brief paper a dual optimization procedure for linear quadratic robust control problems this paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system the model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional this problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found although the direct solution of this problem will be discussed briefly the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available

inclusion pairs satisfying eshelby s uniformity property eshelby conjectured that if for a given uniform loading the field inside an inclusion is uniform then the inclusion must be an ellipse or an ellipsoid this conjecture has been proved to be true in two and three dimensions provided that the inclusion is simply connected in this paper we provide an alternative proof of cherepanov s result that an inclusion with two components can be constructed inside which the field is uniform for any given uniform loading for two dimensional conductivity or for antiplane elasticity for planar elasticity we show that the field inside the inclusion pair is uniform for certain loadings and not for others we also show that the polarization tensor associated with the inclusion pair lies on the lower hashin shtrikman bound and hence the conjecture of polya and szego is not true among nonsimply connected inclusions as a consequence we construct a simply connected inclusion which is nothing close to an ellipse but in which the field is almost uniform

robustness and optimality of linear quadratic controller for uncertain systems in this paper we present a linear quadratic design for uncertain systems in state space representation the parameter uncertainty is structured and value bounded we show also that with a controller of this type the optimality of the lq regulator is preserved in the presence of uncertainty

designing stabilizing controllers for uncertain systems using the riccati equation approach a useful technique for determining a linear feedback control law stabilizes an uncertain system is the riccati equation approach of i r petersen and c v hollot 1986 they consider systems with time varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solutions of a riccati equation the technique is extended to include problems with time varying uncertainty in the input connection matrix several examples are included to demonstrate the efficacy of this result

ideal structure of uniform roe algebras of coarse spaces abstract let c u x e be the uniform roe algebra of a coarse space x e with uniformly locally finite coarse structure by a controlled truncation technique we show that the controlled propagation operators in an ideal i of c u x e are exactly the controlled truncations of elements in i it follows that the lattice of the ideals of the uniform roe algebra c u x e in which controlled propagation operators are dense the lattice of the invariant open subsets in the unit space of the groupoid g x introduced by skandalis tu and yu the lattice of the ideals of the coarse structure e and the lattice of the ideals of the coarse space x are mutually isomorphic these lattices also give rise to a type of classification for the ideals of c u x e

on saint venant s principle in finite anti plane shear an energy approach some time ago a version of saint venant s principle was formulated and established for finite elastostatics 1 as was discussed in 1 the issues of concern in connection with saint venant s principle in the nonlinear theory of elasticity are considerably more involved then those arising in the linear theory for a survey of results on saint venant s principle primarily for linear theories see e g 2 5 one difficulty is that the appropriate saint venant solutions need to be carefully characterized see e g 6 13 and the references cited therein secondly in the absence of superposition consideration of self equilibrated end loads is no longer sufficient furthermore instabilities may have to be taken into account also the decay rate for end effects even if exponential might depend on the overall loading as well as on geometry and material characteristics several of these issues have been considered in recent studies in the nonlinear elasticity context 1 14 23 as well as in investigations of spatial decay of solutions of nonlinear elliptic partial differential equations 24 32

on the robustness of lq regulators it is shown that in spite of its large gain and phase margins the linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system may lead to fast unstable closed loop modes

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

on the asymptotic behavior of a minimal surface over a semi infinite strip abstract this paper is concerned with the asymptotic behavior of solutions of the minimal surface equation in two dimensions which vanish on the long sides of a semi infinite strip it is shown that as the axial coordinate x1 tends to infinity such solutions of the minimal surface equation with nonnegative dirichlet data on the end x1 0 decay exponentially in x1 and at precisely the same rate as do harmonic functions the results are relevant to principles of saint venant and phragmen lindelof type

