a generalized finite element formulation for arbitrary basis functions from isogeometric analysis to xfem many of the formulations of cm rent research interest including iosogeometric methods and the extended finite element method use nontraditional basis functions some such as subdivision surfaces may not have convenient analytical representations the concept of an element if appropriate at all no longer coincides with the traditional definition developing a new software for each new class of basis functions is a large research burden especially if the problems involve large deformations non linear materials and contact the objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file elements ranging from a traditional linear four node tetrahedron through a higher order element combining xfem and isogeometric analysis may be specified entirely through an input file without any additional programming examples of this framework to applications with lagrange elements isogeometric elements and xfem basis functions for fracture are presented

a gauss seidel type solver for the fast computation of input constrained control systems abstract an important class of nonlinear control systems can be represented as the feedback interconnection of two parts a linear time invariant system and a block of decentralized nonlinearities when the linear time invariant part has a nontrivial feedthrough term or the nonlinearity has a feedback gain control computation involves the online implementation of a multivariable algebraic loop which must be resolved at each sampling instant the requirements for such online computation may result in several implementation issues especially in real time and embedded control applications this paper considers the implementation of such algebraic loops arising from several input constrained systems the proposed solution algorithm is globally convergent for a very large class of feedthrough or feedback gains and shows promise for real time and embedded control applications where a fast but approximate solution is of the essence

inherent observer property in a class of anti windup compensators owing to the types of non linearities involved the analysis and the comparison of different anti windup compensators that are available in the literature become difficult towards achieving a better understanding of the mechanisms of these anti windup compensators we here expose the observer property inherent in a class of anti windup compensators this observer property allows us to unify these anti windup compensators as special cases of the generalized anti windup compensator due to astrom and wittenmark 1984 and provides a general framework to investigate their performance

pt symmetric quantum mechanics this paper proposes to broaden the canonical formulation of quantum mechanics ordinarily one imposes the condition h h on the hamiltonian where represents the mathematical operation of complex conjugation and matrix transposition this conventional hermiticity condition is sufficient to ensure that the hamiltonian h has a real spectrum however replacing this mathematical condition by the weaker and more physical requirement h h where represents combined parity reflection and time reversal pt one obtains new classes of complex hamiltonians whose spectra are still real and positive this generalization of hermiticity is investigated using a complex deformation h p2 x2 ix e of the harmonic oscillator hamiltonian where e is a real parameter the system exhibits two phases when e 0 the energy spectrum of h is real and positive as a consequence of pt symmetry however when 1 e 0 the spectrum contains an infinite number of complex eigenvalues and a finite number of real positive eigenvalues b

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

conjecture on the interlacing of zeros in complex sturm liouville problems the zeros of the eigenfunctions of self adjoint sturm liouville eigenvalue problems interlace for these problems interlacing is crucial for completeness for the complex sturm liouville problem associated with the schrodinger equation for a non hermitian pt symmetric hamiltonian completeness and interlacing of zeros have never been examined this paper reports a numerical study of the sturm liouville problems for three complex potentials the large n limit of a ix n potential a quasiexactly solvable x4 potential and an ix3 potential in all cases the complex zeros of the eigenfunctions exhibit a similar pattern of interlacing and it is conjectured that this pattern is universal understanding this pattern could provide insight into whether the eigenfunctions of complex sturm liouville problems form a complete set

siso linear system control via saturating actuator l2 tracking performance in the presence of arbitrary shaped inputs most studies on linear system control in the presence of actuator saturation have focused on closed loop asymptotic stabilisation available tracking results are generally limited to constraint compatible inputs references disturbances with known exogenous input models the problem of output reference tracking in the presence of arbitrary shaped not necessarily constraint compatible inputs has yet to be investigated in this study we show that an tracking performance is achievable for siso linear systems using a given class of saturated controllers accordingly the tracking error energy resp power is bounded by the energy resp power of a well defined mismatch input depending on the disturbance and reference compatibility in the disturbance free case this entails perfect asymptotic tracking of arbitrary shaped constraint compatible reference signals otherwise the average tracking quality is proportional to the mismatch input power in the case of periodic inputs constraint compatible or not

on the reality of the eigenvalues for a class of symmetric oscillators we study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays where is a real polynomial and we prove that if for some we have for all then the eigenvalues are all positive real we then sharpen this to a larger class of polynomial potentials

a magnitude and rate saturation model and its use in the solution of a static anti windup problem in this paper we address the anti windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation using generalized sector condition we provide an lmi based procedure for the construction of a linear anti windup gain acting on the controller state equation such that regional closed loop stability is guaranteed and suitable performance measures are optimized the approach is successfully illustrated on a simulation example

anti windup synthesis for systems with rate limits using riccati equations this article develops an anti windup aw scheme for systems with rate limited actuators the main results show how a full order aw compensator can be synthesised using an algebraic riccati equation and several free parameters a further result then shows how the free parameters may be chosen to influence in an intuitive way the local gain of the system and the size of the region of attraction the results are of interest due to their low computational burden and hence their applicability to the systems of large state dimension

