adaptive backstepping control design for linear multivariable plants a nonlinear backstepping scheme is developed for adaptive control of linear plants with multiple inputs and multiple outputs solutions to plant parametrization state observer and adaptive control law for the multivariable backstepping design are proposed the developed adaptive controller has the desired properties for ensuring closed loop signal boundedness and asymptotical tracking

domain integral formulation for 3 d curved and non planar cracks with the extended finite element method abstract the computation of stress intensity factors sifs in curved and non planar cracks using domain integrals introduces some difficulties related to the use of curvilinear gradients several approaches exist in the literature that consider curvilinear corrections within a finite element framework but these depend on each particular crack configuration and they are not general in this work we introduce the curvilinear gradient correction within the extended finite element method framework xfem based only on the level set information used for the crack description and the local coordinate system definition our formulation depends only on the level set coordinates and therefore an explicit analytical description of the crack is not needed it is shown that this curvilinear correction improves the results and enables the study of generic cracks in addition we have introduced a simple error indicator for improving the sif computed via the interaction integral thanks to the better behavior of the j integral as it does not need auxiliary extraction fields

on morse s new adaptive controller parameter convergence and transient performance some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by a s morse proc us italy joint seminar syst models feedback 1992 it is proved that the l sub 2 norm of the tracking error is uniformly bounded by the initial parameter estimation error further if the initial conditions are sufficiently small it is shown that the l sub infinity norm of the tracking error is uniformly bounded by the l sub m2 norm of the reference signal these transient bounds are independent of the signals richness and the adaptation gain making them arguably the strongest transient results available in the literature second excitation conditions for exponential stability a property which is well known to insure some local performance measures are given to this end it is shown that modulo a signal dependent time scale change morse s estimator is equivalent to a normalized gradient plus filtering identifier

a locking free and optimally convergent discontinuous galerkin based extended finite element method for cracked nearly incompressible solids abstract the extended finite element method xfem is an efficient way to include discontinuities such as a crack into a finite element mesh the singularity at the crack tip restricts standard finite element methods to converge with a rate of at most 1 2 for the stresses and 1 for the displacements with respect to the mesh size this is true for cracks in incompressible materials as well when any of the standard techniques to sidestep locking is adopted to attain an optimal convergence rate of 1 for stresses and of 2 for displacements with piecewise affine elements it is necessary to enrich the finite element space with singular basis functions the support of these singular functions is the entire plane but to avoid decreasing the sparsity of the stiffness matrix too much each of them is then generally localized to a neighborhood of the crack tip by multiplying by a cutoff function or a subset of a partition of unity basis for nearly incompressible materials however the resulting basis functions no longer contain incompressible displacement fields and hence they either lead to locking or suboptimal convergence rates to overcome this problem we introduce here an xfem with optimal convergence rate and without the problem of locking for nearly incompressible materials i e it possesses an error bound that does not diverge as poisson s ratio approaches 0 5 the method is based on a primal or one field formulation of a discontinuous galerkin method that we introduced earlier this one field formulation is obtained through the introduction of a lifting operator but unlike most lifting operators which map inter element discontinuities into elementwise polynomials ours maps such discontinuities into spaces enriched with the singular behavior of the solution this is the key idea for the method to be simultaneously locking free and optimally convergent

a 3d locking free xfem formulation for the von mises elasto plastic analysis of cracks abstract the aim of this paper is to propose a mixed xfem approach for the elasto plastic analysis of cracks in compressible solid metals the formulation proposed is capable of taking into account the plastic incompressibility induced by the von mises yield criterion without leading to a volumetric locking phenomenon in 3d the numerical formulation is regularized without adding parameters to be calibrated or adding equations to be solved as for the subgrid scale methods the mixed xfem technique developed has the benefit not to require special care for the numerical integration hundreds of integration points can be used for integrating the asymptotic enrichment functions into each finite element examples are presented to show the relevance the convergence and the efficiency of the new numerical formulation proposed in the case of linear and quadratic meshes

interactor and multivariable adaptive model matching the necessary minimal prior knowledge of a system in order to implement adaptive model matching and prove global stability is discussed some results concerning the degrees of interactor matrix entries are given it is shown that the bounds on the degrees of the interactor off diagonal terms given by m das j dynam sust measurement contr vol 108 p 151 153 1986 are the best possible ones

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

prior information in the design of multivariable adaptive controllers this note discusses the design of a dynamic precompensator w c s for an m times m mimo plant w p s such that for almost all cases w p s w c s has a diagonal hermite form

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

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

an explicit dynamics extended finite element method part 1 mass lumping for arbitrary enrichment functions this paper presents a general mass lumping technique for explicit dynamics simulations using the extended finite element method with arbitrary enrichment functions the proposed mass lumping technique is a generalization of previously published results for cracks and holes time step estimates are studied for crack singular enrichment functions and for hole enrichment in both cases we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element the performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published x fem results

