closed loop identification for the best asymptotic performance of adaptive robust control discrete linear systems subjected to both additive and parametric deterministic disturbances are considered the certainty equivalence principle is used for the design of adaptive control two different estimation algorithms are proposed to meet different control objectives in the regulation problem with the worst case limsup performance index

on the use of nurbs based discretizations in the scaled boundary finite element method for wave propagation problems abstract we discuss the application of non uniform rational b splines nurbs in the scaled boundary finite element method sbfem for the solution of wave propagation problems at rather high frequencies we focus on the propagation of guided waves along prismatic structures of constant cross section comparisons are made between nurbs based discretizations and high order spectral elements in terms of the achievable convergence rates we find that for the same order of shape functions nurbs can lead to significantly smaller errors compared with lagrange polynomials the difference becomes particularly important at very high frequencies where spectral elements are prone to instabilities furthermore we analyze the behavior of nurbs for the discretization of curved boundaries where the benefit of exact geometry representation becomes crucial even in the low frequency range

model evaluation for robust tracking under unknown upper bounds on perturbations and measurement noise this technical note addresses a problem of model evaluation in the framework of robust steady state tracking in the l1 setup the upper bounds on measurement noise exogenous disturbance and coprime factor perturbations in a discrete time linear time invariant siso system are assumed to be unknown for a given nominal model and a given tracking controller three different model validation tests are considered and the complexity of computing upper bounds on the worst case steady state tracking error consistent with these tests is analysed

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

parameter induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise abstract parameter induced aperiodic stochastic resonance sr in the presence of multiplicative and additive noise is investigated in detail using theoretical and numerical analysis we evaluate the dynamical probability density by which the bit error rate is defined as a quantity to optimize in the aperiodic sr problem via tuning the system parameters tuning the system parameters includes two cases one is parameter optimized and the other is parameter induced sr to distinguish them we use the conventional method in which sr is realized by varying the noise intensity essentially parameter induced sr is based on the cooperative effect between the stochastic subjected dynamical system and the input signal by changing the intrinsic characteristic of the nonlinear system via tuning the system parameters rather than by adding noise the theory is tested against numerical simulations

stable adaptive regulation of arbitrary nth order plants this paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single input single output linear time invariant plant which is controllable and observable of known order n and has unknown parameters no further assumptions are made no external probing signal is required

colored multiplicative and additive non gaussian noise driven dynamical system mean first passage time abstract we have studied the barrier crossing dynamics in presence of non gaussian noises it has been observed that multiplicative colored non gaussian noise can induce resonant activation ra the conspicuous dependence of mean first passage time mfpt on correlation time 2 of additive colored noise having fixed variance have been analyzed beyond a critical value of 2 the mfpt increases for a given rate of increase of noise strength with 2 if the additive colored noise is non gaussian the mfpt first decreases with increase of the non gaussian parameter measures deviation from gaussian character of multiplicative colored noise followed by an increase exhibiting a minimum the appearance of the minimum critically depends on the additive noise

advantageous strategies in differential games for a class of suboptimal control laws abstract this paper deals with suboptimal control policies in differential games sufficient conditions for advantageous strategies of either player are examined for a linear quadratic game in which the players are constrained to use suboptimal control laws of specified form the concept of a bargaining matrix is employed specific scalar and vector examples are included to illustrate the theory

gradient bounds for wachspress coordinates on polytopes we derive upper and lower bounds on the gradients of wachspress coordinates defined over any simple convex d dimensional polytope p the bounds are in terms of a single geometric quantity h ast which denotes the minimum distance between a vertex of p and any hyperplane containing a nonincident face we prove that the upper bound is sharp for d 2 and analyze the bounds in the special cases of hypercubes and simplices additionally we provide an implementation of the wachspress coordinates on convex polyhedra using matlab and employ them in a three dimensional finite element solution of the poisson equation on a nontrivial polyhedral mesh as expected from the upper bound derivation the h 1 norm of the error in the method converges at a linear rate with respect to the size of the mesh elements

