dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative internal variable constitutive laws abstract reference is made to discrete finite element structural models formulated in terms of generalized variables the constitutive laws adopted are elastic plastic nonlinear hardening with internal variables and generally nonassociative the notion of reduced domain is employed as a generalization of a similar concept introduced in earlier developments of shakedown theory on this basis a unified theory is presented which encompasses necessary and separately sufficient conditions for shakedown by a static approach as a further generalization of classical melan s theorem bounds on various post shakedown quantities sufficient and necessary shakedown criteria by a kinematic approach as a further extension of neal symonds koiter theorem by suitable specializations and relaxations of the achievable results the criteria and bounding inequalities established here are formulated as mathematical programming problems in view of numerical applications

kinematical shakedown analysis with temperature dependent yield stress summary this paper describes a direct shakedown analysis of structures subjected to variable thermal and mechanical loading the classical kinematical shakedown theorem is modied to be implemented with any displacementbased nite elements the plastic incompressibility condition is imposed by the penalty function method the shakedown limit is found via a non linear mathematical programming procedure two numerical shakedown methods are developed and implemented to provide alternative numerical means the temperature dependent material model is included in theoretical and numerical calculation in a simple way its eect on shakedown limit is investigated the numerical examination for some pressure vessel structures subjected to thermal and mechanical loading shows a satisfying precision and eciency of the methods presented copyright 2001 john wiley sons ltd

damage assessment of a nonlinear space antenna structure using quasi linearization methods health monitoring of structural systems for the detection of damage is a critical practice in determining their safety and service life a large amount of research has been done in applying damage detection analysis to linear models of structures although many real structures exhibit nonlinear behavior before or as a result of damage there are currently few tools to apply damage detection analysis to structures that are modeled by nonlinear differential equations the objective of this study is to initiate a facet of damage detection analysis applied to such nonlinear models of structures given a parameterized ordinary differential equation model of a structural system linear or nonlinear parameter estimation can serve as an assessment of possible or known damage to the structure a numerical analysis of estimating parameters in a nonlinear structural model is investigated by applying a quasi linearization method the analysis is successfully performed on a nonlinear eight degree of freedom space antenna model

impulsive control and optimization this paper addresses the problem of impulsive control and optimization for linear dynamical systems an essential benefit of impulsive control is that such controls may be simpler to implement and involve cheaper control mechanisms we shall establish some impulsive controllability criteria and obtain some conditions for the existence of optimal solutions an example is also worked though employing maple symbolic computation

boundary controllability of parabolic coupled equations abstract this paper is concerned with the boundary controllability of non scalar linear parabolic systems more precisely two coupled one dimensional parabolic equations are considered we show that in this framework boundary controllability is not equivalent and is more complex than distributed controllability in our main result we provide necessary and sufficient conditions for the null controllability

an edge based smoothed finite element method for primal dual shakedown analysis of structures an edge based smoothed finite element method es fem using three node linear triangular elements was recently proposed to significantly improve the accuracy and convergence rate of the standard finite element formulation for static free and forced vibration analyses of solids in this paper es fem is further extended for limit and shakedown analyses of structures a primal dual algorithm based upon the von mises yield criterion and a non linear optimization procedure is used to compute both the upper and lower bounds of the plastic collapse limit and the shakedown limit in the es fem compatible strains are smoothed over the smoothing domains associated with edges of elements using constant smoothing function only one gaussian point is required for each smoothing domain ensuring that the total number of variables in the resulting optimization problem is kept to a minimum compared with standard finite element formulation three benchmark problems are presented to show the stability and accuracy of solutions obtained by the present method

impulse output rapid stabilization for heat equations abstract the main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain with dirichlet boundary condition two constraints will be compulsory first the controls are active in a subdomain of and at discrete time points second the observations are made in another subdomain and at different discrete time points our strategy consists in linking an observation estimate at one time minimal norm impulse control approximate inverse source problem and rapid output stabilization

