controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

the existence of asymptotically stable solutions for a nonlinear functional integral equation with values in a general banach space abstract motivated by the recent known results about the solvability and existence of asymptotically stable solutions for nonlinear functional integral equations in spaces of functions defined on unbounded intervals with values in the n dimensional real space we establish asymptotically stable solutions for a nonlinear functional integral equation in the space of all continuous functions on r with values in a general banach space via a fixed point theorem of krasnosel skii type in order to illustrate the result obtained here an example is given

controllability on principal fibre bundles with compact structure group abstract in this paper we consider the controllability problem for systems defined on principal fibre bundles in which the set of associated vector fields is invariant under the action of the structure group and projects down on to a set of vector fields on the base space it is shown that if the system is accessible and the structure group is compact then the system is controllable if and only if the system is controllable when projected onto the base space the connection between these systems and systems admitting symmetries generated by free and proper group actions is described and various examples are given relating to systems on homogeneous spaces

differential geometric methods in variable structure control this article presents a differential geometric approach for the design of sliding modes in non linear variable structure feedback systems coordinate free characterizations of local existence conditions for sliding regimes and a geometric reformulation of some of its most salient features are presented the approach uses basic notions from differential geometry involving vector fields distributions and 1 forms both single and multiple input cases are treated with some illustrative examples

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

optimal control of systems possessing symmetries it is shown that a symmetry in an optimization problem induces a decomposition of the optimal feedback control law into factors one factor can be calculated algebraically and depends only on the symmetry the other factor corresponds to a lower dimensional optimization problem this gives a priori information about the structure of the optimal feedback control law and indicates a possibly more efficient method for optimizing such systems

quotients of fully nonlinear control systems in this paper we introduce and study quotients of fully nonlinear control systems our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems we show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state input space this allows one to understand how states and inputs of the quotient system are related to states and inputs of the original system we also introduce a notion of projectability which turns out to be equivalent to controlled invariance this allows one to regard previous work on symmetries partial symmetries and controlled invariance as leading to special types of quotients we also show the existence of quotients that are not induced by symmetries or controlled invariance such decompositions have a potential use in a theory of hierarchical control based on quotients

the structure of nonlinear control systems possessing symmetries a concept of symmetry is defined for general nonlinear control systems it is shown under various technical conditions that nonlinear control systems with symmetries admit local and or global decompositions in terms of lower dimensional subsystems and feedback loops the structure of the individual subsystems is dependent on the structure of the symmetry group for example if the symmetry group is abelian one of the subsystems is a quadrature an additional feature of the decomposition is that the state space dimensions of the subsystems sum to the state space dimension of the original system

local and cluster critical dynamics of the 3d random site ising model abstract we present the results of monte carlo simulations for the critical dynamics of the three dimensional site diluted quenched ising model three different dynamics are considered these correspond to the local update metropolis scheme as well as to the swendsen wang and wolff cluster algorithms the lattice sizes of l 10 96 are analysed by a finite size scaling technique the site dilution concentration p 0 85 was chosen to minimize the correction to scaling effects we calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization as expected cluster algorithms are characterized by lower values of dynamical critical exponent than the local one also in the case of dilution critical slowing down is more pronounced for the metropolis algorithm however the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms this phenomenon is quite opposite to the local dynamics where dilution enhances critical slowing down

the three dimensional dilute ising magnet the dilute ising model with a p 0 8 fraction of the sites occupied by spins is simulated on l3 systems for l up to 300 using a single cluster algorithm of wolff in the range of reduced temperature 0 002 t tc tc 0 03 the susceptibility appears to fit a simple power with an effective exponent eff 1 36

noncommutative rational functions invariant under the action of a finite solvable group abstract this paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in d generators these invariant skew fields are always finitely generated which contrasts with the free algebra case for abelian groups or solvable groups g with a well behaved representation theory it is shown that the invariant skew fields are free on g d 1 1 generators finally positivity certificates for invariant rational functions in terms of sums of squares of invariants are presented

