finite time event triggered mathcal h _ infty control for t s fuzzy markov jump systems this paper investigates the finite time event triggered mathcal h infty control problem for takagi sugeno markov jump fuzzy systems because of the sampling behaviors and the effect of network environment the premise variables considered in this paper are subject to asynchronous constraints the aim of this paper is to synthesize a controller via an event triggered communication scheme such that not only the resulting closed loop system is finite time bounded and satisfies a prescribed mathcal h infty performance level but also the communication burden is reduced first a sufficient condition is established for the finite time bounded mathcal h infty performance analysis of the closed loop fuzzy system with fully considering the asynchronous premises then based on the derived condition the method of the desired controller design is presented two illustrative examples are finally presented to demonstrate the practicability and efficacy of the proposed method

pareto optimal strategy for stochastic weakly coupled large scale systems with state dependent system noise this note is concerned with the decentralized infinite horizon stochastic pareto optimal static output feedback strategy for a class of weakly coupled systems with state dependent noise first pareto optimal control problems are formulated using a static output feedback strategy the necessary conditions are given by the cross coupled stochastic algebraic riccati type equations csares for proving the existence of the static output feedback strategy that minimizes the quadratic cost function after determining the asymptotic structure of the solutions of the csares a new sequential numerical algorithm and newton s method for solving the csares are described the resulting numerical solution is used to develop the pareto optimal strategy finally the efficiency of the proposed algorithm is demonstrated by solving a numerical example for a practical megawatt frequency control problem

h filtering for nonlinear networked systems with randomly occurring distributed delays missing measurements and sensor saturation this paper is concerned with the h filtering problem for a class of networked systems subject to randomly occurring distributed state delays nonlinearities sensor saturation as well as missing measurements via unreliable communication channels the output measurements are affected by sensor saturation which is described by sector nonlinearities the missing measurement is modeled as a linear random variable satisfying the bernoulli distribution and the nonlinearities with the form of global lipschitz cover the well known nonlinear functions the purpose of the addressed problem is to design a full order filter such that in the simultaneous presence of distributed delays randomly occurring nonlinearities sensor saturation and missing measurements the filtering dynamic system is guaranteed to be exponentially mean square stable and the h filtering performance index is achieved a sufficient condition for the solution of the addressed problem is derived and the explicit expression of the desired filter gains is described in terms of the solution to linear matrix inequality lmi finally a numerical example is provided to show the effectiveness of the designed method

pareto optimality in infinite horizon linear quadratic differential games in this article we derive conditions for the existence of pareto optimal solutions for linear quadratic infinite horizon cooperative differential games first we present a necessary and sufficient characterization for pareto optimality which translates to solving a set of constrained optimal control problems with a special structure next we show that if the dynamical system is controllable certain transversality conditions hold true and as a result all the pareto candidates can be obtained by solving a weighted sum optimal control problem further exploiting the linear structure we investigate the relationship between pareto optimality and weighted sum minimization finally for the scalar case we present an algorithm to find all the pareto optimal solutions assuming mild conditions on the control space

a p adaptive scheme for overcoming volumetric locking during plastic flow a feature of many classical plasticity yield functions is that they impose a volumetric constraint on plastic deformation for low order finite elements this results in kinematic restraints on possible deformation modes of an element leading to an overly stiff response the most robust procedure for overcoming volumetric locking is to use higher order finite elements however low order elements are popular for their efficiency and simplicity to remedy volumetric locking in low order elements a p adaptive scheme is proposed where through the partition of unity property of finite element shape functions the underlying basis of low order finite elements undergoing plastic flow is enhanced with higher order polynomial functions the computational result is extra degrees of freedom at existing nodes of elements undergoing plastic flow while the rest of the nodes remain unaltered the performance of the scheme is illustrated through two and three dimensional numerical examples