amenability and paradoxicality in semigroups and c algebras abstract we analyze the dichotomy amenable paradoxical in the context of discrete countable unital semigroups and corresponding semigroup rings we consider also folner type characterizations of amenability and give an example of a semigroup whose semigroup ring is algebraically amenable but has no folner sequence in the context of inverse semigroups s we give a characterization of invariant measures on s in the sense of day in terms of two notions domain measurability and localization given a unital representation of s in terms of partial bijections on some set x we define a natural generalization of the uniform roe algebra of a group which we denote by r x we show that the following notions are then equivalent 1 x is domain measurable 2 x is not paradoxical 3 x satisfies the domain folner condition 4 there is an algebraically amenable dense subalgebra of r x 5 r x has an amenable trace 6 r x is not properly infinite and 7 0 1 in the k 0 group of r x we also show that any tracial state on r x is amenable moreover taking into account the localization condition we give several c algebraic characterizations of the amenability of x finally we show that for a certain class of inverse semigroups the quasidiagonality of c r x implies the amenability of x the reverse implication which is a natural generalization of rosenberg s conjecture to this context is false

folner sequences and finite operators abstract this article analyzes folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by williams in the 70s we prove that each essentially hyponormal operator has a proper folner sequence i e an increasing folner sequence of projections strongly converging to 1 in particular any quasinormal any subnormal any hyponormal and any essentially normal operator has a proper folner sequence moreover we show that an operator is finite if and only if it has a proper folner sequence or if it has a non trivial finite dimensional reducing subspace we also analyze the structure of operators which have no folner sequence and give examples of them for this analysis we introduce the notion of strongly non folner operators which are far from finite block reducible operators in some uniform sense and show that this class coincides with the class of non finite operators

boundary optimal control for nonlinear antiplane problems abstract we consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation the contact is modelled with tresca s law of dry friction in which the friction bound is slip dependent the aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target by acting with a control on the boundary of the body the existence of at least one optimal control is proved next we introduce a regularized problem depending on a small parameter and we study the convergence of the optimal controls when tends to zero an optimality condition is delivered for the regularized problem

on the asymptotic behavior of solutions of linear second order boundary value problems on a semi infinite strip this paper treats the asymptotic behavior of solutions of a linear secondorder elliptic partial differential equation defined on a two dimensional semiinfinite strip the equation has divergence form and variable coefficients such equations arise in the theory of steady state heat conduction for inhomogeneous anisotropic materials as well as in the theory of anti plane shear deformations for a linearized inhomogeneous anisotropic elastic solid solutions of such equations that vanish on the long sides of the strip are shown to satisfy a theorem of phragmen lindelof type providing estimates for the rate of growth or decay which are optimal for the case of constant coefficients the results are illustrated by several examples the estimates obtained in this paper can be used to assess the influence of inhomogeneity and anisotropy on the decay of end effects arising in connection with saint venant s principle

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

solvability of dynamic antiplane frictional contact problems for viscoelastic cylinders abstract we study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation the process is dynamic the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition we derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field then we prove the existence of a weak solution to the model the proof is based on an abstract result for second order evolutionary inclusions in banach spaces also we prove that under additional assumptions the weak solution to the model is unique we complete our results with concrete examples of friction laws for which our results are valid