symmetry reduction contact geometry and partial feedback linearization let pfaffian system omega define an intrinsically nonlinear control system which is invariant under a lie group of symmetries g using the contact geometry of brunovsky normal forms and symmetry reduction this paper solves the problem of constructing subsystems alpha subset omega such that alpha defines a static feedback linearizable control system a method for representing the trajectories of omega from those of alpha using reduction by a distinguished class g of lie symmetries is described a control system will often have a number of inequivalent linearizable subsystems depending upon the subgroup structure of g this can be used to obtain a variety of representations of the system trajectories in particular if g is solvable the construction of trajectories can be reduced to quadrature it is shown that the identification of linearizable subsystems in any given problem can be carried out algorithmically once the explicit lie algebra of g is known all the const

conservation of generalized momentum maps in mechanical optimal control problems with symmetry summary in this paper a structure preserving direct method for the optimal control of mechanical systems is developed the new method accommodates a large class of one step integrators for the underlying state equations the state equations under consideration govern the motion of affine hamiltonian control systems if the optimal control problem has symmetry associated generalized momentum maps are conserved along an optimal path this is in accordance with an extension of noether s theorem to the realm of optimal control problems in the present work we focus on optimal control problems with rotational symmetries the newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem this is true for a variety of one step integrators used for the discretization of the state equations examples are the one step theta method a partitioned variant of the theta method and energy momentum em consistent integrators numerical investigations confirm the theoretical findings copyright 2016 john wiley sons ltd

on controlled invariance in nonlinear systems abstract the notion of generalized controlled invariance gci is introduced to allow for the loss of degrees of freedom in control that may be the necessary price for achieving a desired invariance it is shown that subject to some technical rank restrictions controlled invariance implies gci a sequential procedure that definitively establishes for a given system pair whether is a gci of is introduced and through it a verdict o the solvability of the controlled invariance problem cip is reached

symmetric failures in symmetric control systems abstract this paper discusses the fault tolerance of symmetric systems with respect to controllability which is a fundamental characteristic of control systems in particular we reveal the underlying mathematical mechanism of the loss of controllability for symmetric systems induced by failures based on the decomposition of the symmetric systems into subsystems under the symmetry the controllability of the entire system can be discussed by checking that of each subsystem the analysis of the fault tolerance in this paper is an extension of this idea with the aid of the chain adapted transformation matrix for the decomposition the result is shown as a necessary condition for symmetric systems to retain the controllability despite some symmetric failures we also discuss sufficient conditions

system size dependence of the autocorrelation time for the swendsen wang ising model abstract we present monte carlo simulation results of the autocorrelation time for the swendsen wang method for the simulation of the ising model we have calculated the exponential and the integrated autocorrelation time at the critical point t c of the two dimensional ising model our results indicate that both autocorrelation times depend logarithmically on the linear system size l instead of a power law the simulations were carried out on the parallel computer of the condensed matter theory group at the university of mainz

symmetry preserving observers this paper presents the theory of invariant observers i e symmetry preserving observers we consider an observer to consist of a copy of the system and a correction term and we propose a constructive method based on the cartan moving frame method to find all the symmetry preserving correction terms the construction relies on an invariant frame a classical notion and on an invariant output error a less standard notion precisely defined here using the theory we build three non linear observers for three examples of engineering interest a non holonomic car a chemical reactor and an inertial navigation system for each example the design is based on physical symmetries and the convergence analysis relies on the use of invariant state errors a symmetry preserving way to define the estimation error

a geometric approach to the theory of 2 d systems the authors develop a geometric approach to the theory of 2 d two dimensional systems defining in a suitable way the notion of a sub 1 2 b sub 1 2 invariant subspaces and of controlled invariant subspaces such subspaces are shown to have good computational and feedback properties which make them useful in application in particular sufficient conditions and constructive procedures are obtained for the solutions of disturbance decoupling and model matching problems moreover it is shown that certain structural properties of a 2 d system can be described by means of a set of indexes defined in geometric terms and that such structural indexes can be used to reformulate the sufficient condition for model matching

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

an analysis of swendsen wang and related sampling methods convergence rates statistical efficiency and sampling costs are studied for the original and extended swendsen wang methods of generating a sample path s j j 1 with equilibrium distribution with r distinct elements on a finite state space x of size n 1 given s j 1 each method uses auxiliary random variables to identify the subset of x from which s j is to be randomly sampled let min and max denote respectively the smallest and largest elements in and let n denote the number of elements in with value max for a single auxiliary variable uniform sampling from the subset and n 1 n r min n r max 1 our results show rapid convergence and high statistical efficiency for large min max or n r n 1 and slow convergence and poor statistical efficiency for small min max and n r n 1 other examples provide additional insight for extended swendsen wang methods with non uniform subset sampling the analysis identifies the properties of a decomposition of x that favour fast convergence and high statistical efficiency in the absence of exploitable special structure subset sampling can be costly regardless of which of these methods is employed

on decomposition of nonlinear control systems in this paper the problem is studied when the system x i k 1 u t g t x x 0 x 0 defined on an n dimensional analytic manifold can be decomposed into either independent subsystems or a cascade of subsystems necessary and sufficient conditions for the existence of such local decompositions are given in terms of lie algebras generated by the system

hukuhara kneser property for a nonlinear dirichlet problem abstract the purpose of this paper is to show that the set of solutions of a nonlinear dirichlet problem satisfies the usual hukahara kneser property for ordinary differential equations

synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers this paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers we propose a dynamical network mathematical model with similar nonlinear nodes whose dimensions are different for this kind of network model the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes in addition the synchronisation manifold is defined as an invariant manifold which is regarded as the generalised case of dynamical networks with the same nodes dynamics furthermore some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis finally numerical examples are presented to verify the effectiveness of the obtained theoretical results

a parallel multigrid algorithm for percolation clusters a new parallel cluster finding algorithm is formulated by using multigrid relaxation methods very similar to those used for differential equation solvers for percolation clusters this approach drastically reduces critical slowing down relative to local or scan relaxation methods numerical studies of scaling properties with system size are presented in the case of the 2d percolation clusters of the swendsen wang ising dynamics running on the connection machine

input output decoupling of hamiltonian systems the linear case in this note we give necessary and sufficient conditions for a linear hamiltonian system to be input output decouplable by hamiltonian feedback i e feedback that preserves the hamiltonian structure in a second paper we treat the same problem for nonlinear hamiltonian systems

controlled invariance for nonlinear systems necessary and sufficient conditions are derived for a b invariance called here controlled invariance for nonlinear systems dot x f x u the obtained results generalize and elucidate already known results about systems dot x a x sum min i 1 max m u i b i x a new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given

nonlinearizable single input control systems do not admit stationary symmetries the main result of the paper states that almost any analytic single input control system which is truly nonlinear that is not feedback linearizable with controllable linearization at an equilibrium point does not admit any symmetry preserving that point by almost any system we mean that we exclude a small class of odd systems that admit just one nontrivial symmetry conjugated to minus identity the obtained results are based on a recent classification of nonlinear single input systems under formal feedback we also describe symmetries of feedback linearizable systems

cluster monte carlo algorithms abstract the swendsen wang and wolff monte carlo algorithms are described in some detail using the potts model as an example various generalizations are then reviewed and some applications are discussed two complete fortran programs for the algorithms are provided

controlled invariance by static output feedback for nonlinear systems the paper deals with the notion of static output feedback for nonlinear systems necessary and sufficient conditions are derived for c a b invariance here called measured controlled invariance for nonlinear control systems

efficient search of critical points in ising like systems abstract we propose a simulation method inspired by self organization that drives ising like magnetic systems rapidly to criticality we develop a feedback control rule with very few parameters for use with the standard methods of local spin updatings that spontaneously leads the system to the critical temperature this method for predicting the critical values requires small lattices it gives good results eg 1 accuracy for t c in 3 d for 10 3 systems with reduced computer times for both glauber and metropolis dynamics