a direct method to predict cyclic steady states of elastoplastic structures the asymptotic steady state behavior of an elastic perfectly plastic structure under cyclic loading may be determined by time consuming incremental time stepping calculations direct methods alternatively have a big computational advantage as they attempt to find the characteristics of the cyclic state right from the start of the calculations most of these methods address an elastic shakedown state through the shakedown theorems and on the basis of mathematical programming algorithms in the present paper a novel direct method that has a more physical basis and may predict any cyclic stress state of a structure under a given loading is presented the method exploits the cyclic nature of the expected residual stress distribution at the steady cycle thus after equilibrating the elastic part of the total stress with the external load the unknown residual stress part is decomposed into fourier series whose coefficients are evaluated iteratively by satisfying compatibility and equilibrium with zero loads at time points inside the cycle and then integrating over the cycle a computationally simple way to account for plasticity is proposed the procedure converges uniformly to the true cyclic residual stress for a loading below the elastic shakedown limit or to an unsafe cyclic total stress which may be used to mark the regions with plastic straining inside the cycle the method then continues to determine whether the applied loading would lead the structure to ratcheting or to regions that alternate plastically the procedure is formulated within the finite element method a von mises yield surface is typically used examples of application of one and two dimensional structures are included

an algorithm for shakedown analysis with nonlinear yield functions abstract this paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function firstly variational formulations for shakedown analysis of structures under variable loads are considered secondly the corresponding discrete forms are briefly recalled then the algorithm is derived by combining a newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility the proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models the numerical procedure is applied to a square plate with a circular hole under variable traction in two directions and the obtained approximations are compared with available results finally a rectangular plate with two small holes is considered in both plane strain and plane stress conditions all application use the mises condition without linearization

minimal time for the null controllability of parabolic systems the effect of the condensation index of complex sequences let a d a be a diagonalizable generator of a c0 semigroup of contractions on a complex hilbert space x b l c y y being some suitable extrapolation space of x and u l2 0 t c under some assumptions on the sequence of eigenvalues k k 1 c of a d a we prove the existence of a minimal time t0 0 depending on bernstein s condensation index of and on b such that y ay bu is null controllable at any time t t0 and not null controllable for t t0 as a consequence we solve controllability problems of various systems of coupled parabolic equations in particular new results on the boundary controllability of one dimensional parabolic systems are derived these seem to be difficult to achieve using other classical tools

a comparison between analytical calculations of the shakedown load by the bipotential approach and step by step computations for elastoplastic materials with nonlinear kinematic hardening abstract the class of generalized standard materials is not relevant to model the nonassociative constitutive equations the bipotential approach based on a possible generalization of fenchel s inequality allows the recovery of the flow rule normality in a weak form of an implicit relation this defines the class of implicit standard materials for such behaviours this leads to a weak extension of the classical bound theorems of the shakedown analysis in the present paper we recall the relevant features of this theory considering an elastoplastic material with nonlinear kinematic hardening rule we apply it to the problem of a sample in plane strain conditions under constant traction and alternating torsion in order to determine analytically the interaction curve bounding the shakedown domain the aim of the paper is to prove the exactness of the solution for this example by comparing it to step by step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level a reliable criterion to stop the computations is proposed the analytical and numerical solutions are compared and found to be closed one of each other moreover the method allows uncovering an additional 2 cycle shakedown curve that could be useful for the shakedown design of structure

an iterative method for shakedown analysis abstract shakedown analysis for elastic perfect plastic structures is discussed and a fast incremental iterative solution method is proposed suitable for the fem analyses of large structures the theoretical motivations of the proposed method are discussed in detail and an example of its implementation is described with reference to plane frame analysis some numerical results are presented showing the numerical performances of the method

an observability estimate for the heat equation from a product of two measurable sets this paper presents an observability estimate for the heat equation in 0 t where has a real analytic boundary the observation region is e where and e are positive measurable subsets of and 0 t respectively the building of this estimate is based on a slightly modified version of the new estimate established in apraiz and escauriaza 2012 15 the technique developed in phung and wang 2012 11 and the shortcut of the lebeau robbiano strategy provided in miller 2010 3