l2 anti windup for linear dead time systems in this paper we address and solve the problem of antiwindup augmentation for linear systems with input and output delay in particular we give a formal definition of the anti windup construction problem in the global local robust and nominal cases for each of these cases we show that a specific anti windup compensation structure which is a generalization of the approach in 131 is capable of solving the anti windup problem whenever this is solvable the effectiveness of the proposed scheme is shown on a simple example taken from the literature in which the plant is a marginally stable linear system the anti windup design problem has been qualitatively stated already from the 1950 s both in the analog and in the digital control framework however the arisin solutions were at that time mainly application oriente and not applicable to large classes of control systems it was only in the 1980 s that some design techniques ap plicable to large classes of control systems were formalized although the issue of performance characterization and improvement was still mostly unsolved an interestin survey of these techniques can be found in 141 anotier dhenomenon that is often found in coninnction

design of saturation based switching anti windup gains for the enlargement of the domain of attraction this technical note proposes a saturation based switching anti windup design for the enlargement of the domain of attraction of the closed loop system a widely adopted method of dealing with an m dimensional saturated linear feedback is to express it as a linear combination of a set of 2m auxiliary linear feedbacks for each value of the state these auxiliary linear feedbacks form a convex polyhedron of 2m vertices in the input space we propose to divide this convex polyhedron into several convex sub polyhedrons each of which is defined as the convex hull of a subset of the auxiliary feedbacks whenever the value of the saturated linear feedback falls into a sub polyhedron it can be expressed as a linear combination of a subset of the 2m auxiliary linear feedbacks that define the sub polyhedron and thus a less conservative result can be expected a separate anti windup gain is designed for each sub polyhedron by using a common quadratic lyapunov function and implemented when the value of the saturated linear feedback falls into this sub polyhedron simulation results indicate that such a saturation based switching anti windup design has the ability to significantly enlarge the domain of attraction of the closed loop system

adaptive boundary control of a flexible manipulator with input saturation abstractin this study we consider the anti windup design as one of the approaches for the boundary control problem of a flexible manipulator in the presence of system parametric uncertainties external disturbances and bounded inputs the dynamics of the system are represented by partial differential equations pdes using the singular perturbation approach the pde model is divided into two simpler subsystems with the lyapunov s direct method an adaptive boundary control scheme is developed to regulate the angular position and suppress the elastic vibration simultaneously and the adaptive laws are designed to compensate for the system parametric uncertainties and the disturbances the proposed control scheme allows the application of smooth hyperbolic functions which satisfy physical conditions and input restrictions be easily realised numerical simulations demonstrate the effectiveness of the proposed scheme

nonlinear scheduled anti windup design for linear systems the nonlinear l sub 2 anti windup framework introduced in teel and kapor 1997 reduces the anti windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched l sub 2 disturbances in this note based on the structure proposed in that previous paper we provide a linear matrix ineqaulity lmi formulation of high performance anti windup design for control systems with linear asymptotically stable plants in particular we first give a linear quadratic based formulation of linear anti windup compensation in terms of the solution of a set of always feasible lmi constraints then we propose a nonlinear scheduling technique where hysteresis switching among a family of linear gains is employed for performance improvement both design techniques are demonstrated on an academic example

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed

generalized sector synthesis of output feedback control with anti windup structure this paper considers the control synthesis problem for linear time invariant lti continuous time systems with actuator saturation nonlinearities the control architecture is standard a nominal lti output feedback with an anti windup aw mechanism traditional approaches have focused on aw synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the aw compensator is added to guarantee stability performance properties when the actuators saturate in contrast this paper proposes a synthesis method to design both the nominal controller and the aw compensator simultaneously using the generalized sector gs approach in the multiplier setting a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed loop system our result is shown to include the existing results on the simultaneous circle synthesis and the anti windup gs synthesis as special cases this paper also shows that the direct feed through term in the aw compensator does not contribute to enlarging the achievable domain of attraction within the multiplier gs framework

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

finite element application of erbs extraction abstract in this paper we explore erbs extraction in application to a heat conduction problem two types of basis functions are considered b spline and expo rational b spline erbs combined with bernstein polynomials the first one is a global basis defined on a subdomain whose size is related to the spline degree while the second one is a strictly local basis under the local geometry while all the coefficients of the b spline tensor product surface affect each element of the patch local surfaces of the blending surface conserve both local manipulation and smoothness of the global surface we show the conversion between these bases by using an erbs extraction the extraction operator allows us to convert the control points of the surface evaluated by b splines to control points of the erbs surface and vice versa this approach is demonstrated on an example of the finite element solution approximation of the heat equation