linear convergence of comparison based step size adaptive randomized search via stability of markov chains in this paper we consider emph comparison based adaptive stochastic algorithms for solving numerical optimisation problems we consider a specific subclass of algorithms called cprs cb sars where the state variables at a given iteration are a vector of the search space and a positive parameter the step size typically controlling the overall standard deviation of the underlying search distribution we investigate the emph linear convergence of cb sars on emph scaling invariant objective functions scaling invariant functions preserve the ordering of points with respect to their function value when the points are scaled with the same positive parameter the scaling is done w r t a fixed reference point this class of functions includes norms composed with strictly increasing functions as well as many emph non quasi convex and emph non continuous functions on scaling invariant functions we show the existence of a homogeneous markov chain as a consequence of natural invariance properties of cb sars essentially scale invariance and invariance to strictly increasing transformation of the objective function we then derive sufficient conditions for emph global linear convergence of cb sars expressed in terms of different stability conditions of the normalised homogeneous markov chain irreducibility positivity harris recurrence geometric ergodicity and thus define a general methodology for proving global linear convergence of cb sars algorithms on scaling invariant functions as a by product we provide a connexion between emph comparison based adaptive stochastic algorithms and markov chain monte carlo algorithms

the analysis of zero dynamics of nonlinear control systems with symmetries zero dynamics of nonlinear control systems with symmetries are studied in this paper it is shown that the zero dynamics of a symmetric system is also symmetric and admits a special form of cascade decomposition a local zero dynamics is always possible to be extended to the semiglobal case the relation between the zero dynamics and the quotient system is also discussed

characterization of allowable perturbations for robust decoupling of affine non linear systems for affine non linear systems we study the effects of uncertainties in systems vector fields on decoupled linear input output behaviour a characterization of an allowable class of perturbations which preserve the decoupling properties of the nominal system is given an immediate consequence of this characterization indicates that decoupling position control of rigid robotic manipulators is not robust under any perturbations in robot dynamics the result is applied to simple hamiltonian control systems to characterize the allowable perturbation of total energy function

generalized output regulation problem for a class of nonlinear systems with nonautonomous exosystem the problem of the generalized output regulation is considered here in contrast to the classical output regulation problem where the references to be tracked and disturbances to be rejected are generated by an autonomous exogeneous system for the generalized output regulation an exogenous system is driven by an unknown external reference signal in such a way the class of reference or disturbance signals is expanded presented result solves the full measurement feedback case and is based on the well known notion of the regulator equation combined with the classical concept of the invariant distribution illustrative example including matlab simulink simulations is presented to demonstrate the suggested approach

controllability of poisson systems sufficient conditions for the controllability of affine nonlinear control systems on poisson manifolds are given the important special case when the poisson manifold is the reduced space of a symplectic manifold by a free lie group action is studied the controllability of the reduced system is linked to that of the given affine nonlinear system several examples illustrating the theory are also presented

static and dynamic critical behavior of thin magnetic ising films this work presents a study of the effect of film thickness on the static and dynamic critical behavior of thin magnetic ising films monte carlo simulations using the wolff algorithm were performed to determine the static and dynamic critical exponents of the films a dimensionality crossover from 2d to 3d due to the finiteness of the films in the static and dynamic critical behavior was observed as the film thickness increases in addition a slight increase in the effective dimension deff and a considerable increase in the critical temperature tc were found small values for the dynamic critical exponents were obtained indicating that the wolff algorithm is a very efficient method for these magnetic systems

on solvability of several affine system problems we examine seven problems and properties of single input single output affine control systems and classify the properties topologically as being structural generic or residual these properties are accessibility observability invertibility preservation of a given distribution and partial linearizability the mathematics involved relies upon the thorn transversality theorem

symmetry reduction of optimal control systems and principal connections this paper explores the role of symmetries and reduction in nonlinear control and optimal control systems the focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry in particular we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems affine and kinematic optimal control systems are of particular interest we explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems

cascade decomposition of nonlinear systems foliations and ideals of transitive lie algebras abstract we relate the cascade decomposition of nonlinear systems to the joint notions of foliations and ideals of transitive lie algebras

the hukuhara kneser property for quasilinear parabolic equations on etudie le probleme de dirichlet quasilineaire u t a x t u lu f x t u x t q t u x t t t ou a est une matrice diagonale et l un operateur elliptique on demontre un resultat d invariance pour un ensemble convexe borne d la limitation de l ensemble d donne une borne a priori que l on utilise avec une application de la theorie du degre de leray schauder et un theoreme de structure pour montrer l existence de solutions et la propriete de hukuhara kneser

single cluster monte carlo dynamics for the ising model we present an extensive study of a new monte carlo acceleration algorithm introduced by wolff for the ising model it differs from the swendsen wang algorithm by growing and flipping single clusters at a random seed in general it is more efficient than swendsen wang dynamics ford 2 giving zero critical slowing down in the upper critical dimension monte carlo simulations give dynamical critical exponentszw 0 33 0 05 and 0 44 0 10 ind 2 and 3 respectively and numbers consistent withzw 0 ind 4 and mean field theory we present scaling arguments which indicate that the wolff mechanism for decorrelation differs substantially from swendsen wang despite the apparent similarities of the two methods

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

critical dynamics a consequence of a random stepwise growth of clusters critical dynamics of correlated particles here glauber dynamics of singly flipping ising spins is explained by a random stepwise growth and contraction of clusters as follows at equilibrium a cluster of size s is described by its length l a random walk like path connecting a sequence of neighbor spins the length scales as l s where constitutes a new static critical exponent we assume that on the average the random growth of a cluster from zero to size s and length ls requires a sequence of l2 spin flips this gives for dynamic critical exponent z 2 where and are the usual static exponents exact results at dimension d 1 and 4 and simulation results at d 2 and 3 support the theory

critical dynamics of cluster algorithms in the dilute ising model autocorrelation times for thermodynamic quantities att c are calculated from monte carlo simulations of the site diluted simple cubic ising model using the swendsen wang and wolff cluster algorithms our results show that for these algorithms the autocorrelation timesdecrease when reducing the concentration of magnetic sites from 100 down to 40 this is of crucial importance when estimating static properties of the model since the variances of these estimators increase with autocorrelation time the dynamical critical exponents are calculated for both algorithms observing pronounced finite size effects in the energy autocorrelation data for the algorithm of wolff we conclude that when applied to the dilute ising model cluster algorithms become even more effective than local algorithms for whichincreasing autocorrelation times are expected

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

large scale dissipative and passive control systems and the role of star and cyclic symmetries in this technical note symmetries in large scale dissipative and passive control systems are considered in the framework of dissipativity and passivity theory stability conditions for large scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors building upon previous studies on stability of q s r dissipative large scale systems we show that for cyclic and star shaped symmetric systems there exists an upper bound on the number of subsystems that can be added to preserve stability of dissipative systems in cyclic and star shaped symmetric systems the subsystems can be heterogeneous as long as they satisfy the same dissipative inequalities approximate symmetry with respect to interconnections is also considered and the robustness of the results is demonstrated

a mathcal b invariant distributions and disturbance decoupling of nonlinear systems the concept of a b invariant subspaces has resulted in a unified approach to many of the basic structural properties of time invariant linear systems w m wonham lecture notes in economics and mathematical systems vol 101 springer verlag new york 1974 the purpose of this paper is to introduce the more general notion of a mathcal b invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds

bisimilar control affine systems the notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation these equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning in systems theory a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems in this paper we introduce two notions of bisimulation for nonlinear systems we present differential geometric characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions furthermore we also show that all bisimilar systems of different dimension are of this form