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

limit analysis and convex programming a decomposition approach of the kinematic mixed method this paper proposes an original decomposition approach to the upper bound method of limit analysis it is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields presented in plane strain this method appears to be rapidly convergent as verified in the tresca compressed bar problem in the linear velocity case then using discontinuous quadratic velocity fields the method is applied to the celebrated problem of the stability factor of a tresca vertical slope the upper bound is lowered to 3 7776 value to be compared with the best published lower bound 3 772 by succeeding in solving non linear optimization problems with millions of variables and constraints copyright c 2008 john wiley sons ltd

comments on a regulating and tracking pi d controller eitelberg 1987 presents a modification of the classical pid controller which amounts to a two degree of freedom structure beside the fact that this modification is already known from the literature its potentials are not fully exploited by eitelberg based on a closed loop interpretation of the approach a systematic tuning procedure and an additional extension for pi controllers are presented

necessary and sufficient conditions for pareto optimal solutions of cooperative differential games in this paper we present necessary as well as sufficient conditions for the existence of a pareto optimum for cooperative differential games the obtained results are used to analyze the regular indefinite linear quadratic differential game for the scalar case an algorithm is devised to find all pareto efficient solutions

fractional noether s theorem in the riesz caputo sense abstract we prove a noether s theorem for fractional variational problems with riesz caputo derivatives both lagrangian and hamiltonian formulations are obtained illustrative examples in the fractional context of the calculus of variations and optimal control are given

3d fem formulations of limit analysis methods for porous pressure sensitive materials summary the first purpose of this paper is the numerical formulation of the three general limit analysis methods for problems involving pressure sensitive materials that is the static classic and mixed kinematic methods applied to problems with drucker prager mises schleicher or green materials in each case quadratic or rotated quadratic cone programming is considered to solve the final optimization problems leading to original and efficient numerical formulations as a second purpose the resulting codes are applied to non classic 3d problems that is the gurson like hollow sphere problem with these materials as matrices to this end are first presented the 3d finite element implementations of the static and kinematic classic methods of limit analysis together with a mixed method formulated to give also a purely kinematic result discontinuous stress and velocity fields are included in the analysis the static and the two kinematic approaches are compared afterwards in the hydrostatic loading case whose exact solution is known for the three cases of matrix then the static and the mixed approaches are used to assess the available approximate criteria for porous drucker prager mises schleicher and green materials copyright 2013 john wiley sons ltd

a general non linear optimization algorithm for lower bound limit analysis the non linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided the algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required as with interior point methods for linear programming the number of iterations is affected only little by the problem size some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non linear yield criteria copyright 2002 john wiley sons ltd

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

multiobjective tracking control design of t s fuzzy systems in this study a multiobjective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal h 2 and h reference tracking performance simultaneously first the takagi and sugeno t s fuzzy model is used to represent the nonlinear dynamic system then based on the t s fuzzy model multiobjective h 2 h tracking control design problem is formulated as a multiobjective problem mop to minimize the h 2 tracking error and h disturbance attenuation level for the fuzzy system at the same time since it is not easy to solve this mop directly an indirect method is proposed for the multiobjective h 2 h tracking control design finally in order to achieve the simultaneous optimization of the mop linear matrix inequality lmi based multiobjective evolution algorithm lmi based moea is developed based on non dominating sorting scheme to efficiently search the set of pareto optimal solutions for the mop from which designer can select one design according to his own preference further the multiobjective h 2 h fuzzy control design problem based on the weighted sum method is also solved as an alternative choice finally a simulation example of a robotic system is given to illustrate the design procedure and to confirm the robust and optimal tracking performance of the proposed method

stackelberg strategies for stochastic systems with multiple followers in this paper stackelberg games for linear stochastic systems governed by ito differential equations with multiple followers are investigated stackelberg strategies are developed under two different settings that is the followers act either cooperatively to attain pareto optimality or non cooperatively to arrive at a nash equilibrium after establishing the necessary conditions to obtain stackelberg strategies by using sets of cross coupled algebraic nonlinear matrix equations canmes two numerical algorithms are developed based on newton s method and the semidefinite programming sdp problem to solve the canmes finally a numerical example is solved to demonstrate the validity of the algorithms

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

on the complementary bounding theorems for limit analysis abstract a unified theory for the complementary dual bounding theorems of limit analysis is established with the aid of convex analysis based on the property of superpotential in this theory various variational principles are constructed which include a new lower bound theorem a more precise estimation for the safety factor and a penalty duality type variational principle furthermore an efficient penalty duality algorithm for limit analysis is suggested and the applications of these theorems are illustrated

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

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

pareto optimal strategy for linear stochastic systems with h constraint in finite horizon abstract in this paper we derive conditions for the existence of pareto efficient strategy and pareto solution under h constraint for the linear quadratic lq finite horizon cooperative differential game of stochastic systems with state control and disturbance multiplicative noise firstly we present a stochastic bounded real lemma sbrl with any initial condition for the considered stochastic system next a necessary and sufficient condition for pareto optimal strategy under the h constraint is researched by two cross coupled generalized differential riccati equations gdres which is the key contribution of this paper another contribution is that the pareto solution for every controller is given under the pareto efficient strategy and worst case external disturbance finally a practical example is given to illustrate the effectiveness of our results

multiobjective fractional variational calculus in terms of a combined caputo derivative abstract the study of fractional variational problems in terms of a combined fractional caputo derivative is introduced necessary optimality conditions of euler lagrange type for the basic isoperimetric and lagrange variational problems are proved as well as transversality and sufficient optimality conditions this allows to obtain necessary and sufficient pareto optimality conditions for multiobjective fractional variational problems

necessary sufficient conditions for pareto optimality in finite horizon mean field type stochastic differential game abstract this paper is concerned with necessary and sufficient conditions for the existence of pareto solutions in finite horizon mean field type stochastic cooperative differential game based on the equivalent characterization of pareto optimality the problem is transformed into a set of constrained mean field type stochastic optimal control problems with a special structure utilizing the mean field type stochastic minimum principle the necessary conditions are put forward under certain convex assumptions it is shown that the necessary conditions are also sufficient ones next the indefinite linear quadratic lq case is studied it is pointed out that the solvability of two related generalized differential riccati equations gdres provides a sufficient condition under which pareto efficient strategies are equivalent to weighted sum optimal controls in addition all pareto solutions are obtained based on the solutions of two generalized differential lyapunov equations gdles at last an example sheds light on the effectiveness of the theoretical results

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

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

pareto optimal filter design for nonlinear stochastic fuzzy systems via multiobjective h_ bf 2 h_ bm infty optimization this paper is concerned with the multiobjective h 2 h infty filtering design problem in nonlinear signal processing which can be approximated by a takagi sugerno t s fuzzy signal system we propose a multiobjective filter design to estimate state variables from noisy measurements for nonlinear signal systems and we focus our effort on achieving optimal concurrent performance for h 2 and h infty filtering in general it is difficult to solve the multiobjective mo h 2 h infty fuzzy filter problem directly and we therefore propose an indirect approach to minimize the upper bounds and transform the mo h 2 h infty filtering problem in to a linear matrix inequality lmi constrained multiobjective problem mop in addition we propose an lmi based multiobjective evolution algorithm to efficiently find pareto optimal solutions for the mop of multiobjective fuzzy filter design for nonlinear stochastic signal processing furthermore for comparison we also suggest the mo h 2 h infty filter design problem based on the weighted sum method our proposed indirect method can be widely employed to practically address the mo filter design problem in nonlinear signal processing finally a trajectory estimation of reentry vehicle by radar is provided to illustrate the design procedure of the pareto mo optimal filter

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

tuning of pid type controllers for stable and unstable systems with time delay abstract a graphical technique for tuning pid type controllers based on the method of d partition is proposed for single input single output linear time invariant systems the tuning method shifts all the roots of the characteristic equation of the controlled system to a certain desirable region in the left half of the complex plane lhp to achieve a specified least absolute and least relative stability margin the method can be used to tune a precompensator in a two degree of freedom structure so as to improve tracking behaviour the method can be used for both stable and unstable systems for systems with significant time delay and for various controller configurations including derivative in the feedback path