saint venant end effects for plane deformations of linear piezoelectric solids the recent developments in smart structures technology have stimulated renewed interest in the fundamental theory and applications of linear piezoelectricity in this paper we investigate the decay of saint venant end effects for plane deformations of a piezoelectric semi infinite strip first of all we develop the theory of plane deformations for a general anisotropic linear piezoelectric solid just as in the mechanical case not all linear homogeneous anisotropic piezoelectric cylindrical solids will sustain a non trivial state of plane deformation the governing system of four second order partial differential equations for the two in plane displacements and electric potential are overdetermined in general sufficient conditions on the elastic and piezoelectric constants are established that do allow for a state of plane deformation the resulting traction boundary value problem with prescribed surface charge is an oblique derivative boundary value problem for a coupled elliptic system of three second order partial differential equations the special case of a piezoelectric material transversely isotropic about the poling axis is then considered thus the results are valid for the hexagonal crystal class 6mm the geometry is then specialized to be a two dimensional semi infinite strip and the poling axis is the axis transverse to the longitudinal direction we consider such a strip with sides traction free subject to zero surface charge and self equilibrated conditions at the end and with tractions and surface charge assumed to decay to zero as the axial variable tends to infinity a formulation of the problem in terms of an airy type stress function and an induction function is adopted the governing partial differential equations are a coupled system of a fourth and third order equation for these two functions on seeking solutions that exponentially decay in the axial direction one obtains an eigenvalue problem for a coupled system of fourth and second order ordinary differential equations this problem is the piezoelectric analog of the well known eigenvalue problem arising in the case of an anisotropic elastic strip it is shown that the problem can be uncoupled to an eigenvalue problem for a single sixth order ordinary differential equation with complex eigenvalues characterized as roots of transcendental equations governing symmetric and anti symmetric deformations and electric fields assuming completeness of the eigenfunctions the rate of decay of end effects is then given by the real part of the eigenvalue with smallest positive real part numerical results are given for pzt 5h pzt 5 pzt 4 and ceramic b it is shown that end effects for plane deformations of these piezoceramics penetrate further into the strip than their counterparts for purely elastic isotropic materials

analysis of a dynamic contact problem for electro viscoelastic cylinders abstract we consider a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation the process is mechanically dynamic and electrically static the material behavior is described with a linearly electro viscoelastic constitutive law the contact is frictional and the foundation is assumed to be electrically conductive both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions we derive a variational formulation of the problem which is of the form of a system coupling a second order hemivariational inequality for the displacement field with a time dependent hemivariational inequality for the electric potential field then we prove the existence of a unique weak solution to the model the proof is based on abstract results for second order evolutionary inclusions in banach spaces finally we present concrete examples of friction laws and electrical conductivity conditions for which our result is valid

finite horizon optimal control with pointwise cost functional a finite horizon discrete time optimal control problem is proposed and analyzed where the uncertainty affecting the system is modeled as an input variable disturbance that at any time instant is only known to belong to a given set the functional to be minimized is the highest instantaneous cost that may occur under the worst possible combination of disturbances a dynamic programming algoritm is proposed for the solution two simple but relevant examples of application the target set reachability problem and the control of a storage system are presented

a quasi local characterisation of lp roe algebras abstract very recently spakula and tikuisis provide a new characterisation of uniform roe algebras via quasi locality when the underlying metric spaces have straight finite decomposition complexity in this paper we improve their method to deal with the l p version of uniform roe algebras for any p 1 due to the lack of reflexivity on l 1 spaces some extra work is required for the case of p 1

global regular solutions for the dynamic antiplane shear problem in nonlinear viscoelasticity here a is the two dimensional laplacian g is a scalar function and uo u f are given functions equation 1 occurs in the description of antiplane shear motions of certain viscoelastic solids for background material the reader is referred to 20 let y t denote the position of a particle with reference position at time t and consider an infinite column 2 r consisting of a homogeneous isotropic incompressible solid with the semilinear constitutive equation

uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation multiple elastic inclusions with uniform internal stress fields in an infinite elastic matrix are constructed under given uniform remote in plane loadings the method is based on the sufficient and necessary condition imposed on the boundary value of a holomorphic function that guarantees the existence of the holomorphic function in a multiply connected region the unknown shape of each of the multiple inclusions is characterized by a conformal mapping this work focuses on a major large class of multiple inclusions characterized by a simple condition that covers and is much beyond the known related results reported in previous works extensive examples of multiple inclusions with or without geometrical symmetry are shown our results showed that the inclusion shapes obtained for the uniformity of internal stress fields are independent of the remote loading only when all of the multiple inclusions have the same shear modulus as that of the matrix moreover specific conditions are derived on remote loading elastic constants of the inclusions and uniform internal stress fields which guarantee the existence of multiple symmetric inclusions or multiple rotationally symmetrical inclusions with uniform internal stress fields