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

equivalence between classes of multipliers for slope restricted nonlinearities different classes of multipliers have been proposed in the literature for obtaining stability criteria using passivity theory integral quadratic constraint iqc theory or lyapunov theory some of these classes of multipliers can be applied with slope restricted nonlinearities in this paper the concept of phase containment is defined and it is shown that several classes are phase contained within the class of zames falb multipliers there are two main consequences firstly it follows that the class of zames falb multipliers remains to date the widest class of available multipliers for slope restricted nonlinearities secondly further restrictions may be avoided when exploiting the parametrization of the other classes of multipliers

a subdivision based implementation of the hierarchical b spline finite element method abstract a novel technique is presented to facilitate the implementation of hierarchical b splines and their interfacing with conventional finite element implementations the discrete interpretation of the two scale relation as common in subdivision schemes is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b spline basis the subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same level basis functions their subsequent multiplication with subdivision matrices projects them during the assembly stage to the correct levels of the hierarchical b spline basis the proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one two and three space dimensions

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

variational boundary conditions based on the nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled cahn hilliard equation the primal variational formulation of the fourth order cahn hilliard equation requires c1 continuous finite element discretizations e g in the context of isogeometric analysis in this paper we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the cahn hilliard equation in primal variables our formulation is based on the symmetric variant of nitsche s method does not introduce additional degrees of freedom and is shown to be variationally consistent in contrast to strong enforcement the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree in addition it preserves full accuracy including higher order rates of convergence which we illustrate for boundary fitted discretizations of several benchmark tests in one two and three dimensions unfitted cartesian b spline meshes constitute an effective alternative to boundary fitted isogeometric parametrizations for constructing c1 continuous discretizations in particular for complex geometries we combine our variational boundary condition formulation with unfitted cartesian b spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode this example involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces demonstrates the flexibility of variational boundary conditions in the context of higher order unfitted isogeometric discretizations

bezier projection a unified approach for local projection and quadrature free refinement and coarsening of nurbs and t splines with particular application to isogeometric design and analysis abstract we introduce bezier projection as an element based local projection methodology for b splines nurbs and t splines this new approach relies on the concept of bezier extraction and an associated operation introduced here spline reconstruction enabling the use of bezier projection in standard finite element codes bezier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global l 2 projection bezier projection is used to develop a unified framework for spline operations including cell subdivision and merging degree elevation and reduction basis roughening and smoothing and spline reparameterization in fact bezier projection provides a quadrature free approach to refinement and coarsening of splines in this sense bezier projection provides the fundamental building block for h p k r adaptivity in isogeometric analysis

a class of exactly solvable eigenvalue problems the class of differential equation eigenvalue problems y x x2n 2y x xn ey x n 1 0 1 2 3 on the interval x can be solved in closed form for all the eigenvalues e and the corresponding eigenfunctions y x the eigenvalues are all integers and the eigenfunctions are all confluent hypergeometric functions the eigenfunctions can be rewritten as products of polynomials and functions that decay exponentially as x for odd n the polynomials that are obtained in this way are new and interesting classes of orthogonal polynomials for example when n 1 the eigenfunctions are orthogonal polynomials in x3 multiplying airy functions of x2 the properties of the polynomials for all n are described in detail

a collocated c0 finite element method reduced quadrature perspective cost comparison with standard finite elements and explicit structural dynamics summary we demonstrate the potential of collocation methods for efficient higher order analysis on standard nodal finite element meshes we focus on a collocation method that is variationally consistent and geometrically flexible converges optimally embraces concepts of reduced quadrature and leads to symmetric stiffness and diagonal consistent mass matrices at the same time it minimizes the evaluation cost per quadrature point thus reducing formation and assembly effort significantly with respect to standard galerkin finite element methods we provide a detailed review of all components of the technology in the context of elastodynamics that is weighted residual formulation nodal basis functions on gauss lobatto quadrature points and symmetrization by averaging with the ultra weak formulation we quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort such as higher order elastostatic analysis furthermore we illustrate the potential of collocation for efficient higher order explicit dynamics throughout this work we advocate a straightforward implementation based on simple modifications of standard finite element codes we also point out the close connection to spectral element methods where many of the key ideas are already established copyright 2014 john wiley sons ltd

a non square sector condition and its application in deferred action anti windup compensator design a sector condition for two connected deadzone nonlinearities is provided by introducing an additional non square operator which exploits their connectivity a more general set of sector like matrix inequalities is obtained this non square matrix inequality condition is applied to an anti windup aw problem in which the aw compensator is not activated until the unconstrained control signal reaches a well defined level beyond that of the physical actuator limits the non square sector condition allows such deferred action aw synthesis to be performed in a manner much closer to traditional immediate sector based aw with either lowered conservatism or decreased computational effort in contrast to recent work the non square condition is applicable to other aw problems

non uniform rational lagrange functions and its applications to isogeometric analysis of in plane and flexural vibration of thin plates abstract new basis functions were developed for isogeometric analysis iga to overcome the difficulties of iga using nurbs non uniform rational b splines on coping with dirichlet boundary conditions the new basis functions were constructed through nesting rational local lagrange interpolations like the t spline and were evaluated in similar procedure as the finite difference method explicit expressions for the new basis functions were presented due to their equivalence to the nurbs the new basis functions were named as non uniform rational lagrange nurl basis iga using nurl includes the finite element method as a special case but the geometry in iga using nurl is exact iga using nurl can carry out p refinement that has the nesting feature of the k refinement of nurbs dirichlet boundary conditions can be directly imposed in iga using nurl because the nurl are interpolation basis functions a method of directly transforming the tensor product basis of triangular patches to area coordinates was presented and the singularity problem at the edge degenerated to a single point was solved the methods developed in this work were applied to in plane and flexural vibration of thin plates comparisons with available results in literatures showed the fast convergence and high accuracy of iga using nurl and the transformation method for triangular patches introduction of a matlab toolbox of the nurl was appended

