a regularized stabilized mixed finite element formulation for viscoplasticity of bingham type abstract in this article we present a new mixed stabilized regularized finite element formulation in primitive variables with continuous velocity and discontinuous pressure interpolations for the steady flow of an incompressible fluid of bingham type this formulation is based on an augmented lagrangian regularization technique and a least squares stabilization method mathematical analyses are performed for the new formulation in terms of stability existence and uniqueness of the solution optimal orders of convergence are obtained mathematically improving on classical methods which also present limitations as regards the values of the yield stress numerical results are presented confirming the theory developed here and they show the robustness of the new method with stability obtained for the velocity and especially for the pressure when the yield stress is very high

topology recognition with advice in topology recognition each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph with all ports correctly marked this task is usually unfeasible without any a priori information such information can be provided to nodes as advice an oracle knowing the network can give a possibly different string of bits to each node and all nodes must reconstruct the network using this advice after a given number of rounds of communication during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations the time of completing topology recognition is the number of rounds it takes and the size of advice is the maximum length of a string given to nodes we investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes we provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time in the class of all graphs of size n and diameter d n for any constant 1 in most cases our bounds are asymptotically tight

on a splitting type algorithm for the numerical realization of contact problems with coulomb friction this paper presents and analyses an iterative process for the numerical realization of contact problems with coulomb friction which is based on the method of successive approximations combined with a splitting type approach numerical examples illustrate the efficiency of this method

shape optimization in contact problems with coulomb friction the paper deals with a discretized problem of the shape optimization of elastic bodies in unilateral contact the aim is to extend existing results to the case of contact problems following the coulomb friction law mathematical modelling of the coulomb friction problem leads to a quasi variational inequality it is shown that for small coefficients of friction the discretized problem with coulomb friction has a unique solution and that this solution is lipschitzian as a function of a control variable describing the shape of the elastic body the shape optimization problem belongs to a class of so called mathematical programs with equilibrium constraints mpecs the uniqueness of the equilibria for fixed controls enables us to apply the so called implicit programming approach its main idea consists of minimizing a nonsmooth composite function generated by the objective and the single valued control state mapping in this paper the control state mapping is much more complicated than in most mpecs solved in the literature so far and the generalization of the relevant results is by no means straightforward numerical examples illustrate the efficiency and reliability of the suggested approach

robust control problems in fluid mechanics abstract in this paper we study a class of robust control problems in fluid mechanics recently proposed by bewley et al physica d 138 3 4 2000 360 using a method of shutyaev russ j numer anal math modell 14 2 1999 137 we provide another proof of the existence and the uniqueness of solutions to the robust control problems under weaker assumptions as compared to those of bewley et al physica d 138 3 4 2000 360 from the numerical point of view the method used in this paper is particularly important since it provides a constructive way to approximate the solutions to these nonlinear control problems

a general framework for robust control in fluid mechanics abstract the application of optimal control theory to complex problems in fluid mechanics has proven to be quite effective when complete state information from high resolution numerical simulations is available p moin t r bewley appl mech rev part 2 47 6 1994 s3 s13 t r bewley p moin r temam j fluid mech 1999 submitted for publication in this approach an iterative optimization algorithm based on the repeated computation of an adjoint field is used to optimize the controls for finite horizon nonlinear flow problems f abergel r temam theoret comput fluid dyn 1 1990 303 325 in order to extend this infinite dimensional optimization approach to control externally disturbed flows in which the controls must be determined based on limited noisy flow measurements alone it is necessary that the controls computed be insensitive to both state disturbances and measurement noise for this reason robust control theory a generalization of optimal control theory has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite dimensional linear and nonlinear problems in fluid mechanics an aim of the present paper is to put such algorithms into a rigorous mathematical framework for it cannot be assumed at the outset that a solution to the infinite dimensional robust control problem even exists in this paper conditions on the initial data the parameters in the cost functional and the regularity of the problem are established such that existence and uniqueness of the solution to the robust control problem can be proven both linear and nonlinear problems are treated and the 2d and 3d nonlinear cases are treated separately in order to get the best possible estimates several generalizations are discussed and an appropriate numerical method is proposed