two variational inequality problems for the wave equation in a half space an important problem in the theory of elasticity is the dynamic planestrain type crack problem the subject of dynamic cracks in solids has received much attention in the past two decades see freund 4 poruchikov 11 and walton and herrmann 17 most of the work done however has not explicitly imposed the physical condition that the two faces of the crack do not interpenetrate this type of condition is known as a unilateral constraint imposing this type of condition amounts to imposing certain inequalities on the displacements or tractions to the problem problems in elasticity involving the contact of two elastic bodies give another example of problems with unilateral constraints imposed on boundaries see kikuchi and oden 7 a particular case of a contact problem is the punch problem which consists of a rigid body the punch indenting an elastic halfspace while static contact problems have been studied extensively see kikuchi and oden 7 the case of dynamic contact problems has not been studied nearly as much there is no work to our knowledge on the dynamic crack problem taking into account the condition of noninterpenetration the mathematical formulation of the dynamic crack and punch problems with unilateral constraints involve the dynamic equations of linear elasticity in this paper we consider two simplified dynamic problems with unilateral constraints obtained when the elasticity equations are replaced by a single wave equation although these simplified problems have no physical meaning we will still call them the crack and punch problems respectively

an algorithm for simultaneous stabilization using decentralized constant gain output feedback an algorithm which solves numerically the simultaneous stabilization problem using a constant gain decentralized control law is presented the algorithm is determined from the necessary conditions for minimizing an optimal control problem the optimal control problem consists of n plant models each with its own cost function the costs are summed to create an average cost function and equality constraints are added to yield the decentralized control structure the algorithm can start with any stabilizing full state feedback gain for each model and will converge to the optimal constant feedback gain for all models assuming a solution exists examples of the algorithm are given for kharitonov synthesis and optimal gain scheduled control law synthesis using output feedback

an energy method approach to the problem of elastic strip we analyze a thin elastic homogeneous strip under a smooth load and several different types of boundary conditions the strip is assumed to obey either a plane strain or a plane stress type deformation of linear theory of elasticity we characterize the 2d solution and consider dimension reduction of arbitrary order n both interior and global energy estimates for the reduction error are derived

the optimal projection equations with petersen hollot bounds robust stability and performance via fixed order dynamic compensation for systems with structured real valued parameter uncertainty a feedback control design problem involving structured real valued plant parameter uncertainties is considered a quadratic lyapunov bound suggested by recent work of i r petersen and c v hollot 1986 is utilized in conjunction with the guaranteed cost approach of s s l chang and t k c peng 1972 to guarantee robust stability with robust performance bound necessary conditions that generalize the optimal projection equations for fixed order dynamic compensation are used to characterize the controller that minimizes the performance bound the design equations thus effectively serve as sufficient conditions for synthesizing dynamic output feedback controllers that provide robust stability and performance

the stress field in a pulled cork and some subtle points in the semi inverse method of nonlinear elasticity in an attempt to describe cork pulling we model a cork as an incompressible rubber like material and consider that it is subject to a helical shear deformation superimposed onto a shrink fit and a simple torsion it turns out that this deformation field provides an insight into the possible appearance of secondary deformation fields for special classes of materials we also find that these latent deformation fields are woken up by normal stress differences we present some explicit examples based on the neo hookean the generalized neo hookean and the mooney rivlin forms of the strain energy density using the simple exact solution found in the neo hookean case we conjecture that it is advantageous to accompany the usual vertical axial force by a twisting moment in order to extrude a cork from the neck of a bottle efficiently then we analyse departures from the neo hookean behaviour by exact and asymptotic analyses in that process we are able to give an elegant and analytic example of secondary or latent deformations in the framework of nonlinear elasticity

a riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems this paper presents a procedure for designing a full state observer and feedback control law which will stabilize a given uncertain linear system the uncertain linear systems under consideration are described by state equations which depend on uncertain parameters these uncertain parameters may be time varying their values however are constrained to lie within known compact bounding sets the design procedure involves solving two algebraic riccati equations a feature of the design procedure presented is the fact that it reduces to the standard lqg design procedure if the system contains no uncertain parameters

maximal and reduced roe algebras of coarsely embeddable spaces in 7 gong wang and yu introduced a maximal or universal version of the roe c algebra associated to a metric space we study the relationship between this maximal roe algebra and the usual version in both the uniform and non uniform cases the main result is that if a uniformly discrete bounded geometry metric space x coarsely embeds into a hilbert space then the canonical map between the maximal and usual uniform roe algebras induces an isomorphism on k theory we also give a simple proof that if x has property a then the maximal and usual uniform roe algebras are the same these two results are natural coarse geometric analogues of certain well known implications of a t menability and amenability for group c algebras the techniques used are e theoretic building on work of higson kasparov and trout 11 12 and yu 28

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

correspondence comments on robust optimal parametric lq control with a guaranteed cost bound and applications abstract in a recent paper hu and loh 1989 addressed the problem of designing robust controllers with guaranteed bounds on a given performance index the purpose of this note is to point out several incorrect results presented there

box spaces group extensions and coarse embeddings into hilbert space abstract we investigate how coarse embeddability of box spaces into hilbert space behaves under group extensions in particular we prove a result which implies that a semidirect product of a finitely generated free group by a finitely generated residually finite amenable group has a box space which coarsely embeds into hilbert space this provides a new class of examples of metric spaces with bounded geometry which coarsely embed into hilbert space but do not have property a generalising the example of arzhantseva guentner and spakula

optimal design of robust controllers for uncertain discrete time systems this paper presents a fast algorithm for the design of robust output feedback controllers for linear uncertain discrete time systems the algorithm utilizes a version of the broyden fletcher goldfarb shanno bfgs optimization method of conjugate directions and minimizes a performance index that includes a linear quadratic regulator lqr term to optimize performance and a robustness term based on recently developed bounds the minimization of only the robustness term which corresponds to the maximization of the uncertainty bound is also studied the case of unstructured perturbations in a has been the only one studied in the robust controller design literature the present algorithm introduces a unified approach to both cases of unstructured and structured perturbations in the matrices of a state space model for the special case of unstructured perturbations in a only the algorithm is shown to improve considerably the existing unstructured uncertainty bound several examples including an aircraft cont

the amenability of affine algebras abstract we introduce the notion of amenability for affine algebras we characterize amenability by folner sequences paradoxicality and the existence of finitely invariant dimension measures then we extend the results of rowen on ranks from affine algebras of subexponential growth to amenable affine algebras

anti plane shear deformations in linear and nonlinear solid mechanics the intent of this expository paper is to draw the attention of the applied mathematics community to an interesting two dimensional mathematical model arising in solid mechanics involving a single second order linear or quasi linear partial differential equation this model has the virtue of relative mathematical simplicity without loss of essential physical relevance anti plane shear deformations are one of the simplest classes of deformations that solids can undergo in anti plane shear or longitudinal shear generalized shear of a cylindrical body the displacement is parallel to the generators of the cylinder and is independent of the axial coordinate thus anti plane shear with just a single scalar axial displacement field may be viewed as complementary to the more complicated yet perhaps more familiar plane strain deformation with its two in plane displacements in recent years considerable attention has been paid to the analysis of anti plane shear deformations within the context of variou

robust stability and performance of systems with structured and bounded uncertainties an extension of the guaranteed cost control approach a method is presented for designing a full state feedback linear control law that will ensure the robust stability and performance of a given linear uncertain system the systems under consideration are described by state equations that depend on uncertain parameters these uncertain parameters may be time varying their values are constrained to lie within known compact bounding sets the method is based on the guaranteed cost control concept of chang and peng 1972 the controller gains result from the solution of a riccati equation in which the weighting matrices depend on the uncertainty bounds sufficient conditions for the existence of a solution arise from the standard lqg control theory