revisitation of the localized excitations of the 2 1 dimensional kdv equation in a previous paper lou s y 1995 j phys a math gen 28 7227 a generalized dromion structure was revealed for the 2 1 dimensional kdv equation which was first derived by boiti et al boiti m leon j j p manna m and pempinelli f 1986 inverse problems 2 271 using the idea of the weak lax pair in this paper using a backlund transformation and the variable separation approach we find there exist much more abundant localized structures for the 2 1 dimensional kdv equation the abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution some special types of dromion solution lumps breathers instantons and the ring type of soliton are discussed by selecting the arbitrary functions appropriately the dromion solutions can be driven by sets of straight line and curved line ghost solitons the dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves the breathers may breathe both in amplitude and in shape

some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant comparison between the exact value of the spectral zeta function zh 1 5 6 5 3 2cos 5 2 1 5 3 5 and the results of numeric and wkb calculations supports the conjecture by daniel bessis 1995 private communication that all the eigenvalues of this pt invariant hamiltonian are real for one dimensional schrodinger operators with complex potentials having a monotonic imaginary part the eigenfunctions and the imaginary parts of their logarithmic derivatives have no real zeros

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

subdivision shells with exact boundary control and non manifold geometry we introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with non smooth and non manifold joints to this end extended subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals furthermore shells with boundaries in the form of conic sections such as circles or parabolas are represented with rational subdivision schemes which are defined in analogy to rational b splines in terms of implementation the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features hence the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces the particular subdivision scheme used in this paper constitutes an improved version of the original loop s scheme and is as such based on triangular meshes as in the original subdivision shells surfaces created with the modified scheme are used for interpolating the reference and deformed shell configurations at the integration points the subdivision surface is evaluated using a newly developed discrete parameterization approach in the resulting finite elements the only degrees of freedom are the mid surface displacements of the nodes and additional lagrange parameters for enforcing normal constraints the versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples copyright 2011 john wiley sons ltd

isogeometric collocation cost comparison with galerkin methods and extension to adaptive hierarchical nurbs discretizations abstract we compare isogeometric collocation with isogeometric galerkin and standard c 0 finite element methods with respect to the cost of forming the matrix and residual vector the cost of direct and iterative solvers the accuracy versus degrees of freedom and the accuracy versus computing time on this basis we show that isogeometric collocation has the potential to increase the computational efficiency of isogeometric analysis and to outperform both isogeometric galerkin and standard c 0 finite element methods when a specified level of accuracy is to be achieved with minimum computational cost we then explore an adaptive isogeometric collocation method that is based on local hierarchical refinement of nurbs basis functions and collocation points derived from the corresponding multi level greville abscissae we introduce the concept of weighted collocation that can be consistently developed from the weighted residual form and the two scale relation of b splines using weighted collocation in the transition regions between hierarchical levels we are able to reliably handle coincident collocation points that naturally occur for multi level greville abscissae the resulting method combines the favorable properties of isogeometric collocation and hierarchical refinement in terms of computational efficiency local adaptivity robustness and straightforward implementation which we illustrate by numerical examples in one two and three dimensions

a krein space related perturbation theory for mhd α2 dynamos and resonant unfolding of diabolical points the spectrum of the spherically symmetric 2 dynamo is studied in the case of idealized boundary conditions starting from the exact analytical solutions of models with constant profiles a perturbation theory and a galerkin technique are developed in a krein space approach with the help of these tools a very pronounced resonance pattern is found in the deformations of the spectral mesh as well as in the unfolding of the diabolical points located at the nodes of this mesh non oscillatory as well as oscillatory dynamo regimes are obtained an estimation technique is developed for obtaining the critical profiles at which the eigenvalues enter the right spectral half plane with non vanishing imaginary components at which overcritical oscillatory dynamo regimes form finally frechet derivative gradient based methods are developed suitable for further numerical investigations of krein space related setups such as mhd 2 dynamos or models of symmetric quantum mechanics

system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

a new perspective on static and low order anti windup synthesis by viewing the anti windup problem as a decoupled set of subsystems and relating this configuration to a general static anti windup set up lmi conditions are established which guarantee stability and performance of the resulting closed loop system the approach taken and the mapping used for the performance index are logical and intuitive and it is argued central to the true anti windup objective the approach enables one to construct static anti windup compensators in a systematic and numerically tractable manner the idea is extended to allow low order anti windup compensators to be synthesized which while being sub optimal can improve transient performance and possess several desired properties such as low computational overhead and sensible closed loop pole locations in addition low order anti windup synthesis is often feasible when the corresponding static synthesis is not

