observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

a new procedure for time varying linearization up to output injection new necessary and sufficient conditions for time varying linearization up to output injection tvloi are presented they yield a straightforward tvloi procedure

time scaling for observer design with linearizable error dynamics in this paper we consider the problem of observer design for dynamical systems with scalar output by linearization of the error dynamics via coordinate change output injection and time scaling we present necessary and sufficient conditions which guarantee the existence of a coordinate change and output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

time series analysis and monte carlo methods for eigenvalue separation in neutron multiplication problems a time series approach has been applied to the nuclear fission source distribution generated by monte carlo mc particle transport in order to calculate the non fundamental mode eigenvalues of the system the novel aspect is the combination of the general technical principle of projection pursuit for multivariate data with the neutron multiplication eigenvalue problem in the nuclear engineering discipline proof is thoroughly provided that the stationary mc process is linear to first order approximation and that it transforms into one dimensional autoregressive processes of order one ar 1 via the automated choice of projection vectors the autocorrelation coefficient of the resulting ar 1 process corresponds to the ratio of the desired mode eigenvalue to the fundamental mode eigenvalue all modern mc codes for nuclear criticality calculate the fundamental mode eigenvalue so the desired mode eigenvalue can be easily determined this time series approach was tested for a variety of problems including multi dimensional ones numerical results show that the time series approach has strong potential for three dimensional whole reactor core the eigenvalue ratio can be updated in an on the fly manner without storing the nuclear fission source distributions at all previous iteration cycles for the mean subtraction lastly the effects of degenerate eigenvalues are investigated and solutions are provided

observer design for mimo non uniformly observable systems the design of high gain observers is usually based on normal forms of observability if the system is observable for every input uniform observability the gain of the observer does not required a solution to differential equation for multiple input multiple output mimo non uniformly observable systems we give here a sufficient condition that the input must satisfy in order to design an observer unlike uniformly observable systems the observer gain of non uniformly observable systems is derived from a lyapunov differential equation

an existence theorem for observers of bilinear systems under suitable uniformity assumptions the existence of nonlinear state observers with exponentially decaying error for bilinear systems is proved to be equivalent to that of observers whose corresponding error dynamics is linear with respect to the error

a finiteness criterion for nonlinear input output differential systems we solve the following problem which has been dealt with in several publications when does a system have the same input output behaviour as a system depending linearly on the state variables precise definitions of this question are supplied in the text a particular case of the problem is the equivalence of a system with a bilinear one at the end we illustrate our methods and the scope of our results by a brief study of several examples

error estimation including pollution assessment for nonlinear finite element analysis a residual type error estimator for nonlinear finite element analysis is introduced this error estimator solves local problems avoiding both the computation of the flux jumps and the associated flux splitting procedure pollution errors are taken into account by a feedback strategy that is an error estimate based on local computations is used as the input of the pollution analysis this estimator is used in the frame of an adaptive procedure numerical examples show that the estimator is able to drive adaptive procedures leading to likely good solutions moreover one of the examples demonstrates that adaptive procedures are essential for complex highly nonlinear mechanical problems because they may discover secondary collapse mechanisms

an immersion based observer design for rank observable nonlinear systems in this note an observer design for a wide class of nonlinear systems is proposed it is based on some high gain design for the particular case of state affine systems up to triangular nonlinearity on the one hand and immersion of nonlinear systems into such a form on the other hand conditions for the observer convergence are given in terms of appropriate excitation and a constructive procedure for the immersion is presented the methodology is illustrated by examples of application

state equivalence of discrete time nonlinear control systems to state affine form up to input output injection in this paper the problem of transformation of a discrete time nonlinear control system into a state affine form up to input output injection is addressed a set of coordinate free necessary and sufficient conditions for such a transformation to be possible is first proposed and a more constructive procedure is then presented no restriction of invertibility of the state transition map is required

recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates classical residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact or reference error lower bounds of the error are also needed in goal oriented adaptivity and for bounds on functional outputs this work introduces a simple and cheap strategy to recover a lower bound estimate from standard upper bound estimates this lower bound may also be used to assess the effectivity of the former estimate and to improve it

