further results on output feedback stabilization for a class of stochastic nonlinear systems for a class of stochastic nonlinear systems in which the drift and diffusion vector fields depend on the unmeasurable states besides the measurable output the research purpose of this technical note is to find the maximum value interval of observer gain for the desired control performance for this interval the designed output feedback controller ensures that the equilibrium at the origin is globally asymptotically stable in probability and the inverse optimal stabilization in probability is achieved

a general algorithm for limit solutions of plane stress problems a computational approach to limit solutions is considered most challenging for two major reasons a limit solution is likely to be non smooth such that certain non differentiable functions are perfectly admissible and make physical and mathematical sense moreover the possibility of non unique solutions makes it difficult to analyze the convergence of an iterative algorithm or even to define a criterion of convergence in this paper we use two mathematical tools to resolve these difficulties a duality theorem defines convergence from above and from below the exact solution a combined smoothing and successive approximation applied to the upper bound formulation perturbs the original problem into a smooth one by a small parameter e as e 0 the solution of the original problem is recovered this general computational algorithm is robust such that from any initial trial solution the first iteration falls into a convex hull that contains the exact solution s of the problem unlike an incremental method thut invariably renders the limit problem ill conditioned the algorithm is numerically stable limit analysis itself is a highly efficient concept which bypasses the tedium of the intermediate elastic plastic deformation and seeks the most important information directly with the said algorithm we have produced many limit solutions of plane stress problems certain non smooth characters of the limit solutions are shown in the examples presented two well known as well as one parametric family of yield functions are used to allow comparison with some classical solutions

a homogeneous domination approach to state feedback of stochastic high order feedforward nonlinear systems this paper investigates stochastic high order feedforward nonlinear systems for the first time by introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

a novel augmented lagrangian based formulation for upper bound limit analysis summary this paper describes a novel upper bound formulation of limit analysis this formulation is an innovative variant of an existing two field mixed formulation based on the augmented lagrangian method also developed by the authors a natural approach is used to describe the deformation of each finite element furthermore and in contrast to the previous formulation two independent field approximations are now both used to define the velocity field defined globally and at element level it is shown that this feature allows a governing system of uncoupled linear equations to be obtained some numerical examples in plane strain conditions are presented in order to illustrate the current model performance in conclusion the potential and advantages of this new approach are discussed copyright 2011 john wiley sons ltd

a new discontinuous upper bound limit analysis formulation summary a new upper bound formulation of limit analysis of two and three dimensional solids is presented in contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers however by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions also kinematically admissible discontinuities which have previously been shown to be very efficient are given an interpretation in terms of stresses this allows for a much simpler implementation and in contrast to existing formulations extension to arbitrary yield criteria in two and three dimensions is straightforward finally the capabilities of the new method are demonstrated through a number of examples copyright 2005 john wiley sons ltd

further results on output feedback regulation of stochastic nonlinear systems with siiss inverse dynamics this article further discusses the problem of output feedback regulation for more general stochastic nonlinear systems with stochastic integral input to state stable inverse dynamics and focuses on solving the important and unsolved problem proposed in yu and xie yu x and xie x j 2010 output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics ieee transactions on automatic control 55 304 320 how to weaken the conditions on nonlinearities in drift and diffusion vector fields under the weaker conditions how to make full use of the known information of stochastic nonlinear systems to design an adaptive output feedback controller such that all the closed loop signals are almost surely bounded and the output is driven to zero almost surely

computation of limit loads for computing the collapse state of a perfect plastic continuum we suggest a mixed finite element approximation to the infinite dimensional mathematical programming problem of limit analysis the convergence of the limit load to the exact solution is discussed as well as solution methods for the discrete problem finally the method is applied to a classical problem in plane strain

the weak commutativity construction for lie algebras abstract we study the analogue of sidki s weak commutativity construction defined originally for groups in the category of lie algebras this is the quotient g of the lie algebra freely generated by two isomorphic copies g and g of a fixed lie algebra by the ideal generated by the brackets x x for all x we exhibit an abelian ideal of g whose associated quotient is a subdirect sum in g g g and we give conditions for this ideal to be finite dimensional we show that g has a subquotient that is isomorphic to the schur multiplier of g we prove that g is finitely presentable or of homological type f p 2 if and only if g has the same property but f is not of type f p 3 if f is a non abelian free lie algebra

state feedback control of high order stochastic nonlinear systems with siiss inverse dynamics this technical note considers a class of high order stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states a new design and analysis approach to the problem of state feedback global regulation is developed to guarantee that all the signals of the closed loop system are bounded almost surely and the states can be regulated to zero almost surely

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

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

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

brief paper inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable after considering the stabilization of a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input in this brief paper we further address the problem of state feedback inverse optimal stabilization in probability i e our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals

mesh adaptive computation of upper and lower bounds in limit analysis summary an efficient procedure to compute strict upper and lower bounds for the exact collapse multiplier in limit analysis is presented with a formulation that explicitly considers the exact convex yield condition the approach consists of two main steps first the continuous problem under the form of the static principle of limit analysis is discretized twice one per bound using particularly chosen finite element spaces for the stresses and velocities that guarantee the attainment of an upper or a lower bound the second step consists of solving the resulting discrete non linear optimization problems these are reformulated as second order cone programs which allows for the use of primal dual interior point methods that optimally exploit the convexity and duality properties of the limit analysis model to benefit from the fact that collapse mechanisms are typically highly localized a novel method for adaptive meshing is introduced the method first decomposes the total bound gap as the sum of positive contributions from each element in the mesh and then refines those elements with higher contributions the efficiency of the methodology is illustrated with applications in plane stress and plane strain problems copyright q 2008 john wiley sons ltd

advances in the simulation of viscoplastic fluid flows using interior point methods abstract we present a primal dual interior point algorithm for the resolution of steady state viscoplastic fluid flows formulated as a conic optimization problem we give a complete description of the algorithm including some advanced aspects such as a predictor corrector and scaling scheme to improve its efficiency our interior point approach is shown to be largely more efficient than augmented lagrangian al approaches which are traditionally used to solve such problems in particular the interior point approach is roughly 5 times faster than the modern accelerated version of al algorithms the yield surfaces are shown to be accurately predicted and various examples ranging from channel flows to three dimensional flows through a porous medium demonstrate its efficiency

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

a homogeneous domination approach to state feedback of stochastic high order nonlinear systems with time varying delay the homogeneous domination approach is introduced to solve the state feedback stabilization problem for stochastic high order nonlinear systems with time varying delay under the weaker conditions on the drift and diffusion terms by using the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

a cell based smoothed finite element method for kinematic limit analysis this paper presents a new numerical procedure for kinematic limit analysis problems which incorporates the cell based smoothed finite element method with second order cone programming the application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort the non smooth optimization problem is formulated as a problem of minimizing a sum of euclidean norms ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm plane stress and plane strain problems governed by the von mises criterion are considered but extensions to problems with other yield criteria having a similar conic quadratic form or 3d problems can be envisaged

a combined homogeneous domination and sign function approach to output feedback stabilization of stochastic high order nonlinear systems for a class of stochastic high order nonlinear systems by introducing the combined homogeneous domination and sign function design approach this technical note solves the problem of output feedback control under the weaker high order and nonlinear growth conditions

further results on output feedback stabilization for stochastic high order nonlinear systems with time varying delay this article further discusses the output feedback stabilization problem for stochastic high order nonlinear systems with time varying delay under the weaker conditions on nonlinearities in drift and diffusion vector fields by using the idea of homogeneous domination approach skillfully choosing an appropriate lyapunov krasoviskii functional and successfully solving several troublesome obstacles in the design and analysis procedure an output feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

lower bound limit analysis with adaptive remeshing the objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics unlike conventional finite element meshes a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements these discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately in general the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution limit analysis and soil plasticity 1975 to ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field recently borges et al int j solids struct 2001 38 1707 1720 presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator in the present work this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns the adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field for problems involving strong stress singularities in the boundary conditions e g a strip footing the automatic generation of discontinuity fans centred on the singular points has been implemented the efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut copyright 2005 john wiley sons ltd

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

on weak commutativity in groups abstract for a group g we study homological and homotopical properties of the group g g g g g 1 for g g in particular we show that the operator preserves the soluble of type f p property

weak commutativity and nilpotency abstract we continue the analysis of the weak commutativity construction for lie algebras this is the lie algebra g generated by two isomorphic copies g and g of a fixed lie algebra subject to the relations x x 0 for all x g in this article we study the ideal l l g generated by x x for all x g we obtain an infinite presentation for l as a lie algebra and we show that in general it cannot be reduced to a finite one with this in hand we study the question of nilpotency we show that if g is nilpotent of class c then g is nilpotent of class at most c 2 and this bound can improved to c 1 if g is 2 generated or if c is odd we also obtain concrete descriptions of l g and thus of g if g is free nilpotent of class 2 or 3 finally using methods of grobner shirshov bases we show that the abelian ideal r g g l g is infinite dimensional if g is free of rank at least 3