linear lmi based external anti windup augmentation for stable linear systems we study linear anti windup augmentation for linear control systems with saturated linear plants in the special case when the anti windup compensator can only modify the input and the output of the windup prone linear controller we also measure the arising performance in terms of the finite l 2 gain from exogenous inputs to selected performance outputs our main results are a system theoretic feasibility characterization for fixed order anti windup design and a linear matrix inequality lmi formulation for optimal static and plant order anti windup design interpretations of lower bounds on the achievable performance are also given the effectiveness of the design procedure is demonstrated on a simulation example

quasi exactly solvable quartic potential a new two parameter family of quasi exactly solvable quartic polynomial potentials is introduced heretofore it was believed that the lowest degree one dimensional quasi exactly solvable polynomial potential is sextic this belief is based on the assumption that the hamiltonian must be hermitian however it has recently been discovered that there are huge classes of non hermitian symmetric hamiltonians whose spectra are real discrete and bounded below replacing hermiticity by the weaker condition of symmetry allows for new kinds of quasi exactly solvable theories the spectra of this family of quartic potentials discussed here are also real discrete and bounded below and the quasi exact portion of the spectra consists of the lowest j eigenvalues these eigenvalues are the roots of a jth degree polynomial

interior two dimensional acoustic modelling and modal analysis using isogeometric approach abstract in this paper the interior two dimensional acoustic modelling and modal analysis are presented in the framework of isogeometric analysis iga the acoustic domain governed by the helmholtz equation is parameterized and analysed by non uniform rational lagrange nurl basis which can construct exact geometry model inherently like non uniform rational b spines nurbs and can provide a more straightforward way than nurbs to impose dirichlet boundary conditions the verification and versatility of iga using nurl are assessed in the investigation of a unit square domain and a unit circular domain by comparison with analytical solutions furthermore a quadrilateral domain with concave or convex conics is studied and some innovative results are presented which can be the benchmark data for other algorithm researches the effects of geometric weight and aspect ratio on acoustic eigenvalue and eigenmode of the quadrilateral domain are investigated in detail

a partial parameterization of nonlinear output feedback controllers for saturated linear systems this paper addresses the stabilization problem of linear systems subject to input saturation the major purpose is to introduce nonlinearity into control laws so as to expand the design freedom for performance enhancement to this end a new approach is developed which involves a partial differential matrix inequality pdmi a class of stabilizing feedback laws is explicitly obtained by solving this pdmi analytically and the feedback laws are parameterized by a nonlinear function further it is revealed that any linear observer can be used to realize the output feedback stabilization numerical examples including the seek control of a hard disk drive show that the introduced nonlinearity does contribute to the improvement of system performance the application to integral control is also discussed

uniting local and global output feedback controllers we consider control systems for which we know two stabilizing output feedback controllers one is globally asymptotically stabilizing while the other one is only locally asymptotically stabilizing we look for a composite output feedback control law that is equal to the local feedback on a neighborhood of the origin and that is globally asymptotically stabilizing since we want some robustness with respect to measurement noise actuator errors and external disturbances we need to consider hybrid output feedback controllers under an input output to state stability assumption we exhibit a solution of this uniting problem by means of a dynamic hybrid output feedback controller then we particularize our study to linear control systems with saturation at the input for which we know two stabilizing output feedback controllers one is a nonlinear globally asymptotically stabilizing controller while the other one is a high performance linear only locally asymptotically stabilizing controller we specify numerically tractable conditions to solve this uniting problem finally we illustrate our main results by means of numerical examples

exact pt symmetry is equivalent to hermiticity we show that a quantum system possessing an exact antilinear symmetry in particular pt symmetry is equivalent to a quantum system having a hermitian hamiltonian we construct the unitary operator relating an arbitrary non hermitian hamiltonian with exact pt symmetry to a hermitian hamiltonian we apply our general results to pt symmetry in finite dimensions and give the explicit form of the above mentioned unitary operator and hermitian hamiltonian in two dimensions our findings lead to the conjecture that non hermitian cpt symmetric field theories are equivalent to certain nonlocal hermitian field theories

brief paper anti windup synthesis for linear control systems with input saturation achieving regional nonlinear performance in this paper we present lmi based synthesis tools for regional stability and performance of linear anti windup compensators for linear control systems we consider both static and dynamic compensators algorithms are developed that minimize the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and that minimize this upper bound with a guaranteed reachable set or domain of attraction based on the structure of the optimization problems it is shown that for systems whose plants have poles in the closed left half plane plant order dynamic anti windup can achieve semiglobal exponential stability and finite l 2 gain for exogenous inputs with l 2 norm bounded by any finite value the problems are studied in a general setting where the only requirement on the linear control system is well posedness and internal stability the effectiveness of the proposed techniques is illustrated with an example

finite dimensional pt symmetric hamiltonians this paper investigates finite dimensional pt symmetric hamiltonians it is shown here that there are two ways to extend real symmetric hamiltonians into the complex domain i the usual approach is to generalize such hamiltonians to include complex hermitian hamiltonians ii alternatively one can generalize real symmetric hamiltonians to include complex pt symmetric hamiltonians in the first approach the spectrum remains real while in the second approach the spectrum remains real if the pt symmetry is not broken both generalizations give a consistent theory of quantum mechanics but if d 2 a d dimensional hermitian matrix hamiltonian has more arbitrary parameters than a d dimensional pt symmetric matrix hamiltonian

