robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

a general class of sliding surface for sliding mode control in the conventional sliding mode control the relative degree of the chosen sliding surface is usually one this paper addresses a general class of sliding surface whose relative degree is no longer restricted to one we show that when the relative degree is more than two it is inevitable that there will exist a limit cycle for the nonlinear sign function and for the case of relative degree two the system possesses poor phase margin however these disadvantages can be remedied remarkably by smoothing out the control nonlinearity in a suitable boundary layer with a saturation function that ensures asymptotic stability of the overall system

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

learning variable structure control approaches for repeatable tracking control tasks for the finite period tracking control task repeatable over iterations uniformly bounded learning control is synthesized into variable structure control to approximate the equivalent control and to realize perfect tracking

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

the static condensation reduced basis element method for a mixed mean conjugate heat exchanger model we propose a new approach for the simulation of conjugate heat exchangers first we introduce a dimensionality reduced mathematical model for conjugate fluid solid heat transfer in the fluid channels we consider a mixed mean temperature defined on one dimensional filaments in the solid we consider a detailed partial differential equation conduction representation we then propose a petrov galerkin finite element fe numerical approximation which provides suitable stability and accuracy for our mathematical model we next apply the static condensation reduced basis element scrbe method a domain synthesis approach with parametric model order reduction at the intradomain level to populate a schur complement at the interdomain level we first build a library of components each corresponding to a subdomain with a simple fluid channel geometry for each component we prepare petrov galerkin reduced basis bubble approximations and error bounds we then assemble the system equations by static con

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

remarks on proficient groups if a finite group g has a presentation with d generators and r relations it is well known that r d is at least the rank of the schur multiplier of g a presentation is called efficient if equality holds there is an analogous definition for proficient profinite presentations we show that many perfect groups have proficient presentations moreover we prove that infinitely many alternating groups symmetric groups and their double covers have proficient presentations

robust tracking in nonlinear systems a nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system the tracking error is measured by a general function of system state and the input command the controller is robust in the sense that the tracking error is ultimately bounded in the presence of modeling errors free parameters which affect the form of the controller allow flexibility in determining such factors as the size of the ultimate bound the rate of error decay excursion of the control conditions on the class of modeling errors and the level of system gain restrictive assumptions on the structure of the model and the modeling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature these assumptions hold for robotic manipulators this application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature

a new certification framework for the port reduced static condensation reduced basis element method abstract in this paper we introduce a new certification framework for the port reduced static condensation reduced basis element pr scrbe method which has been developed for the simulation of large component based applications such as bridges or acoustic waveguides in an offline computational stage we construct a library of interoperable parametrized reference components in the subsequent online stage we instantiate and connect the components at the interfaces ports to form a system of components to compute a truth finite element approximation of the say coercive elliptic partial differential equation on the component based system we use a domain decomposition approach for an efficient simulation we employ two different types of model reduction a reduced basis rb approximation within the interior of the component huynh et al 2013 and empirical port reduction eftang and patera 2013 on the ports where the components connect we demonstrate the well posedness of the pr scrbe approximation and introduce a new certification framework to assess the quality of the port reduction we use conservative fluxes we adapt the standard estimators from rb methods to the scrbe setting to derive an a posteriori error estimator for the rb error contribution in order to combine the a posteriori estimators for both error contributions and derive a rigorous a posteriori error estimator for pr scrbe we adapt techniques from multi scale methods and component mode synthesis finally we prove that the effectivity of the derived estimator can be bounded we provide numerical experiments for heat conduction and linear elasticity to show that the derived a posteriori error estimator provides an effective estimator moreover we demonstrate the applicability of the introduced certification framework by analyzing the computational online costs

proper generalized decomposition solutions within a domain decomposition strategy this is the peer reviewed version of the following article huerta antonio enrique nadal and francisco chinesta 2018 proper generalized decomposition solutions within a domain decomposition strategy international journal for numerical methods in engineering 113 13 wiley 1972 94 doi 10 1002 nme 5729 which has been published in final form at https doi org 10 1002 nme 5729 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

a high performance parallel implementation of the certified reduced basis method abstract the certified reduced basis method herein rb method is a popular approach for model reduction of parametrized partial differential equations in this paper we introduce new techniques that are required to efficiently implement the offline construction stage of the rb method on high performance parallel supercomputers this enables us to generate certified rb models for large scale three dimensional problems that can be evaluated on standard workstations and other thin computing resources with speedup of many orders of magnitude compared to the corresponding full order model we use our implementation to perform detailed numerical studies for two computationally expensive model problems a natural convection fluid flow problem and a many parameter heat transfer problem in the heat transfer problem we exploit the computational efficiency of the rb method to perform a detailed study of snapshot selection in the greedy algorithm and we also examine statistics of the output sensitivity derivatives to obtain a global view of the relative importance of the parameters