pareto based guaranteed cost control of the uncertain mean field stochastic systems in infinite horizon pareto based guaranteed cost control gcc problem of uncertain mean field stochastic systems is investigated in infinite horizon firstly the pareto game of nominal mean field stochastic systems is studied applying the convexity of the cost functionals it is shown that all pareto efficient solutions can be obtained by solving a weighted sum optimal control problem based on which pareto based gcc problem is solved by the gcc of the weighted sum objective functional secondly applying the karush kuhn tucker kkt conditions the necessary conditions for the existence of the pareto based guaranteed cost controllers are derived in particular it turns out that all controllers are expressed as linear feedback forms involving the state and its mean based on the solutions of the cross coupled generalized algebraic riccati equations cgares thirdly this paper presents an lmi based approach to reduce greatly the computational complexity in the controller design finally two examples are given to show the effectiveness of the proposed results

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

dissipativity based small gain theorems for stochastic network systems in this paper some small gain theorems are proposed for stochastic network systems which describe large scale systems with interconnections uncertainties and random disturbances by the aid of conditional dissipativity and showing times of stochastic interval small gain conditions proposed for the deterministic case are extended to the stochastic case when some design parameters are tunable in practice we invaginate a simpler method to verify small gain condition by selecting one subsystem as a monitor compared with the existing results the existence and uniqueness of solution and ultimate uniform boundedness of input are removed from requirements of input to state stability and small gain theorems

locking free discontinuous finite elements for the upper bound yield design of thick plates summary this work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of reissner mindlin thick plates in shear bending interaction the main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields in particular it has been demonstrated for 2d plane stress plane strain or 3d limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates for this reason discontinuous interpolations of the transverse velocity and the rotation fields for reissner mindlin plates are proposed the subsequent discrete minimization problem is formulated as a second order cone programming problem and is solved using the industrial software package mosek a comprehensive study of the shear locking phenomenon is also conducted and it is shown that discontinuous elements avoid such a phenomenon quite naturally whereas continuous elements cannot without any specific treatment this particular aspect is confirmed through numerical examples on classical benchmark problems and the so obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates copyright 2015 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

discontinuous velocity domain splitting in limit analysis abstract we present a new limit analysis method originated in ionescu and lachand robert 2005 and called discontinuous velocity domain splitting method dvds dvds is a mesh free method which focuses on the strain localization and completely neglect the bulk deformations it considers the kinematic variational principle on a special class of virtual velocity fields to get an upper bound of the limit load to construct this class of virtual velocity fields the rigid plastic body is splinted into simple connected sub domains and on each such sub domain a rigid motion is associated the discontinuous collapse flow velocity field results in localized deformations only located at the boundary of the sub domains in the numerical applications of the dvds method we introduce a numerical technique based on a level set description of the partition of the rigid plastic body and on genetic minimization algorithms for the anti plane flow of a von mises material dvds is exact in solving the limit analysis problem the collapse flow is a rigid motion of a sub domain the associated deformation rate is localized on the smooth boundary of the moving sub domain representing the fracture surface in the case of in plane deformation of pressure insensitive materials the internal boundaries of the sub domains are parts of circles or straight lines tangent to the collapse velocity jumps in this case dvds reduces to the block decomposition method which was intensively used to get analytical upper bounds of the limit loads when applied to the two notched tensile problem of a von mises material dvds gives excellent results with a low computational cost furthermore dvds was applied to model collapse in pressure sensitive plastic materials illustrative examples for homogenous and heterogeneous coulomb and cam clay materials shows that dvds gives excellent prediction of limit loads and on the collapse flow