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

robust stabilization of lti systems via indirect adaptive controllers this paper presents a robust indirect adaptive stabilization controller for systems with linear time invariant lti nominal parts uncertain dynamic errors and bounded disturbances the a priori knowledge required for designing the adaptive controller is that the nominal part of the system is of known order and is stabilizable

adaptive stabilization of unstable and nonminimum phase stochastic systems abstract the system under consideration is the discrete time stochastic system a z yn zb z un wn driven by a martingale difference sequence wn where a z are polynomilas in backward shift operator z with unknown coefficients and both a z and b z may be unstable with the purpose of demonstrating theoretical possibility rather than designing a practically applicable control law this paper constructs an adaptive control that stabilizes the system and simultaneously guarantees strong consistency of the least squares estimates for unknown coefficients

stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion this paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates specifically the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated the uncertain moduli eigen frequencies and eigen modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis the expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen frequencies and the eigen modes distribution functions of the uncertain moduli are derived from experimental data where the pearson model is used to identify the type of density functions this realization then is employed to construct random orthogonal basis for each uncertain parameter because of available experimental modal analysis data this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results

assessment of spectral representation and karhunen loeve expansion methods for the simulation of gaussian stochastic fields abstract from the wide variety of methods developed for the simulation of gaussian stochastic processes and fields two are most often used in applications the spectral representation method and the karhunen loeve k l expansion in this paper an in depth assessment on the capabilities of the two methods is presented the spectral representation method expands the stochastic field as a sum of trigonometric functions with random phase angles and or amplitudes the version having only random phase angles is used in this work a wavelet galerkin scheme is adopted for the efficient numerical solution of the fredholm integral equation appearing in the k l expansion a one dimensional homogeneous gaussian random field with two types of autocovariance function exponential and square exponential is used as the benchmark test the accuracy achieved and the computational effort required by the k l expansion and the spectral representation for the simulation of the stochastic field are investigated the accuracy obtained by the two approaches is examined by comparing their ability to produce sample functions that match the target correlation structure and the gaussian probability distribution or alternatively its low order statistical moments mean variance and skewness

a stochastic scaled boundary finite element method abstract by extending the existing scaled boundary finite element method sbfem into the random field problem a stochastic scaled boundary finite element method ssbfem is developed in this paper to predict the structural responses with randomly distributed material properties the analyzed domain is discretized into a number of polygons modeled as sub domains of the sbfem so that the non homogeneous material properties are possible to be considered in establishment of the constitutive equation the random field represented by the karhunen loeve kl expansion is then directly incorporated into both the equilibrium equation of the sbfem and its sensitivity analysis formulation the perturbation method is employed to calculate the statistical moments of the structural responses and a semi analytical sensitivity analysis method is used to efficiently calculate the gradients involved particularly the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties four numerical examples are investigated to demonstrate the validity of the proposed method

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

multiplicative stochastic resonance a multiplicative bistable stochastic system perturbed by a periodic forcing term is shown to exhibit stochastic resonance with increasing intensity of the multiplicative noise such an effect is related to the phenomenon of stochastic stabilization which takes place in the unperturbed system

stability robustness bound estimates of discrete systems analysis and comparison robustness bound estimates based on the direct lyapunov method for discrete time nominally linear systems are analysed and compared although various robustness bound estimates were introduced recently little effort has been made to compare them we develop a scheme for obtaining the estimates which brings a new robustness bound estimate and provides a useful tool for the study and comparison of a variety of the estimates a novel technique is presented to compare two superior robustness estimates the results obtained are illustrated on several examples

robust pole placement direct adaptive control a pole placement direct adaptive control for not necessarily minimum phase plants is presented which is robust with respect to unmodeled dynamics and bounded disturbances the robustness is achieved by using both a normalized least squares algorithm with dead zone and appropriate nonlinear feedback the resulting closed loop system is shown to be globally stable subject to standard assumptions

an efficient forward propagation of multiple random fields using a stochastic galerkin scaled boundary finite element method abstract this paper serves to extend the existing literature on the stochastic galerkin scaled boundary finite element method sgsbfem in two ways the first part of this work deals with the formulation of multiple non correlated gaussian random fields using the conventional karhunen loeve expansion technique and its forward propagation through the spectral stochastic scaled boundary finite element setting using the polynomial surface fit method in terms of the scaled boundary coordinates the advantages in adopting such a forward propagation technique in capturing the statistical moments of quantities of interest qoi across the domain are highlighted using carefully chosen linear elastic problems having large to least correlated random fields as inputs the second contribution is the extension of the proposed forward uncertainty quantification uq to take into account multiple independent random fields followed by polynomial chaos expansion pce based sensitivity analysis both the computational efficiency and the accuracy of the proposed framework under different input random field correlation settings are elaborated upon by comparing their results against that obtained using the current existing sgsbfem in the literature moreover the stochastic results are validated for all the numerical examples using the monte carlo method