matrix criterion robust linear quadratic control problem this paper studies a robust linear quadratic lq control problem with multiple quadratic performance indices specifically a linear model is assumed to be available for each of a prespecified set of operating points of a system a vector valued quadratic control performance index is given at each operating point it is then desired to find the constant feedback gains of a linear controller to obtain satisfactory control performance over all the operating points this is a realistic case involving the minimization of a vector criterion of vector criteria i e a matrix valued criterion the matrix valued criterion gives insight into standard robust lq design and leads to several related vector minimization problems and to natural procedures for computing a satisfactory non inferior solution to the matrix valued minimization problem

simultaneous control of linear systems by state feedback in this paper a new method for finding a state feedback matrix in order to control simultaneously a collection of linear systems of the same size by using similarity operations is presented for stabilization of all the systems it is necessary that the eigenvalues of the closed loop systems lie inside a specified region in the left hand side of the complex plane this aim is achieved by solving linear and nonlinear parametric systems of equations using nonlinear programming the presented method is implemented in two examples and the results are verified in view of the norm of the state feedback matrix and stabilizability

amenability and uniform roe algebras abstract amenability for groups can be extended to metric spaces algebras over commutative fields and c algebras by adapting the notion of folner nets in the present article we investigate the close ties among these extensions and show that these three pictures unify in the context of the uniform roe algebra c u x over a metric space x d with bounded geometry in particular we show that the following conditions are equivalent 1 x d is amenable 2 the translation algebra generating c u x is algebraically amenable 3 c u x has a tracial state 4 c u x is not properly infinite 5 1 0 0 0 in the k 0 group k 0 c u x 6 c u x does not contain the leavitt algebra as a unital subalgebra 7 c u x is a folner c algebra in the sense that it admits a net of unital completely positive maps into matrices which is asymptotically multiplicative in the normalized trace norm we also show that every possible tracial state of the uniform roe algebra c u x is amenable

quasidiagonal traces on exact c algebras abstract recently it was proved by tikuisis white and winter that any faithful trace on a separable nuclear c algebra in the uct class is quasidiagonal building on their work we generalise the result and show that any faithful amenable trace on a separable exact c algebra in the uct class is quasidiagonal we also prove that any amenable trace on a separable exact quasidiagonal c algebra in the uct class is quasidiagonal

elliptic equations with measurable nonlinearities in nonsmooth domains abstract we study elliptic equations with measurable nonlinearities in nonsmooth domains we establish an optimal global w 1 p estimate under the condition that the associated nonlinearity is allowed to be merely measurable in one variable but has a sufficiently small bmo semi norm in the other variables while the underlying domain is sufficiently flat in the reifenberg sense that the boundary of the domain is locally trapped between two narrow strips

aperiodic tilings positive scalar curvature and amenability of spaces the object of this paper is to begin a geometric study of noncompact spaces whose local structure has bounded complexity manifolds of this sort arise as leaves of foliations of compact manifolds and as their universal covers we shall introduce a coarse homology theory using chains of bounded complexity and study some of its first properties the most interesting result characterizes when h uf x vanishes as an analogue and strengthening of f0lner s amenability criterion for groups in terms of isoperimetric inequalities see 4 one can view this result as producing a successful infinite ponzi scheme on any nonamenable space each point with only finite resources gives to some of its neighbors some of these resources yet receives more from the remaining neighbors as one can imagine this is useful for eliminating obstructions on noncompact spaces this has a number of applications we present two of them the first produces tilings that are unbalanced on any nonamenable polyhedron unbalanced tilings are automatically aperiodic and this gives many examples of sets of tiles that tile only aperiodically unfortunately imbalance is a particularly unsubtle reason for aperiodicity so that the aperiodic tilings of euclidean space penrose tilings are necessarily not accessible to our method on the other hand most other simply connected noncompact symmetric spaces even have unbalanced tilings using our criterion the second application regards characteristic numbers of manifolds whose universal covers have positive scalar curvature we prove a converse to a theorem of roe we show that for any nonamenable group f one can find a spin manifold with fundamental group f with nonzero a genus whose universal cover has a uniformly positive scalar curvature metric of bounded geometry in the natural strict quasi isometry class