robust adaptive control for a class of mimo nonlinear systems by state and output feedback in this technical note high dimensional integral lyapunov functions are introduced for a class of mimo nonlinear systems with unknown nonlinearities first adaptive state feedback control is presented based on the integral lyapunov function when only the output is measurable by using a high gain observer to estimate the derivative of the system output adaptive output feedback control is also derived the proposed control scheme provides a general approach to stabilize the mimo plant without any restrictive assumptions the control is continuous and ensures closed loop stability and convergence of the tracking error to a small residual set the size of the tracking error at steady state can be specified a priori and guaranteed by choosing the design parameters

practical stabilization of a class of uncertain nonlinear systems abstract in this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed the proposed control algorithm reflects the two level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point

incorporation of linear multipoint constraints in domain decomposition based iterative solvers part ii blending feti dp and mortar methods and assembling floating substructures two approaches are presented for extending the feti dp domain decomposition based iterative method to the solution of problems with linear multipoint constraints lmpcs both cases of arbitrary lmpcs and lmpcs generated by the mortar method for enforcing a weak continuity of the solution across non matching finite element interfaces are considered in the first approach the lmpcs are addressed during the preconditioning step but enforced only at convergence in the second approach the lmpcs are enforced at each iteration through the solution of an auxiliary coarse problem both extended feti dp solvers are benchmarked on a parallel processor for a wide range of constrained structural mechanics problems the obtained results reveal that both solvers are numerically scalable and complement each other from the memory and cpu performance viewpoints

robust output tracking control of nonlinear mimo systems via sliding mode technique abstract the robust output tracking control problem of general nonlinear multi input multi output mimo systems is discussed the robustness against parameter uncertainties and unknown disturbances is considered a second order sliding mode control smc technique is used to establish the desired tracking input output i o linearization relative degree minimum phase and matching condition concepts are reviewed some earlier smc strategies which are restricted to the systems in canonical form are extended to a much broader class of nonlinear dynamics it is also shown that for unperturbed dynamics the sliding phase of the smc applications have a direct correspondence to the i o linearization operations interesting parametric flexibilities emanate within the formation of the second order smc designating the s dynamics and the error dynamics segments as frequency domain filters however a critical impasse is posed in the off line selections of the design parameters a set of example cases is presented for a spacecraft attitude control problem these examples manifest that the proposed control strategy is tunable to a desired response despite the disturbances and uncertainties

robust output tracking for nonlinear uncertain systems abstract the problem of robust output tracking for nonlinear systems in the presence of uncertainties is further studied by extending the results of behtash 1990 to systems with mismatched uncertainties a new design method which is called the stable combined variable perturbation method scvpm is proposed and a robust controller is presented using high gain feedback our results are compatible with those of behtash 1990 in a sense that the new controller will degenerate to the one of behtash 1990 if the so called generalized matching condition is satisfied simulation results verified the effectiveness of the newly proposed method and controller

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

a multiscale reduced basis method for parametrized elliptic partial differential equations with multiple scales we present a technique for solving parametrized elliptic partial differential equations with multiple scales the technique is based on the combination of the reduced basis method c prud homme d rovas k veroy y maday a t patera g turinici reliable real time solution of parametrized partial differential equations reduced basis output bound methods journal of fluids engineering 124 1 2002 70 80 and the multiscale finite element method t y hou x h wu a multiscale finite element method for elliptic problems in composite materials and porous media journal of computational physics 134 1 1997 169 189 to treat problems in which the differential coefficient is characterized by a large number of independent parameters for the multiscale finite element method a large number of cell problems has to be solved at the fine local mesh for each new configuration of the differential coefficient in order to improve the computational efficiency of this method we construct reduced basis spaces that are adapted to the local parameter dependence of the differential operator the approximate solutions of the cell problems are computed accurately and efficiently via performing galekin projection onto the reduced basis spaces and implementing the offline online computational procedure therefore a large number of similar computations at the fine local mesh can be carried out with lower computational cost for each new configuration of the differential coefficient numerical results are provided to demonstrate the accuracy and efficiency of the proposed approach

adaptive component mode synthesis in linear elasticity component mode synthesis cms is a classical method for the reduction of large scale finite element models in linear elasticity in this paper we develop a methodology for adaptive refinement of c

globally stable robust tracking of nonlinear systems using variable structure control and with an application to a robotic manipulator the globally stable robust output tracking for a class of nonlinear systems is considered based only on the knowledge of the bounds on the uncertainties a variable structure control vsc law is developed under the structure matching assumption it is shown that the outputs of the closed loop system asymptotically track given output trajectories despite the uncertainties while maintaining the boundedness of all signals inside the loop all signals inside the loop are shown to be bounded for all time to illustrate the efficiency of the controller the approach is applied to the case of a two degree of freedom dof robotic manipulator with variable payload numerical simulation results are also provided

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

parametric solutions involving geometry a step towards efficient shape optimization abstract optimization of manufacturing processes or structures involves the optimal choice of many parameters process parameters material parameters or geometrical parameters usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model then an appropriate cost function is evaluated and its optimality checked while the optimum is not reached the process parameters should be updated by using an appropriate optimization procedure and then the model must be solved again for the updated process parameters thus a direct numerical solution is needed for each choice of the process parameters with the subsequent impact on the computing time in this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry the main objective of this work is to describe an original approach for computing an off line parametric solution that is a solution able to include information for different parameter values and also allowing to compute readily the sensitivities the curse of dimensionality is circumvented by invoking the proper generalized decomposition pgd introduced in former works which is applied here to compute geometrically parametrized solutions

the post processing approach in the finite element method part 1 calculation of displacements stresses and other higher derivatives of the displacements this is the first in a series of three papers in which we discuss a method for post processing a finite element solution to obtain high accuracy approximations for displacements stresses stress intensity factors etc rather than take the values of these quantities directly from the finite element solution we evaluate certain weighted averages of the solution over the entire region these yield approximations are of the same order of accuracy as the strain energy we obtain error estimates and also present some numerical examples to illustrate the practical effectiveness of the technique in the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation

asymptotic stability for tracking control of nonlinear uncertain dynamical systems described by differential inclusions in this paper we will study the tracking control problem for nonlinear uncertain dynamical systems two generalized feedback control inputs have been proposed such that the feedback controlled systems satisfy the complete tracking control property with exponential asymptotic stability and the trajectories of the systems are steered to the pre specified observation map with an exponential convergence rate moreover an estimate of the tracking time of the trajectories attaining the observation map has also been given an example inspired from a guided missile problem illustrates the use of our main results

advanced simulation of models defined in plate geometries 3d solutions with 2d computational complexity abstract many models in polymer processing and composites manufacturing are defined in degenerated three dimensional domains involving plate or shell geometries the reduction of models from 3d to 2d is not obvious when complex physics are involved the hypotheses to be introduced for reaching this dimensionality reduction are sometimes unclear and most of possible proposals will have a narrow interval of validity the only getaway is to explore new discretization strategies able to circumvent or at least alleviate the drawbacks related to mesh based discretizations of fully 3d models defined in plate or shell domains an in plane out of plane separated representation of the involved fields within the context of the proper generalized decomposition allows solving the fully 3d model by keeping a 2d characteristic computational complexity moreover the pgd features allow the introduction of many extra coordinates as for example the orientation of the different laminate plies without affecting the solvability of the resulting multidimensional model

generalized multiscale finite element methods gmsfem in this paper we propose a general approach called generalized multiscale finite element method gmsfem for performing multiscale simulations for problems without scale separation over a complex input space as in multiscale finite element methods msfems the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space in the proposed approach we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage the enrichment in the online stage is performed based on a spectral decomposition of the offline space in the online stage for any input parameter a multiscale space is constructed to solve the global problem on a coarse grid the online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues the computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re used for solving the forward problem with any forcing and boundary condition compared with the other approaches where global snapshots are used the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse grid level we present various examples in the paper and some numerical results to demonstrate the effectiveness of our method

spectral based discontinuous galerkin reduced basis element method for parametrized stokes problems in this work we extend to the stokes problem the discontinuous galerkin reduced basis element dgrbe method introduced in antonietti etal 2015 by this method we aim at reducing the computational cost for the approximation of a parametrized stokes problem on a domain partitioned into subdomains during an offline stage expensive but performed only once a low dimensional approximation space is built on each subdomain for any new value of the parameter the rapid evaluation of the solution takes place during the online stage and consists in a galerkin projection onto the low dimensional subspaces computed offline the high fidelity discretization on each subdomain used to build the local low dimensional subspaces is based on spectral element methods the continuity of both the velocity and the normal component of the cauchy stress tensor at subdomain interfaces is weakly enforced by a discontinuous galerkin approach

the localized reduced basis multiscale method for two phase flows in porous media summary in this work we propose a novel model order reduction approach for two phase flow in porous media by introducing a global pressure formulation in which the total mobility which realizes the coupling between saturation and pressure is regarded as a parameter to the pressure equation in our approach the mobility itself is an optimal fit of mobility profiles that are precomputed using the time of flight for the initial saturation using this formulation and the localized reduced basis multiscale method we obtain a low dimensional surrogate of the high dimensional pressure equation by applying ideas from model order reduction for parametrized partial differential equations we are able to split the computational effort for solving the pressure equation into a costly offline step that is performed only once and an inexpensive online step that is carried out in every time step of the two phase flow simulation which is thereby largely accelerated usage of elements from numerical multiscale methods allows us to displace the computational intensity between the offline and online steps to reach an ideal runtime at acceptable error increase for the two phase flow simulation this is achieved by constructing reduced dimensional local spaces that lead to a non conforming global approximation space as one example for a coupling on the global space we introduce a discontinuous galerkin scheme copyright 2014 john wiley sons ltd

feedback controlled differential inclusions and stabilization of uncertain dynamical systems deterministic design of stabilizing feedback controls for a class of uncertain dynamical systems is considered adopting a problem formulation based on differential inclusions to encompass all possible realizations of uncertainty the authors describe a class of generalized feedback controls with practical analogues in the form of discontinuous feedbacks that guarantees global uniform ultimate boundedness moreover under a matched uncertainty hypothesis this class of controls guarantees global uniform asymptotic stability of the zero state and ultimate attainment of prescribed model behaviour

the continuous galerkin method is locally conservative we examine the conservation law structure of the continuous galerkin method we employ the scalar advection diffusion equation as a model problem for this purpose but our results are quite general and apply to time dependent nonlinear systems as well in addition to global conservation laws we establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements these results are somewhat surprising and contradict the widely held opinion that the continuous galerkin method is not locally conservative

output tracking control of nonlinear systems with mismatched uncertainties abstract this paper addresses the output tracking problem of a class of nonlinear systems given input output linearizability of the class of nonlinear systems a robust output tracking controller derived via a lyapunov based approach is proposed here the model uncertainties do not need to satisfy the conventional matching condition but states and tracking error remain bounded furthermore the magnitude of the tracking error will bear dominant dependence on the magnitude of the mismatched uncertainties

a unifying design of sliding mode and classical controllers a theory is given to unify output sliding mode control and classical control the idea is based on defining the sliding variable in such a way that once the system begins to slide the classical controller transfer function is realized this idea leads to the development of a hybrid sliding and classical controller which retains the merits of both types of controllers but eliminates their respective limitations the proposed method is robust and applies to non minimum phase single input single output siso systems no state measurement is required

presentations of finite simple groups a quantitative approach there is a constant such that all nonabelian finite simple groups of rank over with the possible exception of the ree groups have presentations with at most generators and relations and total length at most as a corollary we deduce a conjecture of holt there is a constant such that for every finite simple group every prime and every irreducible module

stability radius optimization a geometric approach abstract the subject of this paper is a geometric approach to the robustness optimization problem for uncertain finite dimensional linear systems for the structurally perturbed stabilizable pair a b we show that optimally robust feedback stabilization is possible via the class of feedbacks parameterizing a b feedback invariant subspaces of codimension rk b a direct consequence of this geometric approach is a reduction in dimension of the optimization problem

embeddings into k efficient groups abstract we prove a theorem with the following corollary for each integer k 1 an arbitrary finite group g embeds into some finite group gk for which there exists an eilenberg mac lane cw space x k gk 1 whose finite n skeleton xn has euler poincare characteristic xn 1 1 ndhn gk for all n k the theorem can be viewed as a generalisation of a result of j harlander 1996 j algebra182 511 521 on the embedding of finite groups into groups with efficient presentations

non linear predictive control by inversion discontinuities for critical behaviour the predictive control by inversion pci technique is presented in this paper this technique permits extending in a simple way the predictive control principles to non linear models without any linearizing transformation singularities and non minimum phase phenomena which can arise from inversion are treated by introducing control discontinuities either directly on the control or some of its derivatives or indirectly through reference trajectory discontinuities performance and robustness properties of the technique are illustrated by several simulation results

error control for the localized reduced basis multiscale method with adaptive on line enrichment in this contribution we consider localized robust and efficient a posteriori error estimation of the localized reduced basis multiscale lrbms method for parametric elliptic problems with possibly heterogeneous diffusion coefficient the numerical treatment of such parametric multiscale problems is characterized by a high computational complexity arising from the multiscale character of the underlying differential equation and the additional parameter dependence the lrbms method can be seen as a combination of numerical multiscale methods and model reduction using reduced basis rb methods to efficiently reduce the computational complexity with respect to the multiscale as well as the parametric aspect of the problem simultaneously in contrast to the classical residual based error estimators currently used in rb methods we are considering error estimators that are based on conservative flux reconstruction and provide an efficient and rigorous bound on the full error with respect to the weak solut

output feedback control of uncertain coupled systems the stabilization of uncertain dynamical systems on n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively is studied we refer to the nc dimensional sybsystem as the reduced order system and to the nr dimensional subsystem as the residual system the overall n dimensional system is termed the full system the prototype for which is a mechanical model arising in the study of the active control of structures each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class the output available for feedback purposes is an nc valued linear combination of the state components of the full system and is subject to bounded measurement noise with known bound an output feedback strategy is described and sufficient conditions are obtained for the existence of a calculable global uniform compact attractor containing the state origin for controlled systems of this class

a reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks abstract in this paper we propose a reduced basis hybrid method rbhm for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent the rbhm is applied to stokes equations in domains which are decomposable into smaller similar blocks that are properly coupled the rbhm is built upon the reduced basis element method rbem and it takes advantage from both the reduced basis methods rb and the domain decomposition method we move from the consideration that the blocks composing the computational domain are topologically similar to a few reference shapes on the latter representative solutions corresponding to the same governing partial differential equations are computed for different values of some parameters of interest representing for example the deformation of the blocks a generalized transfinite mapping is used in order to produce a global map from the reference shapes of each block to any deformed configuration the desired solution on the given original computational domain is recovered as projection of the previously precomputed solutions and then glued across subdomain interfaces by suitable coupling conditions the geometrical parametrization of the domain by transfinite mapping induces non affine parameter dependence an empirical interpolation technique is used to recover an approximate affine parameter dependence and a subsequent offline online decomposition of the reduced basis procedure this computational decomposition yields a considerable reduction of the problem complexity results computed on some combinations of 2d and 3d geometries representing cardiovascular networks show the advantage of the method in terms of reduced computational costs and the quality of the coupling to guarantee continuity of both stresses pressure and velocity at subdomain interfaces

pro finite presentations the goal of this paper is to start to present a systematic presentation theory for pro finite groups let g be a fixed finitely generated pro finite group and p a free presentation of it i e p 1 r f g 1 is an exact sequence when f is a finitely generated free pro finite group we write d f for the minimal number of generators of f and d r for f the minimal number of generators of r as a normal subgroup of f in g2 gruenberg presented a systematic study of presentation theory of a discrete group g mainly for a finite group g and presented three basic problems question 1 given p 1 r f g 1 for i 1 2 when f is i i a free group is then d r d r f 1 f 2

recent advances on the use of separated representations separated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh based discretization strategies in our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions as we proved in some of our former works its application is not restricted to multidimensional models obviously separated representation can also be applied in standard 2d or 3d models allowing for high resolution computations because its early life numerous issues persist many of them attracting the curiosity of many research groups within the computational mechanics community in this paper we are focusing in two issues never until now addressed i the imposition of non homogenous essential boundary conditions and ii the consideration of complex geometries copyright 2009 john wiley sons ltd

port reduction in parametrized component static condensation approximation and a posteriori error estimation summary we introduce a port interface approximation and a posteriori error bound framework for a general component based static condensation method in the context of parameter dependent linear elliptic partial differential equations the key ingredients are as follows i efficient empirical port approximation spaces the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system and ii a computationally tractable a posteriori error bound realized through a non conforming approximation and associated conditioner the error in the global system approximation or in a scalar output quantity may be bounded relatively sharply with respect to the underlying finite element discretization our approximation and a posteriori error bound framework is of particular computational relevance for the static condensation reduced basis element scrbe method we provide several numerical examples within the scrbe context which serve to demonstrate the convergence rate of our port approximation procedure as well as the efficacy of our port reduction error bounds copyright 2013 john wiley sons ltd

spectral element feti dp and bddc preconditioners with multi element subdomains abstract the discrete systems generated by spectral or hp version finite elements are much more ill conditioned than the ones generated by standard low order finite elements or finite differences this paper focuses on spectral elements based on gauss lobatto legendre gll quadrature and the construction of primal and dual non overlapping domain decomposition methods belonging to the family of balancing domain decomposition methods by constraints bddc and dual primal finite element tearing and interconnecting feti dp algorithms new results are presented for the spectral multi element case and also for inexact feti dp methods for spectral elements in the plane theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator while there is only a polylogarithmic dependence on the spectral degree p and the ratio h h of subdomain and element sizes parallel numerical experiments on a linux cluster confirm these results for tests with spectral degree up to p 32 thousands of subdomains and coefficient jumps up to 8 orders of magnitude

