the matching of a prescribed linear input output behavior in a nonlinear system in this paper we deal with the problem of finding a feedback under which the input output behavior of a nonlinear system becomes exactly the same as that of a specified linear model the solvability of this problem is shown to depend on a formal infinite zero structure associated with the system

non kolmogorov probability models and modified bell s inequality we analyze the proof of bell s inequality and demonstrate that this inequality is related to one particular model of probability theory namely kolmogorov measure theoretical axiomatics from 1933 we found a numerical statistical correction to bell s inequality such an additional term e on the right hand side of bell s inequality can be considered as a probability invariant of a quantum state this is a measure of nonreproducibility of hidden variables in different runs of experiments experiments to verify bell s inequality can be considered as just experiments to estimate the constant e it seems that bell s inequality could not be used as a crucial reason to deny local realism we consider deterministic as well as stochastic hidden variables models

model matching and factorization for nonlinear systems a structural approach the model matching and the left factorization problems for nonlinear systems are investigated using an approach based on the structural algorithm sufficient conditions for the solvability of the f

essential orders and the non linear decoupling problem abstract the concept of essential orders has recently been introduced into linear system theory and has been shown to be useful in the solution of static and dynamic decoupling problems commauit et al 1986 de luca et al 1985 this paper presents a non trivial extension to the class of non linear affine systems of some of these definitions and results it is shown that these invariant integers give the minimal order for a regular dynamic compensator that decouples a right invertible system

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

a nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem the nonregular dynamic disturbance decoupling problem for nonlinear control systems is introduced a local solution is given by means of a constructive algorithm that is based on singh s algorithm and the clamped dynamics algorithm further studied is the nonlinear model matching problem that is defined as follows given a nonlinear control system to be referred to as the plant and another nonlinear control system to be referred to as the model can a compensator for the plant be found in such a way that the input output behavior of the compensated plant matches that of the model by proving that the solvability of the nonlinear model matching problem is equivalent to the solvability of an associated nonregular dynamic disturbance decoupling problem a complete local solution of this problem can be established

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

bourgain brezis mironescu domains abstract bourgain et al 2001 proved that for p 1 and smooth bounded domain r n lim s 1 1 s f x f y p x y n s p d x d y f x p d x for all f l p this gives a characterization of w 1 p by means of w s p seminorms only for the case p 1 davila 2002 proved that when is a bounded domain with lipschitz boundary lim s 1 1 s f x f y x y n s d x d y f b v for all f l 1 this characterizes b v in terms of w s 1 seminorm in this paper we extend the first result and partially extend the second result to extension domains

the matching of nonlinear models via dynamic state feedback it is well known that for linear systems the model matching problem is equivalent to a disturbance decoupling problem with disturbance measurement the solution of both problems can be expressed in terms of properties of invariant subspaces of the system and of the model in this paper it is shown that for nonlinear systems under appropriate hypotheses analogous results can be obtained the solvability of a model matching problem can be expressed in terms of properties of suitable invariant distributions it is also shown that as for linear systems those properties are related to the so called structures at infinity of the system and of the model

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

frieden wave function representations via an einstein podolsky rosen bohm experiment the appearance of the spin 1 2 and spin 1 representations in the frieden soffer extreme physical information epi statistical approach to the einstein podolsky rosen bohm epr bohm experiment is shown in order to obtain the epr bohm result in addition to the observed structural and variational information principles of the epi method the condition of the regularity of the probability distribution is used the observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function it is suggested that due to the self consistent analysis of both information principles quantum mechanics is covered by the statistical information theory the estimation of the angle between the analyzers in the epr bohm experiment is discussed

local nonlinear model matching from linearity to nonlinearity the model matching problem consists of designing a compensator for a given system called the plant in such a way that the resulting input output behaviour matches that of a prespecified model in this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback the main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model the generic conditions are identified they naturally appear in the solution of the dynamic input output decoupling problem for the plant the theory is illustrated by means of two examples

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

new decoupling invariants the essential orders the aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row by row decoupling problem several equivalent characterizations are provided within both the geometric and the transfer matrix approaches

fractional order orlicz sobolev spaces abstract in this paper we define the fractional order orlicz sobolev spaces and prove its convergence to the classical orlicz sobolev spaces when the fractional parameter s 1 in the spirit of the celebrated result of bourgain brezis mironescu we then deduce some consequences such as convergence of the modulars and convergence of solutions for some fractional versions of the g operator as the fractional parameter s 1

fixed modes and nonlinear noninteracting control with stability the existence of a fixed internal dynamics inherent to the noninteraction requirement is identified when unstable this represents an obstruction to the achievement of noninteracting control with stability by means of static state feedback remarkably whenever one leaves the class of linear systems this obstruction cannot in general be removed by dynamic state feedback

a modified algorithm for invertibility in nonlinear systems the algorithm of hirschorn 1 for the construction of inverses of nonlinear systems is modified and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained for the systems which do not satisfy the invertibility conditions a characterization of input space on which the input output map is injective is derived

controllability distributions and systems approximations a geometric approach given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a taylor series approximation of it the value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant controllability distributions the relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation

hidden variables joint probability and the bell inequalities it is shown that the following statements about a quantum correlation experiment are mutually equivalent 1 there is a deterministic hidden variables model for the experiment 2 there is a factorizable stochastic model 3 there is one joint distribution for all observables of the experiment returning the experimental probabilities 4 there are well defined compatible joint distributions for all pairs and triples of commuting and noncommuting observables 5 the bell inequalities hold