a primal dual algorithm for shakedown analysis of structures abstract the paper describes a primal dual algorithm for shakedown analysis of structures with the use of kinematically admissible finite elements starting from koiter kinematic theorem a primal dual optimization condition is established by adopting static terms as complementary variables newton like iterations are performed to give both upper and quasi lower bounds of the load factor that converge rapidly to the accurate solution of shakedown limit

on orbit damage assessment for large space structures the need for monitoring the dynamic characteristics of large structural systems for the purpose of assessing the potential degradation of structural properties has been established this paper develops a theory for assessing the occurrence location and extent of potential damage utilizing on orbit response measurements the feasibility of the method is demonstrated using a simple structural system as an example

shakedown analysis in poroplasticity by linear programming static lower bound and kinematic upper bound theorems for shakedown analysis and limit analysis as special case are presented for two phase fully saturated poroplastic solids in a context characterized by the following features quasi static non associative non softening perfect or hardening poroplasticity piecewise linearized yield loci and hardening constant permeability linear fluid transport law small deformations non traditional galerkin finite element discretization with reference to cyclic periodic external actions numerical examples centred on linear programming evidence the computational potentialities and limitations of direct non evolutive methods of integrity assessment according to limit state design concepts in poroplasticity copyright 2000 john wiley sons ltd

consistent shakedown theorems for materials with temperature dependent yield functions abstract the elastic shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic plastic rate independent associative material models with temperature dependent yield functions assuming the yield functions convex in the stress temperature space a thermodynamically consistent small deformation thermo plasticity theory is provided in which the set of state and evolutive variables includes the temperature and the plastic entropy rate within the latter theory the known static prager s and kinematic konig s shakedown theorems which hold for yield functions convex in the stress space are restated in an appropriate consistent format in contrast with the above known theorems the restated theorems provide dual lower and upper bound statements for the shakedown limit loads additionally the latter theorems can be expressed in terms of only dominant thermo mechanical loads generally the vertices of a polyhedral load domain in which the loadings are allowed to range the shakedown limit load evaluation problem is discussed together with the related shakedown limit state of the structure a few numerical applications are presented

stiffness matrix adjustment using mode data a procedure is introduced that uses in addition to mode data structural connectivity information to optimally adjust deficient stiffness matrices the adjustments performed are such that the percentage change to each stiffness coefficient is minimized the physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification the theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

on controllability and observability for a class of impulsive systems many dynamic systems in physics chemistry biology engineering and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes these complex dynamic behaviors can be modeled by impulsive differential systems this paper studies the controllability and observability for a class of time varying impulsive control systems several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time invariant impulsive control systems are also obtained meanwhile several new results associated with variation of parameters for time varying impulsive control systems are derived

impulse and sampled data optimal control of heat equations and error estimates we consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multidimensional heat equation with a periodic terminal state constraint this problem has a unique optimal solution which can be characterized by an optimality system derived from the pontryagin maximum principle we define two approximations of this optimal control problem the first one is an impulse approximation and consists of considering a system of linear heat equations with impulse control the second one is obtained by the sample and hold procedure applied to the control resulting in a sampled data approximation of the controlled heat equation we prove that both problems have a unique optimal solution and we establish precise error estimates for the optimal controls and optimal states of the initial problem with respect to its impulse and sampled data approximations

quantitative unique continuation for the semilinear heat equation in a convex domain in this paper we study certain unique continuation properties for solutions of the semilinear heat equation t u u g u with the homogeneous dirichlet boundary condition over 0 t is a bounded convex open subset of r d with a smooth boundary for the subset the function g r r satisfies certain conditions we establish some observation estimates for u v w hereu and v are two solutions to the above mentioned equation the observation is made over t w here is any non empty open subset of a ndt is a positive number such that both u and v exist on the interval 0 t at least two results can be derived from these estimates i if u v t l2 t hen u v t l2 c where constants c 0a nd 0 1 can be independent of u and v in certain cases ii if two solutions of the above equation hold the same value over t then they coincide over 0 t m tm indicates the maximum number such that these two solutions exist on 0 t m