boundary minimum principles for the unilateral contact problems abstract the aim of the present paper is the derivation of boundary variational principles for the unilateral contact problem using the inequality constrained principles of minimum potential and complementary energy and the equivalent variational inequality formulations we derive first saddle point formulations for the problems using appropriate langrangian functions an elimination technique allows the formulation of two minimum principles on the boundary with respect to the unknown normal displacements and reactions of the contact region respectively it is also shown that these two minimum problems are equivalent to multivalued boundary integral equations involving symmetric operators the theory is illustrated by numerical examples solved both by the fem and the bem

topology recognition and leader election in colored networks topology recognition and leader election are fundamental tasks in distributed computing in networks the first of them requires each node to find a labeled isomorphic copy of the network while the result of the second one consists in a single node adopting the label 1 leader with all other nodes adopting the label 0 and learning a path to the leader we consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors and ports at each node of degree d are arbitrarily numbered 0 1 d 1 colored networks are generalizations both of labeled networks in which nodes have distinct labels and of anonymous networks in which nodes do not have labels all nodes have the same color in colored networks topology recognition and leader election are not always feasible hence we study two more general problems consider a colored network and an input i given to its nodes the aim of the problem top for this colored network and for i is to solve topology recognition in this network if this is possible under input i and to have all nodes answer unsolvable otherwise likewise the aim of the problem le is to solve leader election in this network if this is possible under input i and to have all nodes answer unsolvable otherwise we show that nodes of a network can solve problems top and le if they are given as input i an upper bound k on the number of nodes of a given color called the size of this color on the other hand we show that if the nodes are given an input that does not bound the size of any color then the answer to top and le must be unsolvable even for the class of rings under the assumption that nodes are given an upper bound k on the size of a given color we study the time of solving problems top and le in the local model in which during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations we give an algorithm to solve each of these problems in arbitrary networks in time o k d d log n d where d is the diameter of the network and n is its size we also show that this time is optimal by exhibiting classes of networks in which every algorithm solving problems top or le must use time k d d log n d

global solutions to fractional programming problem with ratio of nonconvex functions this paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in r n by introducing a parameter the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint it is proved that under certain conditions the canonical dual is a concave maximization problem in r 2 that exhibits no duality gap therefore the global optimal solution of the primal problem can be obtained by solving the canonical dual problem

variational principles and convergence of finite element approximations of a holonomic elastic plastic problem it is shown that a boundary value problem based on a holonomic elastic plastic constitutive law may be formulated equivalently as a variational inequality of the second kind a regularised form of the problem is analysed and finite element approximations are considered it is shown that solutions based on finite element approximation of the regularised problem converge

a new fixed point algorithm for hardening plasticity based on non linear mixed variational inequalities moving from the seminal papers of han and reddy we propose a fixed point algorithm for the solution of hardening plasticity two dimensional problems the continuous problem may be classified as a mixed non linear non differentiable variational inequality of the second type and is discretized by means of a truly mixed finite element scheme one of the main peculiarities of our approach is the use of the composite triangular element of johnson and mercier for the approximation of the stress field the non differentiability is coped with via regularization whereas the non linearity is approached with a fixed point iterative strategy numerical results are proposed that investigate the sensitivity of the approach with respect to the mesh size and the regularization parameter e the simplicity of the proposed fixed point scheme with respect to more classical return mapping approaches seems to represent one of the key features of our algorithm copyright 2003 john wiley sons ltd

a study on concave optimization via canonical dual function in this study we find a global minimizer of a concave function over a sphere by introducing a differential equation we obtain the invariant characteristics for a given optimization problem by constructing a canonical dual function we present two theorems concerning the global optimality of an extrema of the optimization problem

solving quasi variational inequalities via their kkt conditions we propose to solve a general quasi variational inequality by using its karush kuhn tucker conditions to this end we use a globally convergent algorithm based on a potential reduction approach we establish global convergence results for many interesting instances of quasi variational inequalities vastly broadening the class of problems that can be solved with theoretical guarantees our numerical testings are very promising and show the practical viability of the approach