an error estimator for separated representations of highly multidimensional models fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics most of these models consist of a partial differential equation defined in a highly multidimensional domain e g schrodinger equation fokker planck equations among many others the main challenge related to these models is their associated curse of dimensionality we proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations also known as finite sums decomposition this technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates the issue related to error estimation has never been addressed this paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques

feedback linearization of discrete time systems abstract we give necessary and sufficient conditions for a nonlinear discrete time system to be locally linearizable by a change of state coordinates and a feedback the conditions are expressed in terms of controllability distributions associated to the system

the reduced basis element method application to a thermal fin problem the reduced basis element method is a new approach for the approximation of partial differential equations that takes its roots in the domain decomposition method and in the reduced basis discretization the basic idea is to decompose the domain of computation into a series of subdomains the elements that are similar to a few reference domains these reference domains are actually filled with reduced basis functional spaces that are mapped to each subdomain together with the geometry the discrete approximation space is then composed of functions with the property that a function restricted to a subdomain belongs to the mapped reduced spaces finally a mortar type method is applied to glue the various local functions in this paper we focus on the definition of the reference shapes and together with theoretical and numerical justifications of the method we provide a posteriori error analysis tools that allow us to certify the computational results

optimal local approximation spaces for component based static condensation procedures in this paper we introduce local approximation spaces for component based static condensation sc procedures that are optimal in the sense of kolmogorov to facilitate simulations for large structures such as aircraft or ships it is crucial to decrease the number of degrees of freedom on the interfaces or ports in order to reduce the size of the statically condensed system to derive optimal port spaces we consider a compact transfer operator that acts on the space of harmonic extensions on a two component system and maps the traces on the ports that lie on the boundary of these components to the trace of the shared port solving the eigenproblem for the composition of the transfer operator and its adjoint yields the optimal space for a related work in the context of the generalized finite element method we refer the reader to i babuska and r lipton multiscale model simul 9 2011 pp 373 406 we further introduce a spectral greedy algorithm to generalize the procedure to the parameter

a static condensation reduced basis element method complex problems abstract we extend the static condensation reduced basis element scrbe method to treat the class of parametrized complex helmholtz partial differential equations the main ingredients are i static condensation at the interdomain level ii a conforming eigenfunction port representation at the interface level iii the reduced basis rb approximation of finite element fe bubble functions at the intradomain level and iv rigorous system level error bounds which reflect rb perturbation of the fe schur complement we then incorporate these ingredients in an offline online computational strategy to achieve rapid and accurate prediction of parametric systems formed from instantiations of interoperable parametrized archetype components from a library we introduce a number of extensions with respect to the original scrbe framework first primal dual rb methods for general non symmetric complex problems second stability constant procedures for weakly coercive problems at both the interdomain level and intradomain level third treatment of non port linear functional outputs as well as functions of outputs fourth consideration of particular components and outputs relevant to acoustic applications we consider several numerical examples in acoustics in particular focused on mufflers and horns to demonstrate that the approach can handle models with many parameters and or topology variations with particular reference to waveguide like applications

a new systematic design of high gain feedback for nonlinear systems with unmatched uncertainties the systematic design of a robust output tracking algorithm for a feedback linearizable system with unmatched uncertainties is presented the proposed technique is based on a backstepping procedure to construct a time varying singularly perturbed system and the underlying theoretical approach by the lyapunov theory the main result is that a dynamically parametrized state feedback is developed to cancel the output tracking error finally an illustrative example through a chemical reactor system is given to demonstrate the utilization of the approach developed in this paper

invariant distributions for discrete time nonlinear systems the purpose of this paper is to introduce some notions of invariant distributions for the class of linear analytic discrete time systems and to give an algebraic characterization of them a brief final discussion motivates the usefulness of the notions introduced in the study of the geometric properties of the system

systematic design of robust controllers for nonlinear uncertain systems the design problem of robust stabilizing controllers for nonlinear uncertain systems is considered in this paper the nominal system is input output linearizable and the uncertainty is assumed to be either generalized matching or mismatched the control design combines differential geometric feedback linearization with the deterministic approach in which no statistical property of the uncertainty is assumed and used the only information on the uncertainty which is needed for the design is its possible bound two robust stabilizing controllers for generalized matching uncertain systems are given for mismatched uncertain systems a systematic design procedure is first presented then four robust stabilizing controllers are given the robust controllers which are given in forms of explicit feedback laws based on the nominal system and are parametrized by the robust design parameters related to the bounds of uncertainties are more practicable than the existing ones in the literature numerical example

reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries the aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques the main idea behind this approach is to compute once locally and for few reference shapes some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries these functions will represent the basis of a reduced space where the global solution is sought for the continuity of the latter is assured by a classical domain decomposition approach test results on poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed or the set of boundary conditions used for defining locally the basis functions the proposed approach simplifies the pre computation of the reduced basis space by splitting the global problem into smaller local subproblems thanks to this feature it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed c 2015 elsevier ltd all rights reserved

robust output tracking for non linear systems the problem of output tracking for a single input single output non linear system in the presence of uncertainties is studied the notions relative degree and minimum phase for non linear systems are reviewed given a bounded desired tracking signal with bounded derivatives a control law is designed for minimum phase non linear systems which results in tracking of this signal by the output this control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors two types of uncertainties are considered those satisfying a generalized matching condition but otherwise unstructured and linear parametric uncertainties it is shown that for systems with the first type of uncertainty high gain control laws can result in small tracking errors of o where e is a small design parameter an alternative scheme based on variable structure control strategy is shown to yield zero tracking errors adaptive control te

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

adaptive variational multiscale methods based on a posteriori error estimation energy norm estimates for elliptic problems we develop a new adaptive multiscale finite element method using the variational multiscale framework together with a systematic technique for approximation of the fine scale part of the solution the fine scale is approximated by a sum of solutions to decoupled localized problems which are solved numerically on a fine grid partition of a patch of coarse grid elements the sizes of the patches of elements may be increased to control the error caused by localization we derive an a posteriori error estimate in the energy norm which captures the dependency of the crucial discretization parameters the coarse grid mesh size the fine grid mesh size and the sizes of the patches based on the a posteriori error estimate we present an adaptive algorithm that automatically tunes these parameters finally we show how the method works in practice by presenting various numerical examples

deficiency zero presentations for certain perfect groups in this paper we give two generator two relation presentations for the following perfect groups which were not previously known to have deficiency zero sl 2 32 sl 2 64 sl 2 27 sl 2 49 7 z 8 sl 2 5 sl 2 5 sl 2 5 sl 2 25 we also give two generator two relation presentations for three other finite perfect groups two having sl 2 7 as an image and one having sl 2 5 as an image we also discuss presentations for certain other perfect groups which were known to have deficiency zero and find some neat new presentations for them

a local stabilizing control scheme using an approximate feedback linearization we present a method of stabilizing single input approximately feedback linearizable systems in the generic situation where the linearizing feedback and coordinate transformation map are not directly available in obtaining a stabilizing feedback we utilize a technique of an approximate feedback linearization which is based on an approximate integrating factor calculated from a recursive algorithm we construct a feedback controller for the approximately linearized system so that the system is asymptotically stable in a neighborhood of the origin where the one to one relation holds with the original coordinate system

robust stabilization of mimo nonlinear time varying mismatched uncertain systems abstract this paper considers the problem of robust stabilization of multi input multi output mimo nonlinear systems in the presence of mismatched time varying uncertainties combining the differential geometric feedback linearization with the deterministic approach it derives two robust stabilizing controllers i e the high gain feedback controller and the variable structure controller these two controllers only require the knowledge of the nominal system and the bounds of the uncertainties therefore they are more feasible to be implemented both controllers reduce the effects of arbitrarily large bounded mismatched uncertainties successfully to achieve uniform ultimate boundedness stabilization of the mimo nonlinear timevarying uncertain systems

localization of elliptic multiscale problems this paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients the basis functions are solutions of local problems on vertex patches the error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches hence on a uniform mesh of size h patches of diameter h log 1 h are sufficient to preserve a linear rate of convergence in h without pre asymptotic or resonance effects the analysis does not rely on regularity of the solution or scale separation in the coefficient this result motivates new and justifies old classes of variational multiscale methods see more at http www ams org journals mcom 2014 83 290 s0025 5718 2014 02868 8 sthash z2ccfxig dpuf

viable control for uncertain nonlinear dynamical systems described by differential inclusions in this paper we will study the viable control problem for a class of uncertain nonlinear dynamical systems described by a differential inclusion the goal is to construct a feedback control such that all trajectories of the system are viable in a map moreover for any initial states no viable in the map under the feedback control all solutions of the system are steered to the map with an exponential convergence rate and viable in the map after a finite time t in this case an estimate of the time t of all trajectories attaining the map is given in the nanomedicine system an example inspired from cerebral embolism and cerebral thrombosis problems illustrates the use of our main results