relaxation to equilibrium of single cluster dynamics of the ising model abstract the approach to equilibrium at the critical temperature of the two dimensional ising model from an initial ordered spin configuration is investigated using the single cluster monte carlo dynamics introduced by wolff an initial configuration of all up spins and its dual a checkerboard state are considered we give simple mean field and scaling arguments for the existence of power law decay because the usual arguments for time rescaling might not be applicable when the system is approaching equilibrium we directly determine the relation of the number of cluster flips to the number of monte carlo steps per spin for both initial configurations we find that the effective dynamical critical exponent determined from the power law behavior and the proper time rescaling differs from the estimates of the equilibrium dynamical exponent and depends on the initial conditions for the system sizes and times we have investigated

virtual bond percolation for ising cluster dynamics abstract the fortuin kasteleyn mapping between the ising model and the site bond correlated percolation model is shown to be only one of an infinite class of exact mappings these new cluster representations are a result of renormalized percolation rules correlated to entire blocks of spins for example these rules allow for percolation on virtual bonds between spins not present in the underlying hamiltonian as a consequence we can define new random cluster theories each with its own monte carlo cluster dynamics that exactly reproduce the ising model by tuning parameters on the critical percolation surface it is demonstrated numerically that cluster algorithms can be formulated for the 2d and 3d ising model that have smaller autocorrelations than the original swendsen wang algorithm

new results on f g invariance abstract the existing result for a nonsingular and involutive distribution to be f g invariant has a priori assumption that g is nonsingular this paper treats the problem of f g invariance for the case where g is singular necessary and sufficient conditions for a nonsingular and involutive distribution to be f g invariant are presented the constructive proof provides an algorithm for the construction of the feedback law

dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we study the dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we find that the li sokal bound on the autocorrelation time int const xc h holds along the self dual curve of the symmetric ashkin teller model and is almost but not quite sharp the ratio int c h appears to tend to infinity either as a logarithm or as a small power 0 05 p 0 12 in an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time

the hukuhara kneser property for a nonlinear integral equation abstract applying a structure theorem of krasnosel skii and perov we show that the solution set of a nonlinear integral equation satisfies the classical hukuhara kneser property

non linear symmetry preserving observers on lie groups in this technical note we give a geometrical framework for the design of observers on finite dimensional lie groups for systems which possess some specific symmetries the design and the error between true and estimated state equation are explicit and intrinsic we consider also a particular case left invariant systems on lie groups with right equivariant output the theory yields a class of observers such that the error equation is autonomous the observers converge locally around any trajectory and the global behavior is independent from the trajectory which is reminiscent of the linear stationary case

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

the hukuhara kneser property for parabolic systems with nonlinear boundary conditions the domain of the problem is a cylinder qt r x 0 7 1 the parabolic operator l is the same for each component of u and the nonlinearity f may be strongly coupled the purpose of this paper is to develop some of the fundamental theory for this problem we allow conditions general enough for nonunique solutions and start by giving a set of conditions that requires all the solutions to remain in an invariant region using these conditions we show the existence of at least one such solution and that the problem satisfies the hukuhara kneser property these results are thus extensions of berbernes and schmitt 5 to nonlinear boundary conditions a set d c rm is said to be invariant for the above problem if w g c d implies u q c d let n u denote an outer normal at a point u in the boundary of a nonempty open convex set d in theorem 3 1 the maximum principle is used to show that if the strong tangent inequality

non equilibrium critical relaxation of the wolff dynamics of the ising model abstract the non equilibrium critical relaxation of the single cluster dynamics is studied for the ferromagnetic ising model on the square and cubic lattices power law behavior is observed in the energy relaxation process starting from an all up spin configuration from this power decay the dynamical exponent z is estimated to be 0 50 0 05 and 1 3 0 1 for the square and cubic lattices respectively where the time is defined by the number of cluster flip trials if the time scale is normalized by cluster mass they are 0 25 0 05 and 0 3 0 1 respectively