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

indefinite stochastic linear quadratic control and generalized differential riccati equation a stochastic linear quadratic lq control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite indefinite stochastic lq theory has been extensively developed and has found interesting applications in finance however there remains an outstanding open problem which is to identify an appropriate riccati type equation whose solvability is it equivalent to the solvability of the indefinite stochastic lq problem this paper solves this open problem for lq control in a finite time horizon a new type of differential riccati equation called the generalized differential riccati equation is introduced which involves algebraic equality inequality constraints and a matrix pseudoinverse it is then shown that the solvability of the generalized riccati equation is not only sufficient but also necessary for the well posedness of the indefinite lq problem and the existence of optimal feedback open loop controls moreover all of the optimal controls can be identified via the solution to the riccati equation an example is presented to illustrate the theory developed

a regulating and tracking pi d controller traditionally pi controllers operate solely on the reference error signal modified reference error in the case of pid controllers in the forward path of the classical feedback loop they are designed either as regulating e g to reduce process disturbances or as tracking controllers e g to follow reference changes if both characteristics are important then a compromise design has to be found here a special connection of the classical pi d controller is proposed which allows a greater degree of independence in the design and practical tuning of the regulating and tracking features

computation of limit and shakedown loads using a node based smoothed finite element method summary this paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node based smoothed fem in combination with a primal dual algorithm an associated primal dual form based on the von mises yield criterion is adopted the primal dual algorithm together with a newton like iteration are then used to solve this associated primal dual form to determine simultaneously both approximate upper and quasi lower bounds of the plastic collapse limit and the shakedown limit the present formulation uses only linear approximations and its implementation into finite element programs is quite simple several numerical examples are given to show the reliability accuracy and generality of the present formulation compared with other available methods copyright 2011 john wiley sons ltd

smc design for robust stabilization of nonlinear markovian jump singular systems in this technical note the sliding mode control smc problem is investigated for t s fuzzy model based nonlinear markovian jump singular systems subject to matched unmatched uncertainties to accommodate the model characteristics of such a hybrid system a novel integral type fuzzy sliding surface is put forward by taking the singular matrix and state dependent projection matrix into account simultaneously which is the key contribution of the note the designed surface contains two important features 1 local input matrices for different subsystems in the same system mode are allowed to be different and 2 the matched uncertainties are completely compensated and the unmatched ones are not amplified during sliding motion sufficient conditions for the stochastic admissibility of the corresponding sliding mode dynamics are presented and a fuzzy smc law is constructed to ensure the reaching condition despite uncertainties the applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system

an optimal feedback control strategy pair for zero sum linear quadratic stochastic differential game the riccati equation approach in this paper we study a two person zero sum linear quadratic stochastic differential game problem from a new viewpoint we construct an optimal feedback control strategy pair for the game in a closed loop form based on the solution of a riccati equation a key part of our analysis involves proving the global solvability of this riccati equation which is interesting in its own right moreover we demonstrate an indefinite phenomenon arising from the linear quadratic game

technical communique the regular convex cooperative linear quadratic control problem in this note we consider the cooperative linear quadratic control problem that is the problem where a number of players all facing a different linear quadratic control problem decide to cooperate in order to optimize their performance it is well known when the performance criteria are positive definite how one can determine the set of pareto efficient equilibria for these games in this note we generalize this result for indefinite criteria

necessary and sufficient conditions for pareto optimality of the stochastic systems in finite horizon abstract this paper is concerned with the necessary and sufficient conditions for the pareto optimality in the finite horizon stochastic cooperative differential game based on the necessary and sufficient characterization of the pareto optimality the problem is transformed into a set of constrained stochastic optimal control problems with a special structure utilizing the stochastic pontryagin minimum principle the necessary conditions for the existence of the pareto solutions are put forward under certain convex assumptions it is shown that the necessary conditions are also sufficient ones next we study the indefinite linear quadratic lq case it is pointed out that the solvability of the related generalized differential riccati equation gdre provides the sufficient condition under which all pareto efficient strategies can be obtained by the weighted sum optimality method two examples shed light on the effectiveness of theoretical results

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

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

h h fault detection observer in finite frequency domain for linear parameter varying descriptor systems abstract this paper considers h h fault detection observer design in the finite frequency domain for a class of linear parameter varying lpv descriptor systems we propose a novel fault detection observer with a non singular structure to make the residual sensitive to faults and robust against disturbances we develop a finite frequency h h design method based on a generalized kalman yakubovich popov lemma for lpv descriptor systems design conditions for the proposed fault detection observer are derived and converted as linear matrix inequalities simulation studies are conducted to demonstrate the performance of the proposed method

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

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