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

brief lyapunov based adaptive control of mimo systems the design of model reference adaptive control for mimo linear systems has not yet achieved in spite of significant efforts the completeness and simplicity of its siso counterpart one of the main obstacles has been the generalization of the siso assumption that the sign of the high frequency gain hfg is known here we overcome this obstacle and present a more complete mimo analog to the well known lyapunov based siso design which is significantly less restrictive than the existing analogs our algorithm makes use of a new control parametrization derived from a factorization of the hfg matrix k p sdu where s is symmetric positive definite d is diagonal and u is unity upper triangular only the signs of the entries of d or equivalently the signs of the leading principal minors of k p are assumed to be known

brief paper adaptive dynamic surface control for linear multivariable systems in this paper an output feedback adaptive control is presented for linear time invariant multivariable plants by using the dynamic surface control technique it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated the proposed scheme has the following features 1 the l performance of the system s tracking error can be guaranteed 2 it has least number of updated parameters in comparison with other multivariable adaptive schemes and 3 the adaptive law is necessary only at the first design step which significantly reduces the design procedure simulation results are presented to demonstrate the effectiveness of the proposed scheme

tensor product and hadamard product for the wasserstein means abstract as one of the least squares mean we consider the wasserstein mean of positive definite hermitian matrices we verify in this paper the inequalities of the wasserstein mean related with a strictly positive and unital linear map the identity of the wasserstein mean for tensor product and several inequalities of the wasserstein mean for hadamard product

hysteresis switching adaptive control of linear multivariable systems this paper presents a model reference adaptive control scheme for deterministic continuous time multivariable systems represented by square strictly proper minimum phase transfer function matrices a typical requirement of existing algorithms is to assume that the zero structure at infinity and the high frequency gain matrix are fully or at least partially known it is well known that these requirements may be very restrictive since in general both the zero structure at infinity and the high frequency gain matrix depend on plant parameters in this paper we show that these restrictive assumptions may be considerably weakened using morse et al s hysteresis switching control strategy 1992 the strategy entails running a finite number of parameter estimators in parallel and using a switching algorithm to select between candidate estimators based on their associated prediction errors hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators and all switching ceases within a finite time the results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

multivariable adaptive control using high frequency gain matrix factorization in this note we extend the application of a less restrictive condition about the high frequency gain matrix to design stable direct model reference adaptive control for a class of multivariable plants with relative degree greater than one the new approach is based on a control parametrization derived from a factorization of the high frequency gain matrix k sub p in the form of a product of three matrices one of them being diagonal three possible factorizations are presented only the signs of the diagonal factor or equivalently the signs of the leading principal minors of k sub p are assumed known

3d corrected xfem approach and extension to finite deformation theory in this paper the modified or corrected extended finite element method originally presented in fries int j numer meth engng 2008 75 503 532 for the 2d case is extended to 3d including different remedies for the problem that the crack front enrichment functions are linearly dependent in the blending elements in the context of this extension we address a number of computational issues of the 3d xfem in particular possible quadrature rules for elements with discontinuities also the influence of finite deformation theory for crack simulations in comparison to linear elastic fracture mechanics is investigated a number of numerical examples demonstrate the behavior of the presented possibilities copyright 2010 john wiley sons ltd

multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices in this article a novel output feedback adaptive dynamic surface control scheme is proposed for linear time invariant multivariable plants based on the norm estimation of unknown parameter matrices besides avoiding the explosion of complexity problem in traditional multivariable backstepping design the proposed scheme has the following features 1 only one parameter needs to be updated on line regardless of the plant order and input output dimension 2 only the hurwitz condition is required for the high frequency gain matrix and 3 the performance of the tracking error can be guaranteed it is shown that all signals of the closed loop system are semi globally uniformly bounded simulation results are given to illustrate the effectiveness of the proposed scheme

multivariable adaptive backstepping control a norm estimation approach in this note a novel output feedback adaptive backstepping control is proposed for linear time invariant multivariable plants under a mild assumption that the hurwitz condition for high frequency gain matrix is satisfied by estimating the norm of those unknown parameter matrices instead of their elements it is shown that only one parameter needs to be updated online and therefore the computational burden can be greatly reduced compared with any current multivariable adaptive control scheme

adaptive output feedback control for a class of nonlinear systems with full state constraints this paper studies an adaptive output feedback control for a class of nonlinear single input and single output siso systems with the full state constraints a state observer is designed to estimate those unmeasured states at present all the results in the output feedback area ignore the effects of the full state constraints the presence of these constraints results in a complicated procedure and the major difficulties in the design the barrier lyapunov function blf and a novel design procedure are given to overcome these difficulties the adaptation law and the controllers are obtained based on the backstepping design procedure in addition only one adjustable parameter needs to be updated and thus the online computation burden is alleviated the stability of the closed loop system is proven by using the lyapunov theorem a simulation example is given to verify the effectiveness of the approach

multivariable model reference adaptive control without constraints on the high frequency gain matrix abstract a multivariable model reference adaptive control algorithm is presented for the case when the high frequency gain matrix is unknown only an upper bound on the norm of the matrix needs to be known a priori a transformation of the parameters with a sort of hysteresis is used to guarantee that a controller matrix which is normally the inverse of the estimate of the high frequency gain matrix remains nonsingular it is shown that all the signals in the adaptive system are bounded and that the tracking error and the regressor error converge to zero for all bounded reference inputs furthermore exponential convergence is achieved when the regressor vector is persistently exciting

stability of incompressible formulations enriched with x fem abstract the treatment of near incompressibility is a major concern for applications involving rubber like materials or when important plastic flows occurs as in forming processes the use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit however it also introduces a critical condition for the stability of the formulation called the inf sup or lbb condition recently the finite element method has evolved with the introduction of the partition of unity method the extended finite element method x fem uses the partition of unity method to remove the need to mesh physical surfaces or to re mesh them as they evolve the enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements in this paper some strategies are proposed for the enrichment of low order mixed finite element approximations in the incompressible setting the case of holes material interfaces and cracks are considered numerical examples show that for well chosen enrichment strategies the finite element convergence rate is preserved and the inf sup condition is passed

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach