adaptive pole positioning in mimo linear systems by periodic multirate input controllers abstract in this paper the certainty equivalence principle is used to combine the identification method with a control structure derived from the pole placement problem which rely on periodic multirate input controllers the proposed adaptive pole placers contain a sampling mechanism with different sampling period to each system input and rely on a periodically varying controller which suitably modulates the sampled outputs and reference signals of the plant under control such a control strategy allows us to arbitrarily assign the poles of the sampled closed loop system in desired locations and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system and the knowledge of a set of structural indices namely the locally minimum controllability indices of the continuous time plant an indirect adaptive control scheme is derived which estimates the unknown plant parameters and consequently the controller parameters on line from sequential data of the input and outputs of the plant which are recursively updated within the time limit imposed by a fundamental sampling period t0 using the proposed algorithm the controller determination is based on the transformation of the discrete analogous of the system under control to a phase variable canonical form prior to the application of the control design procedure the solution of the problem can then be obtained by a quite simple utilization of the concept of state similarity transformation known indirect adaptive pole placement schemes usually resort to the computation of dynamic controllers through the solution of a polynomial diophantine equation thus introducing high order exogenous dynamics in the control loop moreover in many cases the solution of the diophantine equation for a desired set of closed loop eigenvalues might yield an unstable controller and the overall adaptive pole placement scheme is unstable with unstable compensators because their outputs are unbounded the proposed control strategy avoids these problems since here gain controllers are essentially needed to be designed moreover persistency of excitation and therefore parameter convergence of the continuous time plant is provided without making any assumption either the richness of the reference signals or on the existence of specific convex sets in which the estimated parameters belong or finally on the coprimeness of the polynomials describing the arma model as in known adaptive pole placement schemes

frequency domain adaptive control band wise compensation abstract the idea of band wise compensation is extended to the design of parametric model based controllers given an lti unknown plant and a frequency domain specification one first choses a frequency set where the open loop compensation is required then for each frequency band one represents the plant by a lower first or second order transfer function and designs a band compensator this procedure allows the reduction of a high dimensional problem pole placement lqg etc to a set of lower dimensional problems avoiding the problem of singularity arising in most adaptive control by using the certainty equivalence a numerical example is included to illustrate this idea

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

new recursive parameter estimation algorithms with varying but bounded gain matrix the main disadvantage of the standard recursive weighted least squares algorithm is the unbounded increase in its gain matrix when the covariance vector is not sufficiently rich we propose a general method for updating the gain matrix this allows us to derive many new specific algorithms in which the boundedness of the gain matrix is ensured automatically

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances a persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in 1 in this note we give a direct and simple proof for the case of bounded signals of the result of 1 and show via a counterexample that an assumption on system signals boundedness which does not appear in 1 is necessary when arbitrary unbounded signals are allowable finally we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component

stable hybrid adaptive control this paper examines the asymptotic properties of a hybrid adaptive control scheme while there are many different meanings of the word hybrid control in the literature we are referring to a scheme where the on line parameter estimation and underlying control design are carried out in a discrete time using digital electronics and do not require any analog multiplications or divisions this is of critical importance in practice since analog multipliers dividers are subject to serious drift and offset errors for such hybrid schemes we establish stability and an output tracking property without recourse to persistence of exitation the proof of stability requires a sufficiently fast sampling rate for the discrete time parameter estimation and the underlying control design

persistency of excitation results for structured nonminimal models it is frequently convenient to use specially structured nonminimal models for parameter estimation such as in the case of direct adaptive control where the model is parameterized in terms of the desired control law parameters this is done for example in direct model reference adaptive control and in direct pole assignment adaptive control algorithms it is shown that the parameters appearing in these nonminimal models can be uniquely estimated if and only if a certain design identity has a unique solution the result is used to develop persistency of excitation results for these models

stable adaptive regulation of arbitrary nth order plants this paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single input single output linear time invariant plant which is controllable and observable of known order n and has unknown parameters no further assumptions are made no external probing signal is required

robustness of an adaptive pole placement algorithm in the presence of bounded disturbances and slow time variation of parameters the robustness properties of a specific adaptive pole placement scheme in the presence of bounded disturbances and slow time variation of parameters are studied it is shown that the least squares algorithm used in this scheme retains the global stability of the overall system in the presence of bounded disturbances of small magnitude and slow time variation of system parameters within a compact set

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

direct adaptive control with integral action for nonminimum phase systems this note presents a direct adaptive control scheme for nonminimum phase systems where controller parameters are estimated from the recursive least squares algorithm some additional auxiliary parameters are obtained from the proposed polynomial identity and a local convergence is guaranteed without any extra conditions integral action is incorporated into the adaptive controller to eliminate the steady state error and to satisfy a condition of the unique solution for the polynomial identity as well

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

adaptive stabilization of unstable and nonminimum phase stochastic systems abstract the system under consideration is the discrete time stochastic system a z yn zb z un wn driven by a martingale difference sequence wn where a z are polynomilas in backward shift operator z with unknown coefficients and both a z and b z may be unstable with the purpose of demonstrating theoretical possibility rather than designing a practically applicable control law this paper constructs an adaptive control that stabilizes the system and simultaneously guarantees strong consistency of the least squares estimates for unknown coefficients

brief interval excitation through impulse sequences a technical lemma we present a technical lemma that establishes in a general framework an interval excitation property using a specific class of impulse sequences according to such an interval excitation property an impulse applied within a time interval generates excitation within the same interval this property does not hold for arbitrary exciting sequences the lemma is a unified statement of previous results corresponding to particular choices of the exciting sequence

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

mesh motion techniques for the ale formulation in 3d large deformation problems efficient mesh motion techniques are a key issue to achieve satisfactory results in the arbitrary lagrangian eulerian ale finite element formulation when simulating large deformation problems such as metal forming in the updated lagrangian ul formulation mesh and material movement are attached and an excessive mesh distortion usually appears by uncoupling mesh movement from material movement the ale formulation can relocate the mesh to avoid distortion to facilitate the calculation process the ale operator is split into two steps at each analysis time step ul step where deformation due to loading is calculated without convective terms and eulerian step where mesh motion is applied in this work mesh motion is performed by new nodal relocation methods developed for eight node hexahedral elements which can move internal and boundary nodes improving and concentrating the mesh in critical zones after mesh motion data is transferred from the ul mesh to the relocated mesh using an expansion of stresses in a taylor s series two numerical applications are presented comparing results of ul and ale formulation with results found in the literature copyright 2004 john wiley sons ltd

nonunital spectral triples and metric completeness in unbounded kk theory abstract we consider the general properties of bounded approximate units in non self adjoint operator algebras such algebras arise naturally from the differential structure of spectral triples and unbounded kasparov modules our results allow us to present a unified approach to characterising completeness of spectral metric spaces existence of connections on modules self adjointness and regularity of induced operators on tensor product c modules and the lifting of kasparov products to the unbounded category in particular we prove novel existence results for quasicentral approximate units in non self adjoint operator algebras allowing us to strengthen kasparov s technical theorem and extend it to this realm finally we show that given any two composable kk classes we can find unbounded representatives whose product can be constructed to yield an unbounded representative of the kasparov product

robust pole placement direct adaptive control a pole placement direct adaptive control for not necessarily minimum phase plants is presented which is robust with respect to unmodeled dynamics and bounded disturbances the robustness is achieved by using both a normalized least squares algorithm with dead zone and appropriate nonlinear feedback the resulting closed loop system is shown to be globally stable subject to standard assumptions

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

singular element construction using a mapping technique conformal mapping regularizes in the new plane the singular stress field around the crack tip so conventional finite elements can be used in the transformed plane the inverse mapping of the above elements gives another class of mapped elements the crack tip mapped element is a singular element thus using various elements the parent elements in the mapped plane we obtain an infinity of singular elements the product elements these singular elements are introduced naturally and have no defect as many other singular elements have