l1 robust performance of discrete time systems with structured uncertainty abstract this paper addresses the robust performance problem when a linear time invariant system is subjected to both norm bounded time varying uncertainty and worst case external bounded input the tightest upper bounds for steady state robust performance measures over classes of finite memory and fading memory perturbations are computed in the regulation and tracking problems since the classes of finite memory and fading memory perturbations are inappropriate to the purposes of model validation and adaptive control approximating subclasses of bounded memory perturbations and perturbations with exponentially decreasing impulse responses are considered it is shown that the robust performance bounds obtained are nonconservative in the case of bounded memory perturbations the worst case steady state robust performance measures for siso system under coprime factor perturbations are computed for illustration

effects of self correlation time and cross correlation time of additive and multiplicative colored noises for dynamical properties of a bistable system considering a bistable system driven by additive and multiplicative colored noises with colored cross correlation we obtain the analytic expressions of the stationary probability distribution pst x the linear relaxation time tc and the correlated function c s the effects of the noise intensity the self correlation time and the cross correlation time for the bistable system are discussed the noise intensity d speeds up relaxation of the system from unstable points which when d q the effects are damped the self correlation time 1 and 2 make the stationary probability distribution of the dynamical variable x be shaper and speed up the fluctuation decay of the dynamical variable x on the contrary the cross correlation time 3 makes the stationary probability distribution of the dynamical variable x be flatter and slows down the fluctuation decay of the dynamical variable x the effect of the self correlation time is more projecting than the effect of the cross correlation time

stable adaptive control of non minimum phase systems abstract an adaptive pole placement design for not necessarily minimum phase systems is analyzed with respect to stability conditions are given for boundedness of closed loop signals when the process is subject to bounded disturbances the most restrictive one can be avoided in a local stability result

convergence study of the truncated karhunen loeve expansion for simulation of stochastic processes a random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coefficients karhunen loeve k l series expansion is based on the eigen decomposition of the covariance function its applicability as a simulation tool for both stationary and non stationary gaussian random processes is examined numerically in this paper the study is based on five common covariance models the convergence and accuracy of the k l expansion are investigated by comparing the second order statistics of the simulated random process with that of the target process it is shown that the factors affecting convergence are a ratio of the length of the process over correlation parameter b form of the covariance function and c method of solving for the eigen solutions of the covariance function namely analytical or numerical comparison with the established and commonly used spectral representation method is made k l expansion has an edge over the spectral method for highly correlated processes for long stationary processes the spectral method is generally more efficient as the k l expansion method requires substantial computational effort to solve the integral equation the main advantage of the k l expansion method is that it can be easily generalized to simulate non stationary processes with little additional effort copyright 2001 john wiley sons ltd

unit impulse response of unbounded medium by scaled boundary finite element method to perform a dynamic analysis of a nonlinear structure interacting with an unbounded medium in the time domain it is desirable to formulate the interaction forces of the unbounded medium on the structure medium interface using displacements the corresponding response matrix to a unit impulse of displacements is calculated using the scaled boundary finite element method this method based solely on finite elements is very suitable to model an unbounded medium as the radiation condition at infinity is rigorously satisfied and the discretization is limited to the structure medium interface

frequency analysis of tick quotes on foreign currency markets and the double threshold agent model abstract power spectrum densities for the number of tick quotes per minute market activity on three currency markets usd jpy eur usd and jpy eur are analyzed for periods from january 2000 to december 2000 we find some peaks on the power spectrum densities at a few minutes we develop the double threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision making of them this model is numerically performed and theoretically investigated by utilizing the mean field approximation we propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants

design of adaptive pole placement controllers for plants of unknown order by an indirect control approach an adaptive pole placement control problem is considered for a scalar discrete time linear plant assuming the knowledge of an upper bound of the plant order a class of models that can be regarded to be input output equivalent to the plant is first constructed based on the parameter estimate generated by a least squares type identification scheme a minimization problem is then derived that enables one to determine the model s coefficients and the pole placing feedback gains so that the desired closed loop poles are assigned in a limit

pure multiplicative stochastic resonance of a theoretical anti tumor model with seasonal modulability pure multiplicative noise induced stochastic resonance which appears in an anti tumor system modulated by a seasonal external field is studied by using theoretical analyses of the generalized potential and numerical simulations for optimally selected values of the multiplicative noise intensity stochastic resonance is observed which is manifested by the quasisymmetry of two potential minima theoretical results and numerical simulations are in good quantitative agreement