quasidiagonality of nuclear c algebras we prove that faithful traces on separable and nuclear c algebras in the uct class are quasidiagonal this has a number of consequences firstly by results of many hands the classification of unital separable simple and nuclear c algebras of finite nuclear dimension which satisfy the uct is now complete secondly our result links the finite to the general version of the toms winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension finally we confirm the rosenberg conjecture discrete amenable groups have quasidiagonal c algebras

weak solutions for nonlinear antiplane problems leading to hemivariational inequalities abstract we analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation for static processes under the small deformation hypothesis based on the knaster kuratowski mazurkiewicz technique in the theory of the hemivariational inequalities we prove that the model has at least one weak solution moreover we present several examples of constitutive laws and friction laws for which our theoretical results are valid finally we comment on the conditions which guarantee the uniqueness of the solution

linear programming approach to nonconvex variational problems in nonconvex optimization problems in particular in nonconvex variational problems there usually does not exist any classical solution but only generalized solutions which involve young measures in this paper after reviewing briefly the relaxation theory for such problems an iterative scheme leading to a sequential linear programming slp scheme is introduced and its convergence is proved by a banach fixed point technique then an approximation scheme is proposed and analyzed and calculations of an illustrative 2d broken extremal example are presented

the design of servomechanism controllers for uncertain plants abstract the design of multivariable servomechanism controllers is considered here for plants whose parameters are uncertain or perturbed within a cone bounding criterion the solution comes from a controller design problem as an lq optimal control problem in which the gain matrices result in a quadratic performance upper bound similar to that described by gilman and rhodes 1976 which depends on the uncertainty under conditions on the nominal plant and on the uncertainty a resulting linear time invariant controller is guaranteed to achieve the objectives of robust tracking and regulation with closed loop stability

leavitt r algebras over countable graphs embed into l2 r abstract for a commutative ring r with unit we show that the leavitt path algebra l r e of a graph e embeds into l 2 r precisely when e is countable before proving this result we prove a generalised cuntz krieger uniqueness theorem for leavitt path algebras over r

spatial and continuous dependence estimates in linear viscoelasticity in this paper we consider the problem determined by the anti plane shear dynamic deformations for the linear theory of viscoelasticity first we prove existence of solutions of the problem determined in a semi infinite strip then we show that the rate of decay of the end effects in this problem is faster than that known for the laplace equation in the last section we study the influence of the mass density on the decay of end effects

guaranteed cost control of tracking problems with large plant uncertainty abstract a linear tracking problem with large plant uncertainty is studied the guaranteed cost method is applied to design the controller so that the system responses follow the reference model a modified riccati matrix equation is obtained from the numerical simulation of a second order system it is shown that the present method provides good performance in both tracking property and sensitivity immunity

the first locking free plane elastic finite element historia mathematica abstract we consider a two parameter family of conforming bilinear quadrilateral finite element formulations for plane elastic problems with homogeneous isotropic material the approach taken earlier by belytschko et al is based on numerical strain reductions and stabilization and may be viewed as an extension reformulation of the classical turner rectangle of 1956 we present the full theory of this approach in the energy norm framework the analysis is based on splitting the error in two orthogonal components the approximation error and the equilibrium or consistency error the theory covers the full parametric dependence of the plane elastic problem emphasizing in particular the case of beam like bodies with arbitrarily small aspect ratios the theory shows that depending on the mesh the stabilized reduced strain formulation is capable of avoiding some or even all the parametric locking effects characteristic to 2d elastic problems we analyze first these locking effects in the context of standard bilinear fem