upper bound limit analysis using discontinuous velocity fields abstract a new method for computing rigorous upper bounds under plane strain conditions is described it is based on a linear three noded triangular element which has six unknown nodal velocities and a fixed number of unknown plastic multiplier rates and uses the kinematic theorem to define a kinematically admissible velocity field as the solution of a linear programming problem unlike existing formulations which permit only a limited number of velocity discontinuities whose directions of shearing must be specified a priori the new formulation permits velocity discontinuities at all edges shared by adjacent triangles and the directions of shearing are found automatically the variation of the velocity jump along each discontinuity is described by an additional set of four unknowns all of the unknowns are subject to the constraints imposed by an associated flow rule and the velocity boundary conditions the objective function corresponds to the dissipated power or some related load parameter of interest and is minimised to yield the desired upper bound since plastic deformation may occur not only in the discontinuities but also throughout the triangular elements as well the method is capable of modelling complex velocity fields accurately and typically produces tight upper bounds on the true limit load the formulation is applicable to materials whose strength is cohesive frictional purely cohesive and uniform or purely cohesive and linearly varying and thus quite general the new procedure is very efficient and always requires fewer elements than existing methods to obtain useful upper bound solutions moreover because of the extra degrees of freedom introduced by the discontinuities the linear elements no longer need to be arranged in a special pattern to model incompressible behaviour accurately

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

brief paper output feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable this brief paper investigates the problem of output feedback stabilization for a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input based on the ideas of the homogeneous systems theory and the adding a power integrator technique an output feedback controller is constructed to ensure that the equilibrium at the origin of the closed loop system is globally asymptotically stable gas in probability the efficiency of the output feedback controller is demonstrated by a simulation example

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

a non linear programming method approach for upper bound limit analysis this paper presents a finite element model based on mathematical non linear programming in order to determine upper bounds of colapse loads of a mechanical structure the proposed formulation is derived within a kinematical approach framework employing two simultaneous and independent field approximations for the velocity and strain rate fields the augmented lagrangian is used to establish the compatibility between these two fields in this model only continuous velocity fields are used uzawa s minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate the use of this technique allows to bypass the complexity of the non linear aspects of the problem since non linearity is addressed as a set of small local subproblems of optimization for each finite element the obtained model is quite versatile and suitable for solving a wide range of collapse problems this paper studies 3d strut and tie structures 2d plane strain stress and 3d solid problems copyright 2007 john wiley sons ltd

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

output tracking of high order stochastic nonlinear systems with application to benchmark mechanical system this note considers output tracking of high order stochastic nonlinear systems without imposing any restriction on the high order and the drift and diffusion terms by using the backstepping design technique a smooth state feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability a practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme

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 stabilized discrete shear gap finite element for adaptive limit analysis of mindlin reissner plates summary this paper presents a numerical formulation for computation of collapse load of mindlin reissner plates that uses stabilized discrete shear gap finite elements and second order cone programming displacement fields are approximated using the discrete shear gap in combination with a stabilized strain smoothing technique ensuring that shear locking problem can be avoided and that accurate solutions can be obtained the underlying optimization problem is formulated in the form of a standard second order cone programming so that it can be solved using highly efficient primal dual interior point algorithm an error indicator based on plastic dissipation will be used in the adaptive refinement scheme various plates with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure copyright 2013 john wiley sons ltd

kinematic limit analysis of frictional materials using nonlinear programming abstract in this paper a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming limit analysis and the conventional displacement based finite element method the analysis is based on a general yield function which can take the form of the mohr coulomb or drucker prager criterion by using an associated flow rule a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization the plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained the nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation the calculation is based entirely on kinematically admissible velocities without calculation of the stress field the finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint the objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load an effective direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem the effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

automatic mesh refinement in limit analysis a strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method in the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition the approach is tested on standard problems in plane strain including the classical punch problem very accurate results are obtained with the use of moderate computational power

stochastic nonlinear stabilization ii inverse optimality after considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper in this second part we address the classical question of when is a stabilizing in probability controller optimal and show that for every system with a stochastic control lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional then we return to the problem from part i and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin

global state feedback stabilisation of nonlinear systems with high order and low order nonlinearities this paper studies the state feedback control problem for a class of nonlinear systems with high order and low order nonlinearities the introduction of the sign function together with the method of adding a power integrator and lyapunov stability theorem makes the closed loop system globally asymptotically stable exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work

backstepping design with local optimality matching in nonlinear h sup spl infin optimal control design for strict feedback nonlinear systems our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order and to be inverse optimal with respect to some computable cost functional our recursive construction of a cost functional and the corresponding solution to the hamilton jacobi isaacs equation employs a new concept of nonlinear cholesky factorization when the value function for the system has a nonlinear cholesky factorization we show that the backstepping design procedure can be tuned to yield the optimal control law

brief paper adaptive state feedback stabilization for a large class of high order stochastic nonlinear systems under the more general conditions on the power order and the nonlinear functions this paper investigates the problem of adaptive state feedback stabilization for a class of high order stochastic nonlinear systems with time varying control coefficients based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the state feedback controller is demonstrated by a simulation example

a polytree based adaptive approach to limit analysis of cracked structures abstract we in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures the key idea is to develop a general refinement algorithm based on a so called polytree mesh structure the method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones which are considered as special cases also polytree meshes are conforming and can be regarded as a generalization of quadtree meshes for the aim of this paper we restrict our main interest in plane strain limit analysis to von mises type materials yet its extension to a wide class of other solid mechanics problems and materials is completely possible to avoid volumetric locking we propose an approximate velocity field enriched with bubble functions using wachspress coordinates on a primal mesh and design carefully strain rates on a dual mesh level an adaptive mesh refinement process is guided by an l 2 norm based indicator of strain rates through numerical validations we show that the present method reaches high accuracy with low computational cost this allows us to perform large scale limit analysis problems favorably

output tracking of stochastic high order nonlinear systems with markovian switching this technical note poses and solves the output tracking problem for a class of stochastic high order nonlinear systems with stationary markovian switching by introducing a ii operator and using dynkin formula for markovian switching systems a switching controller is constructed to ensure that the closed loop system has a unique solution and is bounded in probability also the tracking error converges to an arbitrarily small neighborhood of zero the efficiency of the tracking controller is demonstrated by a simulation example

inverse optimal adaptive control for attitude tracking of spacecraft the attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method the adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals this is achieved by the inverse optimality approach without solving the associated hamilton jacobi isaacs partial differential hjipd equation directly the design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping and a control lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve h sub spl infin disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy the convergence of adaptive parameters is also analyzed in terms of invariant manifold numerical simulations illustrate the performance of the proposed control algorithms

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

a note on upper bound formulations in limit analysis summary in this paper we study some recent formulations for the computation of upper bounds in limit analysis we show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound nor does it provide a velocity field that satisfies the normality rule everywhere we show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power we derive a formulation that furnishes a strict upper bound of the load factor which in fact coincides with a formulation reported in the literature from the analysis of these formulations we propose a post process which consists in computing exactly the dissipation power for the optimum upper bound velocity field this post process may further reduce the strict upper bound of the load factor in particular situations finally we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap copyright 2012 john wiley sons ltd

practical output feedback risk sensitive control for stochastic nonlinear systems with stable zero dynamics this paper addresses the design problem of practical or satisfaction output feedback controls for stochastic strict feedback nonlinear systems in observer canonical form with stable zero dynamics under long term average tracking risk sensitive cost criteria the cost function adopted here is of the quadratic integral type usually encountered in practice rather than the quartic integral one used to avoid difficulty in control design and performance analysis of the closed loop system a sequence of coordinate diffeomorphisms is introduced to separate the zero dynamics from the entire system so that the transformed system has an appropriate form suitable for integrator backstepping design for any given risk sensitivity parameter and desired cost value by using the integrator backstepping methodology an output feedback control is constructively designed such that a the closed loop system is bounded in probability and b the long term average risk sensitive cost is upper bounded by the desired value in addition this paper does not require the uniform boundedness of the gain functions of the system noise furthermore an example is given to show the effectiveness of the theory

quadratic velocity linear stress interpolations in limit analysis summary we compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis the aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them two of these interpolations are used in limit analysis for the first time in this article the inequalities in the proposition are also demonstrated via numerical applications to this end the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements copyright 2014 john wiley sons ltd

upper bound limit analysis with a parallel mixed finite element formulation this paper addresses an implementation of the upper bound limit analysis theorem using a parallel mixed finite element formulation the intrinsic characteristics of the adopted upper bound formulation proved to be suitable to adapt it to an efficient parallelization scheme in order to illustrate the computational power provided by the new parallel processing method accurate upper bound collapse load estimates for 3d problems are produced using a cluster of common pc machines

state feedback stabilization for stochastic high order nonlinear systems with markovian switching abstract this paper aims to investigate the problem of state feedback stabilization for stochastic high order nonlinear systems with markovian switching by using the generalized ito formula and dynkin formula for markovian switching systems a state feedback controller is constructed to ensure that the closed loop system has a unique solution and the solution of the closed loop systems is almost surely asymptotically stable finally the effectiveness of the controller is demonstrated by a simulation example

an adaptive approach to limit analysis abstract the main objective of this paper is to propose an adaptive mesh refinement procedure for finite element models in limit analysis we use an a posteriori indicator based on the local directional interpolation error and a recovering scheme to compute second derivatives of the finite element solution the proposed mesh adaptation process gives improved results in localizing regions of rapid or abrupt variations of the variables whose location is not known a priori limit analysis of bodies in plane strain and plane stress is considered in the applications

output feedback control design for strict feedback stochastic nonlinear systems under a risk sensitive cost in this note we study the problem of output feedback control design for a class of strict feedback stochastic nonlinear systems under an infinite horizon risk sensitive cost criterion the controller designed can guarantee an arbitrary small long term average cost for arbitrary risk sensitivity parameter and achieve boundedness in probability for the closed loop system using the integrator backstepping methodology furthermore the controller preserves the equilibrium at the origin of the nonlinear system

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

adaptive element free galerkin method applied to the limit analysis of plates the implementation of an h adaptive element free galerkin efg method in the framework of limit analysis is described the naturally conforming property of meshfree approximations with no nodal connectivity required facilitates the implementation of h adaptivity nodes may be moved discarded or introduced without the need for complex manipulation of the data structures involved with the use of the taylor expansion technique the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy a stabilized conforming nodal integration scheme is extended for use in error estimation and results in an efficient and truly meshfree adaptive method to demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions

an edge based finite element method es fem with adaptive scaled bubble functions for plane strain limit analysis abstract this paper deals with critical roles of cubic bubble functions for the edge based finite element method es fem formulation within the framework of the kinematic theorem for predicting the plastic collapse loads of structures we show that the bubble function can be scaled by a non zero coefficient alpha while the volumetric locking is entirely eliminated based on this finding the present method is designed in a very small value with a bubble function that is maximum at the center of the element this can lead to the loss of the partition of unity for easy reference the present method is termed as bes fem the significant advantage of the present method lies in the rigorous treatment of the volumetric locking free that can occur in the fully plastic range the bes fem works well with high efficiency by using triangular meshes it achieves both simplicity and computational efficiency for implementation into packages of plastic limit analyses in case of bes fem the locking issue can be solved conveniently by two schemes 1 the usual piecewise linear displacements enriched with a cubic bubble function on a primal mesh of triangular elements and 2 a projection operator of strain rates through a dual mesh associated with the edges in the mesh the optimization formulation of finite element limit analysis is written in the form of a second order cone programming socp the well established interior point solvers can be exploited efficiently the bes fem using a small number of integration points enables to solve the large scale optimization problems efficiently in addition an adaptive meshing procedure based on an alternative indicator of dissipation is also derived to further enhance the quality of the solution without increasing significantly the number of degrees of freedom of the model numerical results show the robustness of the proposed method

an iterative algorithm for limit analysis with nonlinear yield functions abstract a mathematical programming algorithm is proposed for the general limit analysis problem plastic behavior is described by a set of linear or nonlinear yield functions abstract formulations of limit analysis are first considered and a quasi newton strategy for solving the optimality conditions is then sketched the structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

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

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

reduced order observer based control design for nonlinear stochastic systems in this paper we investigate the stabilization control design problem of nonlinear stochastic siso systems in strict feedback form by introducing a novel reduced order observer an output feedback based control is constructively designed which renders the closed loop system asymptotically stable in the large when the nonlinearities and stochastic disturbance equal zero at the equilibrium point of the open loop system and bounded in probability otherwise besides the obtained controller preserves the equilibrium point of the open loop nonlinear system

a posteriori error estimation and adaptive mesh refinement techniques abstract we analyse three different a posteriori error estimators for elliptic partial differential equations they are based on the evaluation of local residuals with respect to the strong form of the differential equation on the solution of local problems with neumann boundary conditions and on the solution of local problems with dirichlet boundary conditions we prove that all three are equivalent and yield global upper and local lower bounds for the true error thus adaptive mesh refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities some numerical examples prove the efficiency of the error estimators and the mesh refinement techniques

further results on adaptive state feedback stabilization for stochastic high order nonlinear systems this paper aims to relax the results in xie and tian 2009 from the following two aspects completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions by using the backstepping design method and homogeneous domination technique this paper investigates the problem of adaptive state feedback stabilization for a class of stochastic high order nonlinear systems with nonlinear parameterization the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the adaptive state feedback controller is demonstrated by a simulation example