error assessment and mesh adaptivity for regularized continuous failure models this paper deals with the adaptive finite element analysis of structural failure a gradient enhanced damage model has been chosen to simulate material degradation since this model is regularized in the post peak regime the finite element solution does not suffer from pathological mesh dependence and thus converges to an objective solution upon mesh refinement however the error analyses have shown that the error in the nonlocal equivalent strain field becomes dominant during the post peak loading stages the accuracy of the nonlocal equivalent strain field and the corresponding damage quantity also greatly influences the accuracy of the quantity of interest two error measures have been proposed the goal oriented error estimates have provided similar error distributions although some small differences have been found in the softening regime objective error estimates together with adaptive criteria have been used to perform automated h adaptivity during computation

an efficient method for observer design with approximately linear error dynamics exact error linearization is a well known full order observer design method which yields linear time invariant stable error dynamics in normal form coordinates the difficult procedure associated with exact error linearization has led to the simpler extended luenberger observer design however extended luenberger observers can only guarantee a first order approximation to the exact error linearization design this paper provides an explicit formula involving only derivative lie derivative and bracket and matrix inversion operations for computing an nth order approximation of the exact error linearization observer hence the proposed method is a computational simple tool for designing observers for systems admitting exact error linearization observers two examples demonstrate the application of the method

a variationally consistent mesh adaptation method for triangular elements in explicit lagrangian dynamics in this paper a variational formulation for mesh adaptation procedures involving local mesh changes for triangular meshes is presented such local adaptive changes are very well suited for explicit methods as they do not involve significant computational expense they also greatly simplify the projection of field variables from the old to the new meshes crucially the variational nature of the formulation used to derive the equilibrium equations at steps where adaptation takes place ensures that conservation of linear and angular momentum is obtained int j numer meth engng 2000 49 1295 1325 several examples in 2 d showing the application of the proposed adaptive algorithms are used to demonstrate the validity of the methodology proposed copyright 2009 john wiley sons ltd

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

on the linearization up to multi output injection for a class of systems with implicitly defined outputs for a class of nonlinear systems we investigate the problem of under what conditions there exists a coordinate transformation that yields a state affine linear system up to output injection with implicit outputs in particular we provide necessary and sufficient conditions for time varying linearization up to multi output injection we highlight that if the conditions hold as a consequence it is possible in the new coordinates to construct an observer with linear error dynamics we propose a methodology to find the coordinate transformation several examples illustrate the proposed procedure

on output transformations for state linearization up to output injection steering a nonlinear system into a so called state affine one up to output injection by change of coordinates is of much interest for observer design this interest is preserved by also considering changes of output the purpose of the paper is then to provide computable conditions for existence of output transformations making a system which is not transformable into a state affine one up to output injection by only a change of coordinates to become so after a change of output such a characterization enlarges the class of systems for which an observer is available

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

a posteriori error estimation for standard finite element analysis a new residual type estimator based on projections of the error on subspaces of locally supported functions is presented the estimator is defined by a standard element by element refinement first an approximation of the energy norm of the error is obtained solving local problems with homogeneous dirichlet boundary conditions a later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces this estimate is a lower bound of the measure of the actual error the estimator does not need to approximate local boundary conditions for the error equation therefore computation of flux jumps is not necessary moreover the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward the presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error as well as its usefulness in adaptive procedures

extension of modified power method to two dimensional problems in this study the generalized modified power method was extended to two dimensional problems a direct application of the method to two dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number the root cause of this instability has been identified as the degeneracy of the transfer matrix in order to resolve this instability the number of sub regions for the transfer matrix was increased to be larger than the number of requested eigenmodes and a new transfer matrix was introduced accordingly which can be calculated by the least square method the stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2d c5g7 benchmark problem

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

bilinearization up to output injection abstract this paper deals with nonlinear systems that can be steered to bilinear systems by output injection and nonlinear change of coordinates we give an abstract non constructive theorem and an algorithm which allows us to recognize such systems

a unified approach to remeshing strategies for finite element h adaptivity in h adaptivity a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution several authors have introduced different remeshing strategies yielding very different results in this work these methods are included in a unified framework emphasizing the role of the underlying hypotheses moreover an objective tool to evaluate the accuracy of the resulting finite element solution is presented thus a new remeshing strategy is introduced to optimize the accuracy of the adapted solutions the different remeshing strategies are compared with well known numerical examples

a general solution strategy of modified power method for higher mode solutions a general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy monte carlo simulation the new approach adopts four features 1 the eigen decomposition of transfer matrix 2 weight cancellation for higher modes 3 population control with higher mode weights and 4 stabilization technique of statistical fluctuations using multi cycle accumulations the numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time the advantages of the new strategy can be summarized as 1 the replacement of the cumbersome solution step of high order polynomial equations required by booth s original method with the simple matrix eigen decomposition 2 faster fission source convergence in inactive cycles 3 more stable behaviors in both inactive and active cycles and 4 smaller variances in active cycles advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi cycle accumulations the application of the modified power method to continuous energy monte carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper modified power method is applied to continuous energy monte carlo simulation transfer matrix is introduced to generalize the modified power method all mode based population control is applied to get the higher eigenmodes statistic fluctuation can be greatly reduced using accumulated tally results fission source convergence is accelerated with higher mode solutions

new advances on a posteriori error on constitutive relation in f e analysis this paper deals with error estimators based on residuals on the constitutive relation which have been developed for the past 20 years at cachan especially in the case of elasticity these error estimators can become poor in situations where the material and the mesh are strongly anisotropic the crucial point herein is the construction of equilibrated stress fields from the computed finite element solution therefore in this paper the approach and in particular this last point are re examined several important modifications are introduced in the concepts and basic techniques hence a new generation of error estimators which seem to be extremely robust upon initial applications has been generated

extension of the noise propagation matrix method for higher mode solutions abstract the noise propagation matrix method npmm has been extended to get higher mode solutions previous studies show that the npmm can be used to compute the dominance ratio of a system it is essentially the same as the coarse mesh projection method cmpm both of which use the noise propagation matrix npm to determine the dominance ratio either after finishing the monte carlo simulation or on the fly during the simulation since only the fundamental fission source information is explicitly utilized while the higher mode information is implicitly contained in the statistical noises the npmm can usually only give an approximate estimation of the dominance ratio after thousands of cycles in this study the npmm is extended by simulating the higher modes explicitly so that the dominance ratio estimation can be more accurate and efficient besides the higher mode solutions can be obtained at the same time with good accuracy and efficiency

symbolic computing of nonlinear observable and observer forms observer design for highly nonlinear dynamics is an important issue particularly when the locally observable dynamics are not linearly observable in such circumstances the ability to reduce the system to observable or observer form is a useful first step to observer design we describe and illustrate symbolic computing tools to do that

high gain estimation for nonlinear systems abstract this work is a continuation of 4 where the third author exhibits a high gain exponential observer for miso nonlinear systems affine in the input and observable for any input with continuous dynamics and measurements in this paper we establish stability results for continuous continuous and continuous discrete extended kalman filters derived from the observer of 4

brief paper full order observer design for a class of port hamiltonian systems we consider a special class of port hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full order observers using a passivity based approach the essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space on which the state estimation error is zero we first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state space and then perform a partial state feedback passivation which leads to the construction of the observer we then illustrate this observer design procedure on two physical examples the magnetic levitation system and the inverted pendulum on the cart system

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

some a posteriori error estimators for elliptic partial differential equations we present three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations the estimators are based on solving local neumann problems in each element the estimators differ in how they enforce consistency of the neumann problems we prove that as the mesh size decreases under suitable assumptions two of the error estimators approach upper bounds on the norm of the true error and all three error estimators are within multiplicative constants of the norm of the true error we present numerical results in which one of the error estimators appears to converge to the norm of the true error

local observer for infinitesimally observable nonlinear systems in this article we present a local observer based on infinitesimal observability along trajectories the gain of this observer derives from a dynamical lyapunov equation the inputs for which the observer converges are those which render the system observable at each point of the limit of the unknown trajectory infinitesimal observability at infinity along trajectories the performance of the proposed observer is illustrated with an application to dc machine

a posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem the reciprocal theorem of betti and rayleigh or in other notions duality arguments are used to derive error estimators for the finite element approximation of various quantities including local variables like single displacements and stresses the proposed error estimator is evaluated solving the set of equations for an additional right hand side simply applying the energy norm error estimators two times furthermore a general h adaptive algorithm is introduced which allows us to optimize meshes with respect to different user specified variables the efficiency of the current approach is demonstrated for plate and shell examples

remeshing criteria and proper error representations for goal oriented h adaptivity a key ingredient in h adaptivity pertains to the transformation of output data from a given error estimator into input data usually in the form of an element size distribution that needs to be supplied to a mesh generator this paper analyzes the different possibilities of defining remeshing criteria in the framework of goal oriented adaptivity in standard energy norm driven adaptivity the optimal mesh is clearly obtained if the local error distribution is uniform the goal oriented paradigm introduces new difficulties associated with the different possibilities for the spatial error representation and the signs of the local error contributions a nodal error representation is introduced in order to improve the communication with the automatic mesh generation tool precluding the transfer of information from elements to nodes numerical experiments demonstrate the ability of the introduced remeshing strategies to drive efficient adaptive procedures and to control the error in quantities of interest the results of the numerical tests fit the expected properties of the different remeshing strategies

nonlinear system immersion observers and finite dimensional filters abstract nonlinear deterministic and stochastic systems which can be immersed into linear observable ones are identified by necessary and sufficient conditions those systems are shown to admit observers in the deterministic case and exact finite dimensional filters in the stochastic case the sufficient conditions obtained generalize earlier results in both cases

error estimation and adaptivity for nonlocal damage models abstract nonlocal damage models are typically used to model failure of quasi brittle materials due to brittleness the choice of a particular model or set of parameters can have a crucial influence on the structural response to assess this influence it is essential to keep finite element discretization errors under control if not the effect of these errors on the result of a computation could be erroneously interpreted from a constitutive viewpoint to ensure the quality of the fe solution an adaptive strategy based on error estimation is proposed here it is based on the combination of a residual type error estimator and quadrilateral h remeshing another important consequence of brittleness is that it leads to structural responses of the snap through or snap back type this requires the use of arc length control with a definition of the arc parameter that accounts for the localized nature of quasi brittle failure all these aspects are discussed for two particular nonlocal damage models mazars and modified von mises and for two tests the brazilian tensile splitting test and the single edge notched beam test for the latter test the capability of the mazars model to capture the curved crack pattern observed in experiments a topic of debate in the literature is confirmed

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

single output dependent observability normal form this paper gives the sufficient and necessary conditions which guarantee the existence of a diffeomorphism in order to transform a nonlinear system without inputs into a canonical normal form that is output dependent moreover we extend our results to a class of systems with inputs

on the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form this article deals with the transformation of a class of nonlinear systems into an extended nonlinear observable canonical form enocf by dynamic extension the dynamic extension is obtained by adding auxiliary dynamics and virtual outputs to the original system thus giving rise to a higher dimensional system in an extended state space sufficient geometrical conditions to guarantee the existence of a local diffeomorphism which allow the transformation of the extended system into the enocf are given in particular an algorithm that permits us to compute such a diffeomorphism is derived

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

the background of error estimation and adaptivity in finite element computations the paper summarizes the present state of the art concerning error estimation and adaptive remeshing recent work shows that methods based on recovery result on most accurate error estimators

upper and lower bounds in limit analysis adaptive meshing strategies and discontinuous loading summary upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimisation problems the membership constraints for von mises and mohrcoulomb plasticity criteria are written as a set of quadratic constraints which permits to solve the optimisation problem using specific algorithms for second order conic program socp from the stress field at the lower bound and the velocities at the upper bound we construct a novel error estimate based on elemental and edge contributions to the bound gap these contributions are employed in an adaptive remeshing strategy that is able to reproduce fan type mesh patterns around points with discontinuous surface loading the solution of this type of problems is analysed in detail and from this study some additional meshing strategies are also described we particularise the resulting formulation and strategies to two dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature copyright c 2007 john wiley sons ltd

a unified approach to a posteriori error estimation using element residual methods this paper deals with the problem of obtaining numerical estimates of the accuracy of approximations to solutions of elliptic partial differential equations it is shown that by solving appropriate local residual type problems one can obtain upper bounds on the error in the energy norm moreover in the special case of adaptiveh p finite element analysis the estimator will also give a realistic estimate of the error a key feature of this is the development of a systematic approach to the determination of boundary conditions for the local problems the work extends and combines several existing methods to the case of fullh p finite element approximation on possibly irregular meshes with elements of non uniform degree as a special case the analysis proves a conjecture made by bank and weiser some a posteriori error estimators for elliptic partial differential equations math comput 44 283 301 1985