variable structure control of robot manipulators with nonlinear sliding manifolds performance characteristics of a sliding mode controller depend essentially on a selected sliding manifold customarily the variable structure controllers operate with linear sliding surfaces however using nonlinear or time varying manifolds may provide definite advantages in particular they may provide faster convergence in this paper a control algorithm is presented which guarantees the occurrence of the sliding mode on nonlinear or time varying manifolds the bounds needed for calculating the switching gains are determined in terms of parameter variations rather than bounds on the system matrices the parameter bounds are usually evident and can be easily established or estimated while matrix bounds can rarely be justified in practical problems in this paper we also present an adaptive version of the controller which provides an automatic estimation of the parameter bounds the robustness of the controller with respect to a class of state dependent uncertainties is analysed by the lyapunov m

acceleration of the spectral stochastic fem using pod and element based discrete empirical approximation for a micromechanical model of heterogeneous materials with random geometry abstract the spectral stochastic fem with local basis functions in the stochastic domain sl fem is one of the most flexible and accurate stochastic methods however also the most computationally expensive these expenses are traditionally associated with the extra large tangent stiffness matrix and a huge number of elements which need to be re integrated in every iteration in this work we incorporate the proper orthogonal decomposition pod into the sl fem thus performing a drastic reduction of the stiffness matrix in order to reduce the integration costs by hyperreduction a novel element based modification of the discrete empirical interpolation the so called element based empirical approximation method edeam is developed and combined with the pod particular advantages of the sl fem for order reduction and hyperreduction compared to other stochastic techniques are discussed the new reduced order sl fem is applied to the computational homogenization of materials with random geometry of the microstructure i e to a general class of problems exhibiting strongly nonlinear non smooth and sometimes discontinuous dependency of the solution on some random parameters the reduced order sl fem demonstrates a high accuracy and a high solution speed whereby the solution time for the reduced order sl fem is comparable to the solution time of only one single monte carlo sample

a new variable structure controller for affine nonlinear systems with non matching uncertainties the problem of output tracking in siso uncertain non autonomous nonlinear systems is treated in this study it is shown that a nonlinear system experiencing non matching disturbances and uncertainties can be transformed to a form similar to the normal form then a novel variable structure controller with disturbance estimation and parameter adaptation is presented this controller while preserving the robustness properties of sliding control avoids a sliding mode and generates a continuous control signal which results in close output tracking

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

closing the relation gap by direct product stabilization abstract the generation gap of a group g is the difference between the minimal number of generators of g and the rank of the augmentation ideal the relation gap of a presentation f n is the difference between the minimal number of elements that generate n as a normal subgroup and the minimal number of g module generators of the relation module n n n we show that if g is a finitely presented group then there exists n such that g i 1 n z p z p being the cyclic group of order p has zero generation and zero relation gap we apply this result to questions concerning the efficiency of finite groups

a transformed lure problem for sliding mode control and chattering reduction the sliding mode control problem is investigated with the frequency domain approach the authors show that the sliding mode control can be transformed into a lure problem with this formulation it is shown that the conventional sliding mode control with a nonlinear sign function can only guarantee to make the overall system stable but not asymptotically stable the authors also consider a practical situation where the sign nonlinearity may contain a hysteresis loop for this situation they show that even if the hysteresis loop is very small there still exists a limit cycle however chattering phenomenon caused by the limit cycle behavior can be eliminated by a certain class of nonlinearities

invertibility of affine nonlinear control systems a geometric approach abstract the paper deals with the invertibility of multivariable non linear control systems by using the recently developed theory on controlled invariant and controllability distributions necessary and sufficient conditions for invertibility are derived

adaptive neural control for strict feedback nonlinear systems without backstepping in this brief a new adaptive neurocontrol algorithm for a single input single output siso strict feedback nonlinear system is proposed most of the previous adaptive neural control algorithms for strict feedback nonlinear systems were based on the backstepping scheme which makes the control law and stability analysis very complicated the main contribution of the proposed method is that it demonstrates that the state feedback control of the strict feedback system can be viewed as the output feedback control problem of the system in the normal form as a result the proposed control algorithm is considerably simpler than the previous ones based on backstepping depending heavily on the universal approximation property of the neural network nn only one nn is employed to approximate the lumped uncertain system nonlinearity the lyapunov stability of the nn weights and filtered tracking error is guaranteed in the semiglobal sense

output tracking design of affine nonlinear plant via variable structure system an output tracking design for affine nonlinear systems via a variable structure system is proposed the structure algorithm is used to determine if the considered system is left invertible it is shown that if such a condition is satisfied then a sliding mode controller can be designed to achieve output tracking the decouplability condition in conventional approaches is now replaced by the weaker left invertibility condition stable tracking is guaranteed if the internal mode is bounded input bounded state stable simulation results are included to demonstrate the design procedure