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

a method of grid optimization for finite element methods a computationally useful criterion for grid optimization is derived based on a measure of the interpolation error associated with the finite element model the result is intended to be used to improve the quality of finite element solutions by changing the location of the nodes within a fixed number of degrees of freedom examples of the application of the criterion are provided the finite element method has become an important tool of engineering analysis and design much of the popularity of the method is due to the freedom that it allows in the construction of the discretized model it has long been realized however that this freedom must be carefully exercised since the quality of the finite element solution greatly depends on how the discretization is performed several methods have been proposed to improve the discretized model in an iterative manner one such method is presented in this paper a natural way of improving the quality of finite element solutions is to increase the number of degrees of freedom the process is normally performed after an initial solution is already available several schemes have been devised to introduce the new degrees of freedom in a selective manner in order to produce the greatest possible improvement of the previous solution this calls for the definition of criteria to identify the regions of the domain where the finite element approximation is poorer the new degrees of freedom are added in these regions by either increasing the order of polynomial approximation inside elements the so called p method or by subdivision of elements or h method the process is continued until a specified accuracy is achieved the quality of the finite element solution may be improved also by optimizing the disposition of the nodes analysts often rely on their experience to construct grids that make an efficient use of the available degrees of freedom it is also possible to improve the quality of existing meshes iteratively using predefined guidelines for the redistribution of the nodes this paper considers the development of such guidelines

a note on the location of the roots of a polynomial two new theorems and two corollaries are presented which give sufficient conditions for a polynomial to have all its roots inside the unit circle these results unify and extend certain earlier stability tests for discrete time systems the significance of the new results is illustrated by a couple of examples

on the rates of convergence of the finite element method abstract the rate of convergence of the finite element method is a function of the strategy by which the number of degrees of freedom are increased alternative strategies are examined in the light of recent theoretical results and computational experience author

adaptive control with finite time persistency of excitation an adaptive control algorithm for discrete time siso systems is presented the main feature is the fact that it requires an external persistently exciting signal for a finite interval of time in this way tracking of a class of signals such as set points can be achieved within an arbitrarily small error

stability analysis of elliott s direct adaptive pole placement abstract the stability of elliott s direct adaptive pole placement algorithm is examined without the persistency of excitation assumption the conditions for the sequence of estimated parameters that are sufficient for the plant input and the plant output to be bounded are given it is also shown that the modifications proposed in many papers for ensuring the global stability of the indirect adaptive pole placement algorithm can be also applied to the direct one if an auxiliary estimation algorithm for identifying the plant parameters is applied

a novel approach to the explicit pole assignment self tuning controller design a recursive algorithm for the controller design phase of the adaptive pole assignment controller is presented compared to other pole assignment adaptive controllers the computation time to get the controller parameters is drastically reduced and the numerical stability of the controller parameters is increased if persistent excitation is imposed the system poles will be located at the desired position in the steady state and the global stability of the system can be easily obtained

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

on global stability of adaptive systems using an estimator with parameter freezing the results of r kosut and b friedlander 1985 on robust global stability of direct adaptive controllers using an integral adaptation law are extended to the case where the adaptation algorithm includes a parameter freezing mechanism i e the control parameters are held constant at certain time intervals the authors main concern is to propose an estimator with freezing capabilities which preserve the property needed for the global stability analysis namely that it defines a passive operator in an adaptive control context the additional degree of freedom provided by the freezing imposes no further assumptions for global stability a crucial requirement for the analysis is that the number of freezing intervals is finite

robust adaptive control of discrete nominally stabilizable plants this paper presents an indirect pole placement based adaptive control scheme for discrete linear time invariant non necessarily inversely stable and stabilizable systems the scheme is a pole placement type without requiring the plant inverse stability assumption the control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal given by an arbitrary stable filter under a bounded tracking error while ensuring robust closed loop stability the adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and possibly bounded disturbances are proved without assuming the controllability of the modeled plant a normalized least squares algorithm with a relative adaptation dead zone and a posteriori modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit such a property is crucial to solve the stable pole placement problem on the other hand the relative adaptation dead zone is included for robustness purposes under unmodeled dynamics and possibly bounded disturbances

on the parameter convergence properties of a combined vs adaptive control scheme during sliding motion the effects of the use of a variable structure control component within an adaptive control scheme previously proposed by the authors 1992 1995 are investigated in this paper the discontinuous control action does not allow the explicit identification of the coefficients of the filters but only the identification of the so called equivalent control coinciding with the ideal control by coupling the variable structure control strategy with a continuous parameter adjustment mechanism it is instead possible to obtain an equivalent control which during the sliding motion turns out to be equal to a suitably constructed prediction error as long as the parameter adaptation is driven by both the tracking error which vanishes in finite time and the prediction error then the controller parameters prove to be exponentially convergent to the ideal values provided that the reference signal is sufficiently persistently exciting

spectral flow and the unbounded kasparov product abstract we present a fairly general construction of unbounded representatives for the interior kasparov product as a main tool we develop a theory of c 1 connections on operator modules we do not require any smoothness assumptions our unitality assumptions are minimal furthermore we use work of kucerovsky and our recent local global principle for regular operators in hilbert c modules as an application we show that the spectral flow theorem and more generally the index theory of dirac schrodinger operators can be nicely explained in terms of the interior kasparov product

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

a parametrization for model reference adaptive pole placement a new parametrization for a linear system is presented this parametrization is the basis for two approaches to design an adaptive controller for pole placement one approach is based on parameter estimation and requires sufficient excitation while the other the model reference adaptive pole placement uses a reference model and an augmented error it is shown that the two distinct approaches result in identical error terms

discrete adaptive observer with exponential weighting properties an adaptive observer based on the exponentially weighted least squares method is studied and a method of selecting the state variable filters is proposed by this method all the past measurement data are weighted exponentially both with weighting coefficient and the state variable filters the proposed scheme guarantees fast convergence and is very stable

robust adaptive regulation without persistent excitation a globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded disturbances is presented the control strategy is designed for a particular input output representation obtained from the state space representation of the system the leading coefficient of the novel representation is the product of the observability and controllability matrices of the system the controller scheme uses a least squares identification algorithm with a dead zone the dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well this allows the definition of modified estimates which secure well conditioned matrices in the adaptive control law explicit bounds on the plant output are given

representations of completely bounded multilinear operators a deli ion of a completely bounded multilinear operator from one c algebra into another is introduced each completely bounded multilinear operator from a algebra into the algebra of bounded linear operators on a hilbert space is shown to be representable in terms of representations of the c algebra and interlacing operators this result extends wittstock s theorem that decomposes a completely bounded linear operator from a c algebra into an injective c algebra into completely positive linear operators 0 1987 academic press inc stinespring s theorem gives a useful representation for a completely positive linear operator from a c algebra into the algebra bl h for continuous linear operators on a hilbert space h 12 11 using this representation with wittstock s theorem that decomposes a completely bounded linear operator as a finite linear combination of completely positive linear operators 14 lo one obtains a representation of a completely bounded linear operator from a c algebra into bl h our main result is a representation theorem for completely bounded multilinear operators from a c algebra into bl h which generalizes this representation of completely bounded linear operators corollaries give multilinear generalizations of several results known for completely bounded linear operators we shall briefly describe the type of representations to be 151

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

adaptive control for systems with bounded disturbances the authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum and nonminimum phase systems subject to bounded disturbances the parameter estimation scheme is a least squares algorithm with dead zone the dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates in the minimum phase case the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value the projection procedure can also be used to avoid pole zero cancellations in an adaptive pole placement algorithm

direct model reference adaptive pole placement control with exponential weighting properties a parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller this parameterized model is one of the structured nonminimal models the exponentially weighted least squares algorithm is employed to estimate the control parameters the direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model

a serre swan theorem for bundles of bounded geometry abstract the serre swan theorem in differential geometry establishes an equivalence between the category of smooth vector bundles over a smooth compact manifold and the category of finitely generated projective modules over the unital ring of smooth functions this theorem is here generalized to manifolds of bounded geometry in this context it states that the category of hilbert bundles of bounded geometry is equivalent to the category of operator modules over the operator algebra of continuously differentiable functions which vanish at infinity operator modules are generalizations of hilbert c modules where the category of c algebras has been replaced by a more flexible category of involutive algebras of bounded operators the operator algebras operator modules play an important role in the study of the unbounded kasparov product

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

three dimensional adaptive meshing by subdivision and edge collapse in finite deformation dynamic plasticity problems with application to adiabatic shear banding this paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three dimensional finite deformation dynamic plasticity problems mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem the particular mesh refinement strategy adopted is based on rivara s longest edge propagation path lepp bisection algorithm our strategy for mesh coarsening or unrefinement is based on the elimination of elements by edge collapse the convergence characteristics of the method in the presence of strong elastic singularities are tested numerically an application to the three dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method copyright c 2001 john wiley sons ltd

some improvements of the finite element solution for one dimensional problems new algorithms which improve the finite element solution on a fixed mesh of the domain are developed for this objective functions which depend on a positive parameter to be determined are proposed these functions lead to criteria which combine in several ways the residual of the solution the approximation in the euclidean norm of the value of the solution at the nodes and the approximations in the energy and hk norms some aspects of optimality are studied and finally numerical results are given

groups acting properly on bolic spaces and the novikov conjecture we introduce a class of metric spaces which we call bolic they include hyperbolic spaces simply connected complete manifolds of nonpositive curvature euclidean buildings etc we prove the novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a bolic weakly geodesic metric space of bounded geometry