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

computing boolean functions on anonymous networks abstract we study the bit complexity of computing boolean functions on anonymous networks let n be the number of nodes the diameter and d the maximal node degree of the network for arbitrary anonymous networks we give a general algorithm of polynomial bit complexity o n 3 d 2 log n for computing any boolean function which is computable on the network this improves upon the previous best known algorithm which was of exponential bit complexity o d n 2 for symmetric functions on arbitrary networks we give an algorithm with bit complexity o n 3 d 2 log 2 n this same algorithm is shown to have even lower bit complexity for a number of specific networks for example tori hypercubes and random regular graphs we also consider the class of distance regular unlabeled networks and show that on such networks symmetric functions can be computed efficiently in o n d log n bits

matrix free methods for the stability and control of boundary layers this paper presents matrix free methods for the stability analysis and control design of high dimensional systems arising from the discretized linearized navier stokes equations the methods are ap

iterative methods for a class of robust control problems in fluid mechanics in this article we consider a class of iterative methods for the numerical solutions of some robust control problems recently studied in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 these methods are based on repeated computations of the state and the adjoint equations using the properties of the control operator we justify these methods and obtain estimates of their convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography using these algorithms are also presented

constrained anisotropic elastic materials in unilateral contact with or without friction we consider time independent problems of linear homogeneous anisotropic elasticiy for materials with internal constraints that are in frictional or frictionless contact with a rigid support

optimal control problems with state constraint governed by navier stokes equations abstract this work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by navier stokes equations with state constraint of pointwise type in 3d strong results in 2d are also given

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

shape optimization in three dimensional contact problems with coulomb friction we study the discretized problem of the shape optimization of three dimensional 3d elastic bodies in unilateral contact the aim is to extend existing results to the case of contact problems obeying the coulomb friction law mathematical modeling of the coulomb friction problem leads to an implicit variational inequality it is shown that for small coefficients of friction the discretized problem with coulomb friction has a unique solution and that this solution is lipschitzian as a function of a control variable describing the shape of the elastic body the 2d case of this problem was studied by the authors in p beremlijski j haslinger m kocvara and j v outrata siam j optim 13 2002 pp 561 587 there we used the so called implicit programming approach combined with the generalized differential calculus of clarke the extension of this technique to the 3d situation is by no means straightforward the main source of difficulties is the nonpolyhedral character of the second order lorentz cone arising in the 3d model to facilitate the computation of the subgradient information needed in the used numerical method we exploit the substantially richer generalized differential calculus of mordukhovich numerical examples illustrate the efficiency and reliability of the suggested approach

convergence analysis of nonmonotone levenberg marquardt algorithms for complementarity problem this paper addresses the convergence of two nonmonotone levenberg marquardt algorithms for nonlinear complementarity problem under some mild assumptions and requiring only the solution of a linear system at each iteration the nonmonotone levenberg marquardt algorithms are shown to be globally convergent

global optimization by canonical dual function in this paper the canonical dual function gao 2004 4 is used to solve a global optimization we find global minimizers by backward differential flows the backward flow is created by the local solution to the initial value problem of an ordinary differential equation some examples and applications are presented

convergence rates of distributed average consensus with stochastic link failures we consider a distributed average consensus algorithm over a network in which communication links fail with independent probability in such stochastic networks convergence is defined in terms of the variance of deviation from average we first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures we then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise we give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks we also present simulation free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability

h control theory of fluid dynamics robust or h control theory has been an expanding subject in recent years because of its wide applications and its close connection to operator theory on hardy spaces we develop an hcontrol theor

sensitivity of inverse advection diffusion reaction to sensor and control a low computational cost tool a two dimensional 2d concentration field may be reconstructed using inverse advection diffusion reaction based on pointwise sensor outputs the studied reconstruction process consists in defining fictitious boundaries and identifying the optimal concentrations on these boundaries that minimize the data misfit the minimization is performed by means of the adjoint method the reconstruction process is observed to fail for some sets of sensor placements therefore in this paper we aim to develop a low computational cost framework that can be used to identify badly placed sensors and to reveal potentially optimal sensor placement from this framework we have derived a sensitivity tool that can predict for a given set of sensors which boundary concentrations are easy or difficult to identify using the inverse method this tool only requires the resolution of an adjoint problem it is compared with the sensitivity to observation method in a 2d water pipe junction with 2000 reynolds number and 1000 peclet number the compared methods do produce similar quantitative and qualitative results