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

stochastic modeling of uncertainties in computational structural dynamics recent theoretical advances this paper deals with a short overview on stochastic modeling of uncertainties we introduce the types of uncertainties the variability of real systems the types of probabilistic approaches the representations for the stochastic models of uncertainties the construction of the stochastic models using the maximum entropy principle the propagation of uncertainties the methods to solve the stochastic dynamical equations the identification of the prior and the posterior stochastic models the robust updating of the computational models and the robust design with uncertain computational models we present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties and for their identification with experimental data we also present the construction of the posterior stochastic model of uncertainties using the bayesian method

the stochastic galerkin scaled boundary finite element method on random domain summary the research work extends the scaled boundary finite element method sbfem to non deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random field uncertainties the aim is to blend the sbfem into the galerkin spectral stochastic methods which leads to a proficient procedure for handling the stress singularity problems and crack analysis the young s modulus of structures is considered to have random field uncertainty resulting in the stochastic behaviour of responses mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses displacement strain and stress and stress intensity factors of cracked structures the feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples this article is protected by copyright all rights reserved

numerical solution of spectral stochastic finite element systems abstract this paper addresses the issues involved in solving systems of linear equations which arise in the context of the spectral stochastic finite element ssfem formulation two efficient solution procedures are presented that dramatically reduce the amount of computations involved in numerically solving these problems a brief review is first provided of the underlying spectral approach which highlights the peculiar structure of the matrices generated and how their properties are related to both the level of approximation involved as well as to the convergence behavior of the proposed solution procedure the differences between these matrices from their deterministic finite element counterparts are illustrated an iterative solution scheme is proposed which utilizes their specific properties for efficient memory management and enhanced convergence behavior results from numerical tests are presented comparisons with standard algorithms illustrate the efficiency of the proposed algorithm the second solution procedure presented in this paper is based on hierarchical basis concepts results from numerical tests are again provided and the limitations of this approach are assessed the performance of both proposed algorithms indicates that the linear algebraic systems from the underlying ssfem formulation can be solved with considerably less effort in memory and computation time than their size suggests furthermore the data structures and the hierarchical concept introduced in this study are found to have great potential for the future development of adaptive procedures in stochastic fem

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

adaptive robust control for siso systems abstract this paper addresses the problem of nonconservative adaptive robust regulating a siso system allowing for model perturbations in the coprime factor representation of the system as well as external additive bounded disturbance signals the perturbations and disturbances are assumed to belong to a particular parameterized class and are norm bounded the norm bounds are not available for control design but the class knowledge is available the performance measure is the worst possible steady state absolute value of the controlled output over the class of allowable disturbances and model perturbations an identification based adaptive control method is proposed where the identification criterion coincides with the control objective the proposed adaptive scheme achieves near optimal performance simulations comparing the new scheme with an adaptive controller based on classical recursive least squares identification are presented

coherence enhancement in nonlinear systems subject to multiplicative ornstein uhlenbeck noise we show that for two biologically relevant models with self sustained oscillations under the action of a multiplicative ornstein uhlenbeck process their coherence response behaves nonmonotonically with the process correlation time there is a correlation time for which the quality factor is optimized this phenomenon is a consequence of the interplay between the correlation time and the system s periodicity this relation is evidenced through a power law relation with an exponent close to 1 2

isogeometric analysis enhanced by the scaled boundary finite element method abstract by leveraging the information of a typical cad model in the analysis the intensive process of discretization can be circumvented this unification has led to the isogeometric analysis iga hughes et al 2005 however as the cad model provides information only of the boundary a 2d 3d stress analysis is still one major step away in this work the concepts of isogeometric analysis and the scaled boundary finite element method sbfem are combined the sbfem requires only the boundary information and hence provides a seamless integration with the cad modeling within the proposed framework the nurbs basis functions are used to discretize the unknown fields in the circumferential direction whilst analytical solution is sought in the radial direction we further extend the framework to problems with singularities and to dynamic analysis the accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics

scaled boundary polygons with application to fracture analysis of functionally graded materials summary this study presents a framework for the development of polygon elements based on the scaled boundary fem underpinning this study is the development of generalized scaled boundary shape functions valid for any n sided polygon these shape functions are continuous inside each polygon and across adjacent polygons for uncracked polygons the shape functions are linearly complete for cracked polygons the shape functions reproduce the square root singularity and the higher order terms in the williams eigenfunction expansion this allows the singular stress field in the vicinity of the crack tip to be represented accurately using these shape functions a novel scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed the stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions the material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates the intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions the new formulation is validated and its salient features are demonstrated using five numerical benchmarks copyright 2014 john wiley sons ltd

polygon scaled boundary finite elements for crack propagation modelling summary an automatic crack propagation modelling technique using polygon elements is presented a simple algorithm to generate a polygon mesh from a delaunay triangulated mesh is implemented the polygon element formulation is constructed from the scaled boundary finite element method sbfem treating each polygon as a sbfem subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks stress intensity factors are computed directly from their definitions without any nodal enrichment functions an automatic remeshing algorithm capable of handling any n sided polygon is developed to accommodate crack propagation the algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths the efficiency of the polygon sbfem in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features the predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature copyright 2012 john wiley sons ltd

buckling analysis of imperfect shells with stochastic non gaussian material and thickness properties in this paper the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections is investigated to this purpose a random spatial variability of the elastic modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric deviations of the shell structure from its perfect geometry the main novelty of this paper compared to previous works is that a non gaussian assumption is made for the distribution of the two aforementioned uncertain parameters i e the modulus of elasticity and the shell thickness which are described by two dimensional uni variate 2d 1v homogeneous non gaussian stochastic fields the initial geometric imperfections are described as a 2d 1v gaussian non homogeneous stochastic field with properties derived from corresponding experimental measurements numerical examples are presented focusing on the influence of the non gaussian assumption on the variability of the buckling load which is calculated by means of the monte carlo simulation method it is shown that the choice of the marginal probability distribution for the description of the material and thickness variability is crucial since it affects significantly the statistics of the buckling load of imperfection sensitive shell type structures

an adaptive lq controller for non minimum phase systems abstract the paper studied the problem of the adaptive tracking of a reference signal by the output of any deterministic discrete siso linear system with unknown parameters an adaptive control scheme based on the lq control solution is proposed the stability of the resulting adaptively controlled system and conditions for a good tracking are studied several simulations illustrate the proposal

reformulation of the parameter identification problem for systems with bounded disturbances abstract the problem of deriving parameter identification algorithms that incorporate prior knowledge of a bound on the disturbance is studied particular emphasis is given to the following aspects firstly to motivate from geometrical and optimization considerations the modifications dead zones required to cope with the disturbances secondly to guarantee the convergence properties which are essential in the establishment of stability of identification based adaptive control systems projection and least squares algorithms are studied in both cases an interpretation is given to the new dead zone that has proven to be a key ingredient in recent robustness studies e g goodwin et al 1986 automatica 22 199 207 kreisselmeier and anderson 1985 ieee trans aut control 31 127 133 and lozano leal and ortega 1986 2nd ifac workshop on adapt syst in control and signal proc lund sweden

mittag leffler noise induced stochastic resonance in a generalized langevin equation with random inherent frequency abstract the generalized stochastic resonance gsr and the bona fide stochastic resonance sr in a generalized langevin equation driven by a periodic signal multiplicative noise and mittag leffler noise are extensively investigated the expression of the frequency spectrum of the mittag leffler noise is studied using the shapiro loginov formula and laplace transformation technique the exact expressions of the output amplitude gain and the signal to noise ratio are obtained the simulation results turn out that the output amplitude gain and the signal to noise ratio are non monotonic functions of the characteristics of noise parameters and system parameters especially the influence of the memory exponent and memory time of mittag leffler noise could induce the gsr phenomenon the influence of the driving frequency could induce the bona fide stochastic resonance it is found that the system with fractional memory exponent could be more easily induced sr phenomenon than the system with integer memory exponent