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

adaptive pole placement without excitation probing signals this paper presents an indirect adaptive control scheme for linear systems which may possibly be a nonminimum phase the control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters the system order is the only a priori knowledge required on the plant the adaptive control law is free from singularities in the sense that the estimated plant model is always controllable the singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties the analysis of the stability and the global convergence of a closed loop system is given in detail for both discrete time and continuous time systems

global adaptive pole placement detailed analysis of a first order system this paper studies a deterministic adaptive pole positioning problem for a linear first order system the principal contribution is to specify an adaptive control law which secures global convergence the key conditions required are that an externally available plant input be persistently exciting and that an underbound not necessarily tight be known on the magnitude of the input coupling gain the pattern of the solution to the problem can carry over to high order systems

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

global stability proofs for continuous time indirect adaptive control schemes this note presents a general stability proof for continuous time adaptive control with very general assumptions on the identifier and controller we show that if the exogenous input signal is rich enough then both the identifier and the controller converge to their true values applications of the proof to pole placement design and design based on the factorization approach are discussed

a model study of the quality of a posteriori error estimators for linear elliptic problems error estimation in the interior of patchwise uniform grids of triangles abstract this paper is the first in a series in which we discuss computational methodologies for checking the quality of a posteriori error estimators for finite element approximations of linear elliptic problems in this first part we study the asymptotic properties of error estimators in the interior of patchwise uniform grids of triangles a completely numerical methodology for the analysis of the quality of estimators is presented results from the application of the methodology to the study of the quality of several well known error estimators are reported in subsequent papers we shall discuss methods to study the properties of estimators for meshes of quadrilaterals non uniform grids at boundaries grid interfaces and near singular points

on an h type mesh refinement strategy based on minimization of interpolation errors abstract an adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre assigned limit the estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives applications to several two dimensional model problems are discussed the results indicate that the method can be very effective for both regular problems and problems with strong singularities

on the necessity of block invariance for the convergence of adaptive pole placement algorithm with persistently exciting input global convergence of a number of discrete time adaptive control algorithms with persistently exciting inputs has been established in the literature a key element of the convergence proof is the block invariance feature of the algorithm while the parameters are estimated at every sample the controller parameters remain invariant throughout a block of samples and are updated only at the end of each such block the necessity of this block invariance feature for guaranteeing convergence is established here by a counterexample

a note on indirect adaptive control with stabilizable plant estimates recent on line estimation schemes presented in 1 and 2 suitable for indirect adaptive control applications are extended to general estimation procedures and can be fully justified on the basis of simple arguments

boundedness properties of simple indirect adaptive control systems examining adaptive controllers for a class of first order linear continuous time plants with different estimators and control laws the authors obtain explicit solutions completely describing the nonlinear behavior of the resultant adaptive systems some of these adaptive systems exhibit either finite time escapes or other forms of unbounded behavior due to a loss of stabilizability of the estimated model some fixes for the loss of stabilizability problem are analyzed implications of these results for the general indirect adaptive control case are discussed

error indicators for adaptive mesh refinement in the boundary element method a new approach in this paper a new approach to the development of a posteriori error indicators for the direct boundary element method bem is presented it takes advantage of a unique opportunity offered by the collocation bem that is the possibility of obtaining more than one numerical solution from a given boundary element mesh unlike other approaches the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution in order to test the capability of the proposed error indicators to actually control a selective mesh refinement process an h adaptive refinement strategy is also described together with the criteria for refinement and for the termination of the adaptive process full details on the whole numerical implementation for two dimensional problems are provided in particular there is described a direct method for the numerical evaluation of cauchy principal value integrals numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst

robust adaptive control of discrete time systems using persistent excitation abstract an important result in the robust adaptive control of continuous time systems using the persistent excitation of the reference input was recently given by narendra and annaswamy 1986 ieee trans aut control ac 31 306 315 according to this result the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance the main theorem in narendra and annaswamy 1986 is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real a condition which involves constraints on the relative degree of the plant this paper presents a generalization of the above result to plants of arbitrary relative degree together with the work reported in the earlier paper it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input

goal oriented r adaptivity based on variational arguments in the physical and material spaces abstract the error in a local quantity of interest depends on the error in the corresponding dual solution or generalized green s function this fact is used in dual weighted based goal oriented error estimation techniques and h or p adaptive algorithms this contribution is concerned with a novel approach for goal oriented r adaptivity based on energy minimization principles for the primal and the dual problems the minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals respectively these residuals are error indicators for the discretization error on the current mesh we propose a goal oriented mesh optimization algorithm which ends in an optimized mesh with respect to a chosen quantity of interest by means of selected computational examples we demonstrate the capability of the proposed framework

on optimal triangular meshes for minimizing the gradient error construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed using an appropriate linear coordinate transformation rigorously optimal meshes for controlling the error in quadratic data functions are constructed it is shown that the transformation can be generated as a curvilinear coordinate transformation for anyc data function with nonsingular hessian matrix using this transformation a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed in particular it is shown that equilibration of errors is not a sufficient condition for optimality a comparison of meshes generated under several different criteria is made and their equilibrating properties illustrated

multilinear maps and tensor norms on operator systems abstract we extend work of christensen and sinclair on completely bounded multilinear forms to the case of subspaces of c algebras and obtain a representation theorem and a hahn banach extension theorem for such maps in the second part of the paper the haagerup norms on tensor products are investigated and we obtain new characterizations of these quantities

poincare duality for cuntz pimsner algebras abstract we present a new approach to poincare duality for cuntz pimsner algebras we provide sufficient conditions under which poincare self duality for the coefficient algebra of a hilbert bimodule lifts to poincare self duality for the associated cuntz pimsner algebra with these conditions in hand we can constructively produce fundamental classes in k theory for a wide range of examples we can also produce k homology fundamental classes for the important examples of cuntz krieger algebras following kaminker putnam and crossed products of manifolds by isometries and their non commutative analogues

multi level finite element solution algorithms based on multiplicative and additive correction procedures owing to the failure of the finite element analyst to employ a properly refined computational model the accuracy of preliminary finite element computations is often low thus it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution such a procedure is presented in this paper in this procedure the solution error components are decomposed into two parts one of the error components is assumed to have a long period variation the other component is assumed to have a short period variation multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components the multiplicative and additive correction procedures are implemented using multi level solution techniques

advances on adaptive learning control the case of non minimum phase linear systems abstract the adaptive learning control theory is extended to include the case of non minimum phase time invariant linear systems with uncertain parameters the existence of two approximate solutions to the related output tracking problem is proved exponential tracking of periodic output reference signals is guaranteed along with the exponential estimation of the constant system parameters and of the constant coefficients characterizing the truncated fourier series expansion for the periodic input reference signal

persistent excitation in adaptive systems the importance of the concept of persistent excitation pe in adaptive identification and control has been recognized for some time recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems there is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control hence there is a real need for a deeper understanding of the concept the paper is written with three objectives the first which is tutorial in nature is to provide a general framework for the discussion of persistent excitation and to collect results in the area which are scattered throughout the adaptive literature the second objective is to present some new results related to the uniform asymptotic stability u a s and robustness of adaptive systems and the relation of pe to the stability properties of a class of non linear systems the final objective is to di

an adaptive h r boundary element algorithm for the laplace equation in this paper the combination of the h method mesh refinement and the r method mesh redistribution is employed to solve the laplace equation using the boundary element procedure the key in this approach is to derive on upper bound for the residual associated with the boundary element solution and minimize this bound with respect to an unknown grading function the latter part is achieved by employing techniques of the calculus of variations

stable pole placement direct adaptive control for systems with arbitrary zeros this paper extends a recently proposed adaptive regulation algorithm to the general case where a non zero bounded reference signal is allowed the desired control objectives are asymptotically satisfied in the sense that the estimated plant together with the adaptive controller yield a characteristic polynomial arbitrarily close to the desired one furthermore in the case of a zero reference signal the regulation objective is asymptotically achieved

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces