finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

global existence results for oldroyd b fluids in exterior domains the case of non small coupling parameters consider the set of equations describing oldroyd b fluids in an exterior domain it is shown that this set of equations admits a unique global solution in a certain function space provided the initial data but not necessarily the coupling constant is small enough

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

a learning result for continuous time recurrent neural networks abstract the following learning problem is considered for continuous time recurrent neural networks having sigmoidal activation functions given a black box representing an unknown system measurements of output derivatives are collected for a set of randomly generated inputs and a network is used to approximate the observed behavior it is shown that the number of inputs needed for reliable generalization the sample complexity of the learning problem is upper bounded by an expression that grows polynomially with the dimension of the network and logarithmically with the number of output derivatives being matched

lifting bell inequalities a bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers measurement settings or measurement outcomes in this article such liftings of bell inequalities are studied it is shown that if the original inequality defines a facet of the polytope of local joint outcome probabilities then the lifted one also defines a facet of the more complex polytope

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

on realizability of neural networks based input output models in the classical state space form this paper proves that the typical neural network based input output model does not have a state space realization and suggests the additive nonlinear auto regressive with exogenous input anarx structure as an excellent choice for neural network based input output models the advantage of the anarx model is that the time steps in the argument are pair wise decomposed which allows the anarx model to be realized in state space and to be linearized via dynamic output feedback moreover accessibility of the state space realization has been proved

lur e systems with multilayer perceptron and recurrent neural networks absolute stability and dissipativity sufficient conditions for absolute stability and dissipativity of continuous time recurrent neural networks with two hidden layers are presented in the autonomous case this is related to a lur e system with multilayer perceptron nonlinearity such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form the conditions are expressed as matrix inequalities and can be employed for nonlinear h sub spl infin control and imposing closed loop stability in dynamic backpropagation

technical communique finite time control of linear systems subject to parametric uncertainties and disturbances in this paper we consider finite time control problems for linear systems subject to time varying parametric uncertainties and to exogenous constant disturbances the main result provided is a sufficient condition for robust finite time stabilization via state feedback it can be applied to problems with both non zero initial conditions and unknown constant disturbances this condition is then reduced to a feasibility problem involving linear matrix inequalities lmis a detailed example is presented to illustrate the proposed methodology

global small solutions of 3d incompressible oldroyd b model without damping mechanism abstract in this paper we prove the global existence of small smooth solutions to the three dimensional incompressible oldroyd b model without damping on the stress tensor the main difficulty is the lack of full dissipation in stress tensor to overcome it we construct some time weighted energies based on the special coupled structure of system such type energies show the partial dissipation of stress tensor and the strongly full dissipation of velocity in the view of treating nonlinear term as a linear term we also apply this result to 3d incompressible viscoelastic system with hookean elasticity and then prove the global existence of small solutions without the physical assumption div curl structure as previous works

complete controllability of continuous time recurrent neural networks this paper studies controllability for the class of control systems commonly called continuous time recurrent neural networks it is shown that under a generic condition on the input matrix the system is controllable for every possible state matrix the result holds when the activation function is the hyperbolic tangent

recurrent neural networks coupled with linear systems observability in continuous and discrete time we give necessary and sufficient conditions for observability of a class of recurrent neural networks having a subsystem where the activation function is the identity an algorithm for computing all pairs of indistinguishable states is also given

blow up and global existence for the periodic phan thein tanner model abstract in this paper we mainly investigate the cauchy problem for the periodic phan thein tanner ptt model this model is derived from network theory for the polymeric fluid we prove that the strong solutions of ptt model will blow up in finite time if the trace of initial stress tensor tr 0 x is negative it is thus very different from the other viscoelastic model on the other hand we obtain the global existence result with small initial data when tr 0 x c 0 0 for some c 0 moreover we study about the large time behavior

bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant lyapunov functions or storage functions satisfying appropriate linear matrix inequalities results are also presented for model reduction errors for such systems

brief paper finite time stability and instability of stochastic nonlinear systems this paper presents a new definition of finite time stability for stochastic nonlinear systems this definition involves stability in probability and finite time attractiveness in probability an important lyapunov theorem on finite time stability for stochastic nonlinear systems is established a theorem extending the stochastic lyapunov theorem is also proved moreover an example and a lemma are presented to illustrate the scope of extension a useful inequality extended from bihari s inequality is derived which plays an important role in showing the lyapunov theorem finally a lyapunov theorem on finite time instability is proved which states that almost surely globally asymptotical stability is not equivalent to finite time stability for some stochastic systems two simulation examples are given to illustrate the theoretical analysis

identification of structured nonlinear systems this paper is concerned with the identification of static nonlinear components in a complex interconnected system these nonlinear components are treated nonparametrically in the sense that no natural parameterization is assumed to be available

learning complexity dimensions for a continuous time control system this paper takes a computational learning theory approach to a problem of linear systems identification it is assumed that inputs are generated randomly from a known class consisting of linear combinations of k sinusoidals the output of the system is classified at some single instant of time the main result establishes that the number of samples needed for identification with small error and high probability independently from the distribution of inputs scales polynomially with n the system dimension and logarithmically with k

uniqueness of circuits and systems containing one nonlinearity we study systems containing one memoryless nonlinearity we show that two such systems have the same i o operator only when they are related by simple scaling delay and loop transformations the theory is applied to one port networks containing one nonlinear element

global solutions for incompressible viscoelastic fluids we prove the existence of both local and global smooth solutions to the cauchy problem in the whole space and the periodic problem in the n dimensional torus for the incompressible viscoelastic system of oldroyd b type in the case of near equilibrium initial data the results hold in both two and three dimensional spaces the results and methods presented in this paper are also valid for a wide range of elastic complex fluids such as magnetohydrodynamics liquid crystals and mixture problems

modeling and simulation of three dimensional planar contraction flow of viscoelastic fluids with ptt giesekus and fene p constitutive models abstract the planar contraction flow is a representative benchmark problem that is often used as a stringent test for the robustness of the numerical method to predict real flow patterns of viscoelastic fluids a numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three dimensional flow of viscoelastic fluids through planar contraction the viscoelastic rheological responses are described by using three kind differential constitutive models including the phan thien tanner ptt model the giesekus model and the finite extensible nonlinear elastic dumbbell with a peterlin closure approximation fene p model the discrete elastic viscous split stress devss formulation in cooperating with the inconsistent streamline upwind su scheme is employed to improve the computational stability the simulation results of flow velocity and stress on different sections of the flow field are compared with quinzani s experimental results that detected by laser doppler velocimetry and flow induced birefringence technologies it is found that the simulation results predicted with three kind differential constitutive models agree well with the experimental results the numerical methodology proposed in the study can be used successfully to predict complex flow patterns of viscoelastic fluids

stabilization and performance synthesis for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered given a plant of this form sufficient conditions are derived for 1 the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant lyapunov function and 2 the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level several of these conditions can be written into linear matrix inequalities

robust decentralized stabilization of markovian jump large scale systems a neighboring mode dependent control approach abstract this paper is concerned with the decentralized stabilization problem for a class of uncertain large scale systems with markovian jump parameters the controllers use local subsystem states and neighboring mode information to generate local control inputs a sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers a numerical example is given to illustrate the developed theory

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

sample complexity for learning recurrent perceptron mappings recurrent perceptron classifiers generalize the usual perceptron model they correspond to linear transformations of input vectors obtained by means of autoregressive moving average schemes or infinite impulse response filters and take into account those correlations and dependences among input coordinates which arise from linear digital filtering this paper provides tight bounds on the sample complexity associated to the fitting of such models to experimental data the results are expressed in the context of the theory of probably approximately correct pac learning