a prange hellinger reissner type finite element formulation for small strain elasto plasticity abstract in this contribution we propose a mixed variational formulation of the prange hellinger reissner type for elasto plasticity at small strains here the displacements and the stresses are interpolated independently which are balanced within the variational functional by the relation of the elastic strains and the partial derivative of the complementary stored energy with respect to the stresses for the elasto plastic material behavior a von mises yield criterion is considered where we restrict ourselves w l o g to linear isotropic hardening in the proposed formulation we enforce the constraints arising from plasticity point wise in contrast to the element wise realization of the plastic return mapping algorithm suggested in simo et al 1989 the performance of the new formulation is demonstrated by the analysis of several benchmark problems here we compare the point wise treatment of elasto plasticity with the original element wise formulation of simo et al 1989 furthermore we derive an algorithmic consistent treatment for plane stress as well as for plane strain condition

multi scale modelling and canonical dual finite element method in phase transitions of solids this paper presents a multi scale model in phase transitions of solid materials with both macro and micro effects this model is governed by a semi linear nonconvex partial differential equation which can be converted into a coupled quadratic mixed variational problem by the canonical dual transformation method the extremality conditions of this variational problem are controlled by a triality theory which reveals the multi scale effects in phase transitions therefore a potentially useful canonical dual finite element method is proposed for the first time to solve the nonconvex variational problems in multi scale phase transitions of solids applications are illustrated results shown that the canonical duality theory developed by the first author in nonconvex mechanics can be used to model complicated physical phenomena and to solve certain difficult nonconvex variational problems in an easy way the canonical dual finite element method brings some new insights into computational mechanics

h boundary control with state feedback the hyperbolic case we solve the h control problem with state feedback for infinite dimensional boundary control systems of hyperbolic type with distributed disturbances

on the construction of optimal mixed finite element methods for the linear elasticity problem the mixed finite element method for the linear elasticity problem is considered we propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement the ideas are applied in some examples

h_ infty boundary control with state feedback the hyperbolic case necessary and sufficient conditions of existence for the h infty control problem associated with infinite dimensional boundary control systems of hyperbolic type are given

on the finite element method for mixed variational inequalities arising in elastoplasticity we analyze the finite element method for a class of mixed variational inequalities of the second kind which arises in elastoplastic problems an abstract variational inequality of which the elast

analysis of some mixed finite element methods for plane elasticity equations we analyze some mixed finite element methods based on rectangular elements for solving the two dimensional elasticity equations we prove error estimates for a method proposed by taylor and zienkiewicz and for some new variants of the known equilibrium methods a numerical example is given demonstrating the performance of the various algorithms considered 1 introduction in the numerical solution of problems of continuum mechanics the stresses are normally of primary interest in the elastic region it is therefore natural to design the numerical algorithms so that the stresses can be obtained directly without first computing the displacements such methods can be derived from the dual variational formulation of the elasticity problem the corresponding finite element algorithms are usually formulated as mixed methods where both the displacements and the stresses are first approximated and the displacements are then eliminated from the discrete equations in many cases the elimination can be rather effectively done using penalty perturbation techniques or their iterative variants cf 3 11 12 the best known finite element methods of the above type are the so called equilibrium methods first proposed by fraejis de veubeke 17 cf also 14 16 18 and analyzed theoretically by johnson and mercier 9 cf also 8 in these methods one uses specific composite elements which allow the equilibrium condi tion between the stresses and the volume load to be satisfied exactly in the case where the volume load is zero