robust anti windup controller design of time delay fuzzy systems with actuator saturations this study presents a robust anti windup fuzzy control approach for uncertain nonlinear time delay systems with actuator saturations the discussed system dynamics is presented by the takagi sugeno t s fuzzy model to facilitate the design process the nonlinearity of input saturation is characterized by a specific sector condition given a stabilizing dynamic output feedback fuzzy controller an anti windup control approach is then developed to maximize the size of estimate of the domain of attraction significantly the convergence of all admissible initial states within this region could be ensured based on the lyapunov krasovskii delay independent and delay dependent analyses sufficient conditions for the robust stabilization are derived these conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities allowing the fuzzy controller to be synthesized more efficiently finally numeric simulations are given to validate the proposed approach

brief multiplier theory for stability analysis of anti windup control systems we apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti windup bumpless transfer awbt schemes for appropriate choices of the multipliers we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities lmis we show that a number of previously reported attempts to analyze awbt stability using seemingly diverse techniques such as the popov circle and off axis circle criteria the optimally scaled small gain theorem generalized m upper bound and describing functions can all be generalized within the framework of this paper

isogeometric analysis for explicit elastodynamics using a dual basis diagonal mass formulation abstract we propose a method to obtain diagonal mass matrices for nurbs based approximation spaces by a dual lumping method the use of lumped mass matrices is of great importance in elastodynamics problems as they can be employed in explicit time integration schemes which do not require the solution of a linear system in finite elements several well established methods such as row sum diagonal scaling or nodal quadrature methods have been used to obtain lumped mass matrices for different applications however for higher order and higher continuity approximation spaces such as those derived from nurbs these approaches have only limited second order accuracy in this work we derive a dual basis which has optimal approximation and dispersion properties while maintaining local support the dual space has discontinuities at the element boundaries knots and it is used to provide the test functions in the context of a petrov galerkin method this results in a general framework for the study of lumped mass matrices which can be employed in explicit time integration schemes with high order accuracy numerical experiments are presented to demonstrate the applicability of the method to problems with smooth solutions as well as to wave propagation problems with reduced regularity

multi level bezier extraction for hierarchical local refinement of isogeometric analysis abstract one of the main topics of research on isogeometric analysis is local refinement among the various techniques currently studied and developed one of the most appealing referred to as hierarchical b splines consists of defining a suitable set of basis functions on different hierarchical levels this strategy can also be improved for example to recover partition of unity resorting to a truncation operation giving rise to the so called truncated hierarchical b splines despite its conceptual simplicity implementing the hierarchical definition of shape functions into an existing code can be rather involved in this work we present a simple way to bring the hierarchical isogeometric concept closer to a standard finite element formulation practically speaking the hierarchy of functions and knot spans is flattened into a sequence of elements being equipped with a standard single level basis in fact the proposed multi level extraction is a generalization of the classical bezier extraction and analogously offers a standard element structure to the hierarchical overlay of functions moreover this approach is suitable for an extension to non linear problems and for a parallel implementation the multi level extraction is presented as a general concept that can be applied to different kinds of refinements and basis functions finally few basic algorithms to compute the local multi level extraction operator for knot insertion on spline spaces are outlined and compared and some numerical examples are presented

linear discrete time global and regional anti windup an lmi approach in this article we address linear anti windup design for linear discrete time control systems guaranteeing regional and global stability and performance the techniques that we develop are the discrete time counterpart of existing techniques for anti windup augmentation which lead to convex constructions by way of linear matrix inequalities lmis when adopting static and plant order anti windup augmentation interesting system theoretic interpretations of the performance bounds for the non linear closed loop can also be given we show here that parallel results apply to the discrete time case we derive the corresponding conditions and prove their effectiveness by adapting the continuous time approaches to the discrete time case

convex design of a robust antiwindup controller for an lft model in the context of a closed loop lft model an lmi technique is proposed for the synthesis of a static or dynamic antiwindup controller which can be seen as a nontrivial extension of existing lmi methods for designing a robust filter or feedforward controller a missile example is given to illustrate the feasibility of the technique