decision theoretic generalizations of the pac model for neural net and other learning applications we describe a generalization of the pac learning model that is based on statistical decision theory in this model the learner receives randomly drawn examples each example consisting of an instance x in x and an outcome y in y and tries to find a hypothesis h x a where h in h that specifies the appropriate action a in a to take for each instance x in order to minimize the expectation of a loss l y a here x y and a are arbitrary sets l is a real valued function and examples are generated according to an arbitrary joint distribution on x times y special cases include the problem of learning a function from x into y the problem of learning the conditional probability distribution on y given x regression and the problem of learning a distribution on x density estimation we give theorems on the uniform convergence of empirical loss estimates to true expected loss rates for certain hypothesis spaces h and show how this implies learnability with bounded sample size disregarding computational complexity as an application we give distribution independent upper bounds on the sample size needed for learning with feedforward neural networks our theorems use a generalized notion of vc dimension that applies to classes of real valued functions adapted from pollard s work and a notion of capacity and metric dimension for classes of functions that map into a bounded metric space supersedes 89 30 and 90 52 also in information and computation vol 100 no 1 september 1992

on hydrodynamics of viscoelastic fluids in this paper we study a hydrodynamic system describing fluids with viscoelastic properties after a brief examination of the relations between several models we shall concentrate on a few analytical issues concerning them in particular we establish local existence and global existence with small initial data of classical solutions for an oldroyd system without an artificially postulated damping mechanism

no fine theorem for macrorealism limitations of the leggett garg inequality tests of local realism and macrorealism have historically been discussed in very similar terms leggett garg inequalities follow bell inequalities as necessary conditions for classical behavior here we compare the probability polytopes spanned by all measurable probability distributions for both scenarios and show that their structure differs strongly between spatially and temporally separated measurements we arrive at the conclusion that in contrast to tests of local realism where bell inequalities form a necessary and sufficient set of conditions no set of inequalities can ever be necessary and sufficient for a macrorealistic description fine s famous proof that bell inequalities are necessary and sufficient for the existence of a local realistic model therefore cannot be transferred to macrorealism a recently proposed condition no signaling in time fulfills this criterion and we show why it is better suited for future experimental tests and theoretical studies of macrorealism our work thereby identifies a major difference between the mathematical structures of local realism and macrorealism

all clauser horne shimony holt polytopes the correlations that admit a local hidden variable model are described by a family of polytopes whose facets are the bell inequalities the clauser horne shimony holt chsh inequality is the simplest such bell inequality and is a facet of every bell polytope we investigate for which bell polytopes the chsh inequality is also the unique non trivial facet we prove that the chsh inequality is the unique facet for all bipartite polytopes where at least one party has a binary choice of dichotomic measurements irrespective of the number of measurement settings and outcomes for the other party based on numerical results we conjecture that it is also the unique facet for all bipartite polytopes involving two measurements per party where at least one measurement is dichotomic finally we remark that these two situations can be the only ones for which the chsh inequality is the unique facet i e any polytope that does not correspond to one of these two cases necessarily has facets that are not of the chsh form as a byproduct of our approach we derive a new family of facet inequalities this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

operational characterization of divisibility of dynamical maps in this work we show the operational characterization to the divisibility of dynamical maps in terms of the distinguishability of quantum channels it is proven that the distinguishability of any pair of quantum channels does not increase under divisible maps in which the full hierarchy of divisibility is isomorphic to the structure of entanglement between system and environment this shows that i channel distinguishability is the operational quantity signifying detecting divisibility indivisibility of dynamical maps and ii the decision problem for the divisibility of maps is as hard as the separability problem in entanglement theory we also provide the information theoretic characterization to the divisibility of maps with conditional min entropy

partially mode dependent design of h filter for stochastic markovian jump systems with mode dependent time delays abstract this paper is concerned with the h filtering problem for stochastic delay systems with markovian jump parameters where both the state dynamics and measurements of systems are corrupted by wiener process in contrast with traditional mode dependent and mode independent filtering methods a new partially mode dependent filter is established via using a mode dependent lyapunov function where the system mode available to filter implementation is transmitted through an unreliable network and the stochastic property of mode available to a filter is considered sufficient conditions for the existence of h filters are obtained as linear matrix inequalities finally an example is used to show the effectiveness of the given theoretical results

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