper we give an alternative constructive proof of these results for discrete and continuous time systems the main result of the paper shows that in both cases the l sup 1 norm achieved by any stabilizing state feedback linear dynamic controller can be also achieved using a memoryless variable structure controller

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

a simple solution to the l 1 optimization problem abstract it is pointed out in this brief paper that the l 1 optimization problem min q l qp 1 h u q v 1 h l mn 1 u l mq 1 v l pn 1 can be solved in one step rather than two the solution of the dual problem is obviated by the direct solution of the primal problem via linear programming the method here is applicable to finite dimensional problems or approximating finite dimensional problems in the general case

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

eigenvalue assignment robustness the analysis for autonomous system matrices abstract new techniques are presented for the analysis of eigenvalue assignment robustness the basic idea is to use a root locus approach to ensure that the eigenvalues of a dynamic system under parameter perturbations are restricted in the distinct desired regions no restriction is imposed on the shapes of the specified regions both the norm bound and the element bound for the allowable perturbations are obtained scaling techniques are proposed to increase the allowable element bound the proposed methods are applicable to the continuous time case as well as to the discrete time case when the eigenvalues are just required to locate in the stable region the proposed criteria will become the stability robustness criteria

robust eigenstructure assignment for the extended medium range air to air missile abstract a new sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty is presented this sufficient condition is a sum of terms each of which involves the ith right eigenvector the ith left eigenvector and the real part of the ith eigenvalue this new robustness result is less conservative than an earlier result which involves the modal matrix and the real part of the eigenvalue which is closest to the imaginary axis in the complex plane a robust design is computed for the extended medium range air to air missile and the new design is compared with an earlier orthogonal projection eigenstructure assignment design the new design method uses the matlabtm optimization toolbox to minimize the integral of the deviations of the integrated roll rate which is approximately the bank angle from zero the integral is approximated by a sum of discrete samples of the integrated roll rate while normalizing the integration width to unity constraints are placed on the real part of the dutch roll and roll mode eigenvalues the damping ratios of the dutch roll and roll mode the aileron and rudder deflection rates and the sufficient condition for robust stability the new design satisfies the robustness condition while also yielding an improved transient response

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

phase transition in the abc model recent studies have shown that one dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules the mathrm abc model which comprises three particle species that diffuse asymmetrically around a ring shows anomalous coarsening into a phase separated steady state in the limiting case in which the dynamics is symmetric and the parameter q describing the asymmetry tends to one no phase separation occurs and the steady state of the system is disordered in the present work we consider the weak asymmetry regime q mathrm exp ensuremath ensuremath beta n where n is the system size and study how the disordered state is approached in the case of equal densities we find that the system exhibits a second order phase transition at some nonzero ensuremath beta c the value of ensuremath beta c 2 ensuremath pi sqrt 3 and the optimal profiles can be obtained by writing the exact large deviation functional for nonequal densities we write down mean field equations and analyze some of their predictions

on static feedback for the l 1 and other optimal control problems although e 1 optimal linear state feedback controllers are known to be dynamic it has been shown that suboptimal performance arbitrarily closed to optimal can be achieved by using a static non linear feedback law in this paper this fact is established by using a novel approach which shows that the result is a natural consequence of elementary state space theory the approach is motivated by recent works in active vision systems which have considered a state feedback problem tightly connected with e 1 optimization this problem which has independent interest is discussed in some detail the new formulation of the problem provides additional insight in e 1 state feedback in particular it leads naturally to some extensions which do not follow in a straightforward manner from previous works on the subject

perturbation theory of output feedback pole assignment perturbation theory for output feedback eigenstructure assignment is considered the analysis is based on general conditions for eigenstructure assignment together with the well known perturbation theory for the pseudo inverse of a matrix this enables us to present a variety of sensitivity analyses for this problem and to indicate some precautions when choosing eigenvectors in the pole assignment problem

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

a new approach to eigenstructure assignment by output feedback the eigenstructure assignment problem for a linear time invariant multi input multi output system using output feedback is considered a new approach is developed which identifies the eigenspaces for the desired set of all the closed loop eigenvalues for the assignment of this desired set necessary and sufficient conditions are established these conditions contain two coupled sylvester matrix equations one of which is proven to be a reduced order square sylvester matrix equation this results in an efficient analytical procedure numerically superior to known techniques for the determination of the output feedback gain matrix

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

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

state feedback e 1 optimal controllers can be dynamic abstract this paper considers l 1 optimal control problems given by discrete time systems with full state feedback scalar control and scalar disturbance motivation stems from the central role that this problem structure played in the development of the h 2 and h theories first systems with a scalar regulated output are studied singular problems sufficient conditions are given based on the non minimum phase zeros of the transfer function from the control to the regulated output for the existence of a static l 1 optimal controller a simple way to compute the static gain is provided using pole placement ideas it is shown however that having full state information does not prevent the l 1 optimal controller from being dynamic in general and that examples with arbitrarily high order optimal controllers can be easily constructed second problems with two regulated outputs one of them being the scalar control are considered non singular problems it is shown by means of a class of fairly general examples for which exact l 1 optimal solutions are constructed that such problems may not have static controllers that are l 1 optimal thus concluding that a separation structure does not occur in these problems in general

exact pole assignment with regularity by output feedback in descriptor systems part 2 in this paper the first of two we examine the problem of modal control of linear time invariant multivariable descriptor systems in particular for systems satisfying a certain inequality we will give necessary and sufficient conditions for the existence of an output feedback matrix possibly complex which exactly assigns an arbitrary set of r the number of independent semi state variables of the system distinct complex numbers to a generalized eigenspectrum of the closed loop system while ensuring that the resulting system has a unique smooth solution for each admissible initial condition furthermore it is shown that if the set of proposed poles contains only real elements the assignment can be carried out using real feedback next we present conditions that are necessary and sufficient for pole assignability by real feedback of a self conjugate set of complex numbers provided that the system satisfies a further inequality

computation of matrix chain products part ii this paper considers the computation of matrix chain products of the form m 1 times m 2 times cdots times m n 1 if the matrices are of different dimensions the order in which the product is computed affects the number of operations an optimum order is an order which minimizes the total number of operations we present some theorems about an optimum order of computing the matrices based on these theorems an o n log n algorithm for finding an optimum order will be presented in part ii