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

robust controller synthesis using the maximum entropy design equations this note presents an application of the optimality conditions obtained in 1 for dynamic compensation in the presence of state control and measurement dependent noise by solving these equations which represent a fundamental generalization of standard steady state lqg theory a series of increasingly robust control designs is obtained for the example considered in 2

comments on robust stability and performance of system with structured and bounded uncertainties an extension of the guaranteed cost control approach recently kosmidou 1990 addressed the problem of designing a full state feedback linear control law that will ensure the robust stability and guaranteed bound on a given performance index the purpose of this note is to point out that the main results presented there are incorrect

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

efficient algorithms for problems with friction in this paper a nonconforming discretization method for the frictional contact between two bodies subjected to antiplane shear deformation is considered the method is based on a mixed variational formulation where dual basis functions are used for the discretization of the lagrange multiplier under some regularity assumptions on the solution an optimal a priori error estimate is obtained to solve the discrete nonlinear problem an inexact primal dual active set strategy is introduced finally numerical examples confirming the theoretical result for the a priori error estimate and illustrating the performance of the algorithm are presented the results can easily be generalized to the case of coulomb friction for this case a numerical example is given

generalization of the zabolotskaya equation to all incompressible isotropic elastic solids ep and gs have been partially supported for this work by the gruppo nazionale per la fisica matematica gnfm of the italian non profit research institution istituto nazionale di alta matematica francesco severi indam and the prin2017 project mathematics of active materials from mechanobiology to smart devices funded by the italian ministry of education universities and research miur we are most grateful to gianmarco pinton and david esp indola for sharing the experimental data used to generate figure 1

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

multiple models multiplicative noise and linear quadratic control algorithmic aspects numerical solution of certain linear quadratic lq control problems for robust design is addressed an iterative method is suggested and analysed for solving a minimax multiple model lq control problem a convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants furthermore a convergent iterative method is proposed for solving the maximum entropy parametric lq control problem with multiplicative noise

generalized riccati equations associated with guaranteed cost control an overview of solutions and features robust control of dynamic linear systems with parametric uncertainties is based on the solution of generalized riccati equations i e riccati equations with additional terms depending on the uncertainties in particular guaranteed cost controller design requires the existence and computation of positive definite solutions of such equations in the present paper an overview of the riccati equations arising in guaranteed cost control approaches is presented it is shown that different uncertainty descriptions and the corresponding upper bounding functions lead to various forms of generalized riccati equations that may admit either analytical or computational positive definite solutions the associated closed loop systems robustness features are also discussed

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

asymptotic analysis of an end loaded transversely isotropic elastic semi infinite strip weak in shear abstract we use linear elasticity to study a transversely isotropic or specially orthotropic semiinfinite slab in plane strain free of traction on its faces and at infinity and subject to edge loads or displacements that produce stresses and displacements that decay in the axial direction the governing equations which are identical to those for a strip in plane stress free of traction on its long sides and at infinity and subject to tractions or displacements on its short side are reduced in the standard way to a fourth order partial differential equation with boundary conditions for a dimensionless airy stress function we study the asymptotic solutions to this equation for four sets of end conditions traction mixed two displacement as g3 the ratio of the shear modulus to the geometric mean of the axial and transverse extensional moduli approaches zero in all cases the solutions for consist of a wide boundary layer that decays slowly in the axial direction over a distance that is long compared to the width of the strip plus a narrow boundary layer that decays rapidly in the axial direction over a distance that is short compared to the width of the strip moreover we find that the narrow boundary layer has a sinuous part that varies rapidly in the transverse direction but which to lowest order does not enter the boundary conditions nor affect the transverse normal stress or the displacements because the exact biorthogonality condition for the cigenfunctions associated with can be replaced by simpler orthogonality conditions in the limit as e b 0 we are able to obtain to lowest order explicit formulae for the coeflicients in the eigenfunction expansions of for the four different end conditions