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

a framework for multivariable algebraic loops in linear anti windup implementations abstract this brief paper addresses the implementation and well posedness aspects of multivariable algebraic loops which arise naturally in many anti windup control schemes using the machinery of linear complementarity problems a unified framework is developed for establishing well posedness of such algebraic loops enforcing well posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti windup design stage several existing anti windup implementations appear as special cases of the unified framework presented in this brief paper

anti windup synthesis using riccati equations the aim of this paper is to give a novel solution to the full order anti windup aw compensation problem for stable systems with input saturation the solution is obtained by completing the square in three steps and requires the solution to a single bounded real riccati equation characterized by the open loop plant s norm the riccati equation plays the role of the lmis usually found in anti windup synthesis but in addition to its numerical advantages it yields a family of anti windup compensators with the same performance this family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti windup compensator and the robustness properties of the closed loop saturated system thus this matrix allows a robust anti windup problem to be solved in a straightforward and intuitive manner the effectiveness of the proposed technique is demonstrated on a simple example

piecewise quadratic lyapunov functions for systems with deadzones or saturations a piecewise quadratic lyapunov function is developed for the analysis of the global and regional performances for systems with saturation deadzone in a general feedback configuration with an algebraic loop this piecewise quadratic lyapunov function effectively incorporates the structure of the saturation deadzone nonlinearity several sector like conditions are derived to describe the complex nonlinear algebraic loop these conditions transform several performance analysis problems into optimization problems with linear or bilinear matrix inequalities the effectiveness of the results is demonstrated with numerical examples

spectral analysis of the complex cubic oscillator using the exact semiclassical analysis we study the spectrum of a one parameter family of complex cubic oscillators the invariance property of the complex hamiltonians and the reality property of the spectrum are discussed analytic continuations of the spectrum in the complex parameter and their connections with the resonance problem for the real cubic oscillator are investigated the global analytic structure of the spectrum yields a branch point structure similar to the multivalued analytic structure discovered by bender and wu for the quartic oscillator

dynamic output feedback for discrete time systems under amplitude and rate actuator constraints this work proposes a technique for the design of stabilizing dynamic output feedback controllers for discrete time linear systems with rate and amplitude saturating actuators the nonlinear effects introduced by the saturations in the closed loop system are taken into account by using a generalized sector condition which leads to theoretical conditions for solving the problem directly in the form of linear matrix inequalities

brief paper output feedback design for saturated linear plants using deadzone loops in this paper we present an lmi based synthesis approach on output feedback design for input saturated linear systems by using deadzone loops algorithms are developed for minimizing the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and for minimizing this upper bound with a guaranteed reachable set or domain of attraction the proposed synthesis approach will always lead to regionally stabilizing controllers if the plant is exponentially unstable to semi global results if the plant is non exponentially unstable and to global results if the plant is already exponentially stable where the only requirement on the linear plant is detectability and stabilizability the effectiveness of the proposed techniques is illustrated with one example

brief paper an anti windup technique for lmi regions the anti windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time invariant plant and controller this paper presents a linear matrix inequality lmi based method that attempts to minimize performance deterioration while explicitly restricting the anti windup closed loop dynamics the restriction placed on the dynamics is described via lmi regions which is a form of regional pole placement finally the techniques discussed in this paper are demonstrated on an electro hydraulic testbed

pseudo hermiticity and generalized pt and cpt symmetries we study certain linear and antilinear symmetry generators and involution operators associated with pseudo hermitian hamiltonians and show that the theory of pseudo hermitian operators provides a simple explanation for the recent results of bender brody and jones quant ph 0208076 on the cpt symmetry of a class of pt symmetric non hermitian hamiltonians we present a natural extension of these results to the class of diagonalizable pseudo hermitian hamiltonians h with a discrete spectrum in particular we introduce generalized parity p time reversal t and charge conjugation c operators and establish the pt and cpt invariance of h

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

observer based anti windup compensator design for saturated control systems using an lmi approach in practical control systems actuator saturation usually induces a windup phenomenon and potentially results in system instability accordingly this paper develops an observer based auxiliary anti windup compensation scheme to mitigate the effects of actuator limitations on the performance and stability of the controlled system in the proposed approach the controller output signal passing through the saturation element is treated as an external disturbance imported to the designed controller and an auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal the conditions required to maintain the system performance in the presence of actuator saturation are formulated as an lmi criterion the l 2 stability criterion of the anti windup compensator design is also formulated as an lmi condition it is shown that by integrating the two lmi conditions and solving the resulting optimization problem the resulting anti windup controller both minimizes the performance attenuation of the saturated control system and guarantees its l 2 stability

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

synthesis of stabilizing antiwindup controllers using piecewise quadratic lyapunov functions we consider the problem of antiwindup controller synthesis based on the general antiwindup framework presented in kothare automatica vol 30 no 12 pp 1869 1883 1994 applicable to linear time invariant systems lti subject to a saturating actuator our synthesis approach takes advantage of the fact that the antiwindup system is a piecewise affine system and thus we can utilize piecewise quadratic lyapunov function theory johansson and rantzer ieee trans autom control vol 43 no 4 pp 555 559 apr 1998 rantzer and johansson ieee trans autom control vol 45 no 4 pp 629 637 apr 2000 and johansson proc 14th world congr beijing china 1999 pp 521 5260 to determine a stabilizing antiwindup control law the synthesis problem is expressed in terms of bilinear matrix inequalities bmis and is solved using an iterative approach as well as using commercial software the performance of the system is optimized by minimizing an upper bound on the induced gain of the system the proposed approach is demonstrated using examples