adaptive suboptimal control of a linear system with bounded disturbance abstract an adaptive suboptimal control of a linear discrete system with unknown parameters is proposed an additive disturbance v t acting on the system is supposed to be uniformly bounded the criterion is sup v t i y 1 u 1 where y t is the output u t is the control the adaptive control law gives almost the same guaranteed value of the criterion as the optimal linear feedback does for a system with known parameters

a feti preconditioned conjugate gradient method for large scale stochastic finite element problems in the spectral stochastic finite element method for analyzing an uncertain system the uncertainty is represented by a set of random variables and a quantity of interest such as the system response is considered as a function of these random variables consequently the underlying galerkin projection yields a block system of deterministic equations where the blocks are sparse but coupled the solution of this algebraic system of equations becomes rapidly challenging when the size of the physical system and or the level of uncertainty is increased this paper addresses this challenge by presenting a preconditioned conjugate gradient method for such block systems where the preconditioning step is based on the dual primal finite element tearing and interconnecting method equipped with a krylov subspace reusage technique for accelerating the iterative solution of systems with multiple and repeated right hand sides preliminary performance results on a linux cluster suggest that the proposed solution method is numerically scalable and demonstrate its potential for making the uncertainty quantification of realistic systems tractable

extended stochastic finite element method for the numerical simulation of heterogeneous materials with random material interfaces an extended stochastic finite element method has been recently proposed for the numerical solution of partial differential equations defined on random domains this method is based on a marriage between the extended finite element method and spectral stochastic methods in this article we propose an extension of this method for the numerical simulation of random multi phased materials the random geometry of material interfaces is described implicitly by using random level set functions a fixed deterministic finite element mesh which is not conforming to the random interfaces is then introduced in order to approximate the geometry and the solution classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables which leads to a deterioration of the accuracy and convergence properties of the approximate solution in order to recover optimal convergence properties of the approximation we propose an extension of the partition of unity method to the spectral stochastic framework this technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure copyright 2010 john wiley sons ltd

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

nonlinear stochastic equations with multiplicative levy noise the langevin equation with a multiplicative levy white noise is solved the noise amplitude and the drift coefficient have a power law form a validity of ordinary rules of the calculus for the stratonovich interpretation is discussed the solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the stratonovich interpretation the problem of escaping from a potential well is analyzed numerically predictions of different interpretations of the stochastic integral are compared

spectral stochastic isogeometric analysis of linear elasticity abstract the stochastic isogeometric analysis of linear elasticity problem is investigated in this study the spectral stochastic analysis is introduced into isogeometric analysis iga and a novel yet robust stochastic analysis framework namely the spectral stochastic isogeometric analysis ssiga is freshly proposed unlike traditional numerical solutions of the karhunen loeve k l expansion the non uniform rational b spline nurbs and t spline basis functions are employed within the proposed framework of ssiga so the random fields acting on a continuous physical medium with complex geometry can be handled in an appropriate physically feasible and efficient fashion the polynomials chaos expansion pce is implemented to represent the stochastic structural response e g displacement strain and stress such that all corresponding statistical characteristics e g mean and standard deviation can be robustly acquired furthermore by utilizing the nonparametric statistical analysis both probability density functions pdfs and cumulative distribution functions cdfs of concerned structural displacements and stresses can be effectively established within the framework of iga by meticulously implementing the concept of the higher order k refinement the proposed ssiga provides a more legitimate and efficient stochastic computational approach for modern engineering structures which are complicated by both spatially dependent uncertainties and complex geometries

exact recursive polyhedral description of the feasible parameter set for bounded error models a method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements it provides a parameterized expression of this set which can be used for robust control design or for optimizing any criterion over the set this approach is based on a new variant of the double description method for determining the edges of a polyhedral cone it can be used in real time and provides a suitable context for implementation on a computer whenever a new measurement modifies the set the characterization is updated the technique is illustrated with a simple example

new robust stability bounds of linear discrete time systems with time varying uncertainties this paper presents new uncertain parameter variation bounds for linear discrete time systems to preserve asymptotic stability the lyapunov method is utilized to treat both structured and unstructured uncertainties and the results are optimized with respect to a parameter in the inequality used when applied to examples considered by previous authors our results give less conservative bounds