a computational framework for the regularization of adjoint analysis in multiscale pde systems this paper examines the regularization opportunities available in the adjoint analysis and optimization of multiscale pde systems regularization may be introduced into such optimization problems by modifying the form of the evolution equation and the forms of the norms and inner products used to frame the adjoint analysis typically l2 brackets are used in the definition of the cost functional the adjoint operator and the cost functional gradient if instead we adopt the more general sobolev brackets the various fields involved in the adjoint analysis may be made smoother and therefore easier to resolve numerically the present paper identifies several relationships which illustrate how the different regularization options fit together to form a general framework the regularization strategies proposed are exemplified using a id kuramoto sivashinsky forecasting problem and computational examples are provided which exhibit their utility a multiscale preconditioning algorithm is also proposed that noticeably accelerates convergence of the optimization procedure application of the proposed regularization strategies to more complex optimization problems of physical and engineering relevance is also discussed

numerical simulations of a two layer quasi geostrophic equation of the ocean our object in this article is to present some numerical schemes for a two layer quasi geostrophic model of the ocean and to study the stability of these schemes we prove the unconditional stability of our numerical schemes numerical results from a wind driven two layer quasi geostrophic model of the ocean using these schemes are also presented

a mixed hemivariational variational problem and applications abstract we consider an abstract system with lagrange multipliers which consists of a hemivariational inequality and a variational inequality the hemivariational inequality is governed by a hemicontinuous generalized monotone possibly nonlinear operator as well as by a bilinear form this bilinear form also governs the variational inequality we are looking for a pair solution in a subset of a product of two real reflexive banach spaces in order to illustrate the applicability of the abstract results two examples in terms of pdes are delivered each example is related to the weak solvability of a boundary value problem arising in contact mechanics

a primal dual finite element approximation for a nonlocal model in plasticity we study the numerical approximation of a static infinitesimal plasticity model of kinematic hardening with a nonlocal extension here the free energy to be minimized is a combination of the elastic energy and an additional term depending on the curl of the plastic variable first we introduce the stress as dual variable and provide an equivalent primal dual formulation resulting in a local flow rule the discretization is based on curl conforming nedelec elements to obtain optimal a priori estimates the finite element spaces have to satisfy a uniform inf sup condition this can be guaranteed by adding locally defined face and element bubbles second the discrete variational inequality system is reformulated as a nonlinear equality we show that the classical radial return algorithm applied to the mixed inequality formulation is equivalent to a semismooth newton method for the nonlinear system of equations numerical results illustrate the convergence of the applied discretization and the solver

a new mixed formulation for elasticity we propose a new mixed variational formulation for the equations of linear elasticity it does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations

computing on anonymous networks with sense of direction sense of direction refers to a set of global consistency constraints of the local labeling of the edges of a network sense of direction has a large impact on the communication complexity of many distributed problems in this paper we study the impact that sense of direction has on computability and we focus on anonymous networks we establish several results in particular we prove that with weak sense of direction the intuitive knowledge computability hierarchy between levels of a priori structural knowledge collapses a powerful implication is the formal proof that shortest path routing is possible in anonymous networks with sense of direction we prove that weak sense of direction is computationally stronger than topological awareness we also consider several fundamental problems for each we provide a complete characterization of the anonymous networks on which it is computable with sense of direction

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

distinguishing views in symmetric networks the view of a node in a port labeled network is an infinite tree encoding all walks in the network originating from this node we prove that for any integers n d 1 there exists a port labeled network with at most n nodes and diameter at most d which contains a pair of nodes whose infinite views are different but whose views truncated to depth d log n d are identical

well posedness of the fundamental boundary value problems for constrained anisotropic elastic materials we consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well posed for materials fulfilling the condition we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system as an application we determine the orthotropic materials for which the fundamental problems are well posed in terms of their young s moduli shear moduli and poisson ratios finally we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements for a two dimensional constrained material a further reduction to a single scalar equation is outlined

constrained optimal control of navier stokes flow by semismooth newton methods abstract we propose and analyze a semismooth newton type method for the solution of a pointwise constrained optimal control problem governed by the time dependent incompressible navier stokes equations the method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equation we analyze the flow control problem and prove q superlinear convergence of the method in the numerical implementation adjoint techniques are combined with a truncated conjugate gradient method numerical results are presented that support our theoretical results and confirm the viability of the approach