effects of softening in elastic plastic structural dynamics softening understood as unstable behaviour of material or structural components is considered herein for its possible consequences on the overall behaviour of discrete dynamic models of elastic plastic beam structures in the absence of geometric effects it is shown that multiplicity of incremental solutions response bifurcations and manifestations of overall instability may occur the bifurcated responses may exhibit different scenarios for the same excitation e g shakedown or local damage up to failure an insight into and criteria for such occurrences are achieved by formulating the rate and the finite increment problem as linear complementarity problems period doubling and deterministic chaos under harmonic excitation are observed when reversible holonomic softening behaviour is assumed the strong sensitivity of the phenomena investigated with respect to the choice of the structural model is pointed out the findings are elucidated by illustrative examples

finite element shakedown analysis of two dimensional structures in the present paper the formulation proposed by casciaro and garcea comput meth appl mech eng 2002 191 5761 5792 and applied to the shakedown analysis of plane frames is extended to the analysis of two dimensional flat structures in both the cases of plane stress and plane strain the discrete formulation is obtained using a mixed finite element in which both stress and displacement fields are interpolated the material is assumed to be elasto plastic and a linearization of the elastic domain is performed the result is a versatile iterative scheme well suited to implementation in general purpose fem codes an extensive series of numerical tests is presented showing the reliability of the proposed formulation copyright 2005 john wiley sons ltd

controllability of impulse controlled systems of heat equations coupled by constant matrices abstract this paper studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair a b of constant matrices we present a necessary and sufficient condition for the approximate controllability which is exactly kalman s controllability rank condition of a b we prove that when such a system is approximately controllable the approximate controllability over an interval 0 t can be realized by adding controls at arbitrary q a b different control instants 0 1 2 q a b t provided that q a b 1 d a where d a min im a and q a b n we also show that in general such systems are not null controllable

finite element approximations of impulsive optimal control problems for heat equations abstract in this paper we study the priori error analysis for semidiscrete galerkin finite element approximation of the impulsive optimal control problem governed by linear heat equation with control constraint we first derive pontryagin s maximum principle and construct the semidiscrete finite element approximation scheme for our impulsive optimal control problem then the error estimates for optimal control u the related state y and the adjoint state will be obtained finally an efficient algorithm for our numerical experiment is designed which verifies the theoretical results obtained in this paper

analytical integration of elasto plastic uniaxial constitutive laws over arbitrary sections summary we present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto plastic uniaxial constitutive laws by means of a suitable application of gauss theorem we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely at the vertices of the section for this reason the proposed approach has been termed fiber free to emphasize the fact that it does not require any subdivision of the section in fibers numerical results show that the fiber approach is grossly inaccurate and that the number of fibers required to achieve a degree of accuracy comparable with that entailed by the fiber free approach is at least one order of magnitude greater than the one commonly suggested in commercial software for nonlinear frame analysis copyright 2012 john wiley sons ltd

a numerical approach for limit analysis of orthotropic composite laminates a numerical approach for limit analysis of structures whose constituent material exhibits orthotropic behaviour is presented and discussed attention is focused on orthotropic composite laminates under plane stress conditions the proposed approach is an extension in the context of orthotropic materials of the linear matching method lmm the latter is based on a sequence of linear analyses performed on the analysed structure made of a fictitious linear viscous material with spatially varying moduli here the lmm is applied to structures made of materials obeying the tsai wu criterion an appropriate choice of the fictitious material which in this case is assumed linear viscous orthotropic and suffering a distribution of assigned initial stresses reduces the number of parameters to be spatially varied thus rendering the whole procedure applicable and reliable the results obtained are highly promising as witnessed by a number of numerical examples which are carried out to verify the effectiveness of the proposed approach copyright 2006 john wiley sons ltd

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

structural damage identification a probabilistic approach a method is presented to improve the robustness of current damage detection methodologies measured statistical changes in natural frequencies and mode shapes along with a correlated analytical stochastic finite element model are used to assess the integrity of a structure the approach accounts for variations in the modal properties of a structure due to experimental errors in the test procedure a perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix this stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix the determination of damaged stiffness statistics permits the comparison of probability density functions between the healthy and estimated damaged stiffnesses a set of graphical and statistical probability damage quotients are then found that indicate a confidence level on the existence of damage the effectiveness of the proposed technique is illustrated using simulated data on a three degree of freedom spring mass system and on an euler bernoulli cantilever aluminum beam

shakedown analysis of structures made of materials with temperature dependent yield stress in this work the shakedown of structures made of materials with temperature dependent yield stress is considered under some restrictions on the thermal loading condition the yield stress is linearized and shakedown theorems are established based on these linearized shakedown theorems the shakedown limit is formulated as a problem of convex optimization an algorithm is built to compute shakedown limits numerical tests show good agreement with analytic solutions and experimental data

structural damage detection using modal test data references uang j n optimal design of a passive vibration absorber for a truss beam journal of guidance control and dynamics vol 7 no 6 1984 pp 733 739 balas m j active control of flexible systems journal of optimization theory and applications vol 25 no 3 1978 pp 415 436 aubrun j n theory of control structures by low authority controllers journal of guidance control and dynamics vol 3 no 5 1980 pp 444 451 meirovitch l and baruch h control of self adjoint distributed parameter systems journal of guidance control and dynamics vol 5 no 1 1982 pp 60 66 sun c t and wang r t enhancement of frequency and damping in large space structures with extendible members proceedings of the aiaa asme asce ahs 29th structures structural dynamics and materials conference aiaa washington dc 1988 pp 1774 1780 hughes t j r and liu w k implicit explicit finite elements in transient analysis stability theory journal of applied mechanics vol 45 no 2 1978 pp 371 374

a unified approach for variationally consistent finite elements in elastoplasticity abstract a general variationally consistent approach for elastoplastic finite element analysis is presented a weak formulation of the finite step i e in terms of finite increments elastoplastic boundary value problem is obtained by enforcing the stationarity of a mixed functional of hu washizu type a peculiarity of the present formulation is that the constitutive equations are expressed in weak form also all fields are then independently discretized in terms of so called generalized variables the result is a set of non linear algebraic equations a subset of which can be interpreted as the backward difference time integrated constitutive law of the finite element an iterative procedure where all calculations are at the element and not at the gauss point level resting on newton raphson scheme is proposed for the solution of the governing equations it is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation

l infty null controllability for the heat equation and its consequences for the time optimal control problem in this paper we establish a certain l infty null controllability for the internally controlled heat equation in omega times 0 t with the control restricted to a product set of an open nonempty subset in omega and a subset of positive measure in the interval 0 t based on this we obtain a bang bang principle for the time optimal control of the heat equation with controls taken from the set mathcal u ad u cdot t 0 infty rightarrow l 2 omega measurable u cdot t in u a e in t where u is a closed and bounded subset of l 2 omega namely each optimal control u cdot t of the problem satisfies necessarily the bang bang property u cdot t in partial u for almost all t in 0 t where partial u denotes the boundary of the set u and t is the optimal time we also get the uniqueness of the optimal control when the target set s is convex and the control set u is a closed ball

three dimensional limit analysis of rigid blocks assemblages part ii load path following solution procedure and validation a novel solution procedure for the non associated limit analysis of rigid blocks assemblages is proposed this proposal produces better solutions than previously proposed procedures and it is also able to provide an insight into the structural behaviour prior to failure the limit analysis model proposed in part i of this paper and the solution procedure are validated through illustrative examples in three dimensional masonry piers and walls the use of limit analysis for three dimensional problems incorporating non associated flow rules and a coupled yield surface is novel in the literature

incremental shakedown analysis in the case of thermal effects a new method of performing the shakedown analysis of structures subjected to variable repeated loads and temperature fields is presented the method employs the standard incremental elastic plastic finite element algorithm and is based upon a cyclic repetition of piecewise proportional paths that contain all the vertices of the load temperature variation domain a numerical example illustrates the approach

damage detection in elastic structures using vibratory residual forces and weighted sensitivity a methodology is presented for detecting structural damage in elastic structures by nondestructiv e means measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and or stiffness variations where damage is characterized as a stiffness reduction the current approach is unique among other approaches in that it accounts for 1 variations in system mass system stiffness and mass center locations 2 perturbations of both the natural frequencies and modal vectors and 3 statistical confidence factors for the structural parameters and potential experimental instrumentation error moreover this procedure can be used with either full or reduced models a wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage lexible space structures launch vehicles and satellites are susceptible to structural damage over their operating lives from impact operating loads and fatigue undetected and uncorrected damage can lead to structural deterioration of their members and consequently jeopardize the flight safety of the structure thus numerous damage inspection methods and monitoring procedures have been developed examples include x ray ultrasonic testing magnetic resonance coin tap dye penetration and visual inspection these methods can be time consuming and are local assessments often requir ing the exposure of structural elements to the inspector and equipment for detecting damage as a monitoring system for detecting damage of spacecraft in orbit i e space station freedom none of these methods are appropriate an alterna tive approach which formed the basis for our current study is to recognize the fact that modal vibration test data struc tural natural frequencies and mode shapes characterize the state of the structure 1 therefore postflight and in flight e g monitoring data can be used to distinguish whether changes damage have occurred to the structure by comparing these data with a set of baseline data modal testing as a means of inspection has several advantages direct exposure of struc tural elements is not required and at the same time more of the complete structure can be inspected in one modal test by having appropriately placed sensors the consequences of this are a reduction in schedule and cost the use of vibration test data to locate structural damage has been attempted to evaluate the integrity of offshore oil and gas platforms 2 3 composite laminates 4 continuum struc tures 5 8 and recently large space structures 9 11 the early ana lytical and experimental approaches2 3 had limited success as a result of inadequate instrumentation and addressing only fre quency shifts associated with stiffness changes while ignoring changes in the modal vectors the continuum based meth ods5 8 provide valuable insight into the magnitude of fre quency shifts but their usefulness is severely limited to simple structures bars beams plates with unrealistic boundary con

controllability and observability of a class of linear impulsive systems this paper studies the controllability and observability of a class of linear piecewise constant impulsive systems necessary and sufficient criteria for reachability and controllability are established respectively it is proved that the reachability is equivalent to the controllability under some mild conditions then necessary and sufficient criteria for observability and determinability of such systems are established respectively it is also proved that the observability is equivalent to the determinability under some mild conditions our criteria are of geometric type they can be transformed into algebraic type conveniently finally a numerical example is given to illustrate the utility of our criteria

how to improve efficiency and robustness of the newton method in geometrically non linear structural problem discretized via displacement based finite elements abstract in this paper we show how to significantly improve the robustness and the efficiency of the newton method in geometrically non linear structural problems discretized via displacement based finite elements the strategy is based on the relaxation of the constitutive equations at each integration point this leads to an improved iterative scheme which requires a very low number of iterations to converge and can withstand very large steps in step by step analyses the computational cost of each iteration is the same as the original newton method the impressive performances of the proposal are shown by many numerical tests in geometrically non linear analysis the proposed strategy called mip newton seems worthy to replace the standard newton method in any finite element code based on displacement formulations its implementation in existing codes is very easy

null controllability of some reaction diffusion systems with one control force this work is concerned with the null controllability of semilinear parabolic systems by a single control force acting on a subdomain

controllability of some coupled stochastic parabolic systems with fractional order spatial differential operators by one control in the drift this paper is addressed to a study of the null approximate controllability for a class of coupled systems governed by two linear forward stochastic parabolic equations with fractional order spatial differential operators our method is based on the lebeau robbiano strategy the key is to establish a suitable observability estimate for some coupled fractional order backward stochastic parabolic systems with terminal states in finite dimensional spaces compared to deterministic coupled parabolic systems the coupling appearing in diffusion terms in the stochastic case introduces quite interesting new phenomena we present a somewhat surprising counterexample to show that the controllability of coupled stochastic parabolic systems is not robust with respect to the coupling coefficient in diffusion terms this indicates that the usual carleman type estimate approach does not seem to work for our controllability problem moreover our controllability results for parabolic systems with fractional order spatia