global weak solutions of the fractional landau lifshitz maxwell equation abstract the fractional landau lifshitz maxwell equation is considered in this paper we show the global existence of suitable weak solutions by galerkin method and the vanishing viscosity method the main difficulties in this study are due to the loss of compactness of this system and the fact that the nonlinear term is nonlocal and of the same order of the equation to overcome these difficulties we introduce the commutator estimates and some cancellation properties to this equation which prove to be proper tools in the study of landau lifshitz type equations

bi complementarity and duality a framework in nonlinear equilibria with applications to the contact problem of elastoplastic beam theory abstract nonlinear complementarity problems and variational inequalities in nonlinear equilibrium problems are studied within a unified framework based on the generalized rockafellar tonti diagram a bi complementarity problem with both internal and external nonlinear complementarity conditions is proposed a general duality theory in variational inequality is established and the mosco dual variational inequality has been generalized to the nonsmooth systems in order to study the frictional contact problem of beam theory a two dimensional elastoplastic beam model is proposed the external complementarity condition provides the free boundary of contact region while the internal complementarity condition gives the interface of the elastic plastic regions our results shown that in nonsmooth equilibrium problems the dual approaches are much easier than the primal problems

duality for non convex variational principles abstract this paper treats the construction of dual variational principles for non convex problems using lagrangian methods besides the well known saddle point theory there are dualities involving minimizing the lagrangian in both variables and dualities where one first maximizes and then minimizes the lagrangian in each variable when the primal problem has certain structure an associated canonical lagrangian is defined which leads to the appropriate dual variational principle and to a hamiltonian description the properties of and correspondence between the critical points are analyzed the last five sections are devoted to examples of these dual principles

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal control of fluid dynamic systems with state constraint of pointwise type abstract the aim of this work is to obtain the maximum principle by spike perturbation for the optimal control problem with pointwise type state constraint governed by 3 dimensional fluid dynamic systems

adjoint based iterative method for robust control problems in fluid mechanics in this article we study the convergence of an adjoint based iterative method recently proposed in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 for the numerical solution of a class of nonlinear robust control problems in fluid mechanics under weaker assumptions than those of t tachim medjo numer funct anal optim 23 2002 pp 849 873 we prove the convergence of the algorithm and we obtain an estimate of the convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography are presented to illustrate the method

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher

on the multiplier penalty approach for quasi variational inequalities the multiplier penalty approach is one of the classical methods for the solution of constrained optimization problems this method was generalized to the solution of quasi variational inequalities by pang and fukushima comput manag sci 2 21 56 2005 based on the recent improvements achieved for the multiplier penalty approach for optimization we generalize the method by pang and fukushima for quasi variational inequalities in several respects a we allow to compute inexact kkt points of the resulting subproblems b we improve the existing convergence theory c we investigate some special classes of quasi variational inequalities where the resulting subproblems turn out to be easy to solve some numerical results indicate that the corresponding method works quite reliable in practice

a fundamental limit on the heat flux in the control of incompressible channel flow this paper proves that there are no zero net wall transpiration control strategies that can sustain net heat flux below the laminar level in an incompressible channel flow with constant temperature walls the result represents a fundamental limit on the performance of a controlled nonlinear system as measured by a linear cost function over a broad class of admissible initial conditions and control inputs not a zero sum tradeoff in the frequency domain or time domain both buoyancy effects via the boussinesq approximation and viscous heating effects are accounted for and phenomenological justification for the result is also given the boundedness of solutions of the two way coupled navier stokes energy equations when both buoyancy and viscous heating are accounted for is also discussed and a new proof of existence under an appropriate small data assumption is provided

the reciprocal variational approach to the signorini problem with friction approximation results in this paper a new variational formulation of the signorini problem with friction is given in terms of the contact stresses the method corresponds to the direct integral equation approach in classical elastostatic problems first the displacement and mixed problems are briefly described together with some numerical results next the displacements are eliminated by the use of green s function and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived then the resulting approximation procedure is studied and certain convergence results are proved finally some remarks on the signorini problem with coulomb friction are presented numerical results illustrate the theory