mathcal p mathcal t symmetry as a generalization of hermiticity the hilbert space in symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product the most general symmetric matrix hamiltonians are constructed for the 2 2 and 3 3 cases in the former case the symmetric hamiltonian represents the most general matrix hamiltonian with a real spectrum in both cases hermitian matrices are shown to be special cases of symmetric matrices this finding confirms and strengthens the early belief that the symmetric quantum mechanics is a generalization of the conventional hermitian quantum mechanics

isogeometric spline forests in this paper we present isogeometric spline forests an isogeometric spline forest is a hierarchical spline representation capable of representing surfaces or volumes of arbitrarily complex geometry and topological genus spline forests can accomodate arbitrary degree and smoothness in the underlying hierarchical basis as well as non uniform knot interval configurations we describe adaptive h refinement and coarsening algorithms for isogeometric spline forests and develop a bezier extraction framework which provides a simple and efficient single level finite element description of the complex multi level unstructured hierarchical spline basis we then demonstrate the potential of spline forests as a basis for analysis in the context of transient advection diffusion problems where fully integrated adaptivity is demonstrated for the first time in an isogeometric simulation in all cases the adaptive process remains local even in the case of moving fronts and preserves exact geometry at the coarsest level of the discretization the accuracy and robustness of the approach is demonstrated in all cases

isogeometric analysis for nonlinear planar kirchhoff rods weighted residual formulation and collocation of the strong form abstract high order shape functions used in isogeometric analysis allow the direct solution not only to the weighted residual formulation of the strong form opening the door to new integration schemes e g reduced gauss lobatto quadrature integration at superconvergent sites but also to collocation approaches e g using greville or superconvergent collocation points the goal of the present work is to compare these different methods through the application to the planar kirchhoff rod a fourth order rotation free formulation used to model slender beams under large deformations robustness of the geometrically nonlinear solution is improved using the mixed integration point mip newton a method that combines the advantages of displacement and mixed formulations based on the observations of the convergence plots convergence order estimates are provided for each discretization method advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks

robust stabilizing controller design for takagi sugeno fuzzy descriptor systems under state constraints and actuator saturation abstract the aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by takagi sugeno fuzzy descriptor systems and subject to input and state constraints for this a novel structure of modified parallel distributed compensation control laws is proposed the controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from lyapunov s stability theory and the choice of an original lyapunov function this ensures the stabilization of the closed loop system and the respect of the state and input constraints regionally the technique is illustrated through three numerical examples

the l2 anti windup problem for discrete time linear systems definition and solutions abstract the anti windup problem for discrete time linear systems is formalized in terms of the l 2 norm of the deviation of the actual response of the system with saturation and anti windup compensation from the ideal unconstrained response we show that paralleling continuous time results a r teel n kapoor the l 2 anti windup problem its definition and solution in proceedings of the 4th ecc brussels belgium july 1997 the problem is globally solvable if and only if the plant is non exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable we provide a constructive solution whenever the problem is solvable also offered is a high performance global solution for exponentially stable plants based on receding horizon control illustrative simulations are included

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

hierarchical t splines analysis suitability bezier extraction and application as an adaptive basis for isogeometric analysis abstract in this paper hierarchical analysis suitable t splines hasts are developed the resulting spaces are a superset of both analysis suitable t splines and hierarchical b splines the additional flexibility provided by the hierarchy of t spline spaces results in simple highly localized refinement algorithms which can be utilized in a design or analysis context a detailed theoretical formulation is presented bezier extraction is extended to hasts simplifying the implementation of hasts in existing finite element codes the behavior of a simple hasts refinement algorithm is compared to the local refinement algorithm for analysis suitable t splines demonstrating the superior efficiency and locality of the hasts algorithm finally hasts are utilized as a basis for adaptive isogeometric analysis

spiked and symmetrized decadic potentials supporting elementary n plets of bound states we show that the potential wells v x x10 ax8 bx6 cx4 dx2 f x2 with a central spike possess arbitrary finite multiplets of elementary exact bound states their strong asymptotic growth implies an ambiguity in their symmetrically generalized quantization via complex boundary conditions but the three eligible methods coincide at our exceptional solutions

anti windup based dynamic controller synthesis for nonlinear systems under input saturation this paper describes the design of dynamic controller and static anti windup compensator awc for lipschitz nonlinear systems under input saturation global and local awc based control schemes for stabilization of the nonlinear systems are proposed and necessary conditions for feasibility of the control approaches are investigated a one step approach for simultaneous design of h controller and awc by means of linear matrix inequalities lmis is presented herein which supports multi objective synthesis to attain stabilization or tracking robustness against disturbance and noise and penalization of large and high frequency control signals this multi objective synthesis can be accomplished by incorporating design weights as commonly used in the standard h control theory to design a performance oriented anti windup based control scheme lmis for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic lyapunov function the lipschitz condition the global sector condition l 2 gain reduction substantial matrix algebra and variable transformation in order to cope with unstable and oscillatory nonlinear systems lmi based local results are established using a local sector condition additional conditions are derived by incorporating properties of the saturation function to ensure well posedness of the controller two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation

anti windup control design for exponentially unstable lti systems with actuator saturation in this paper a new saturation control technique in the framework of anti windup compensation is developed for exponentially unstable linear time invariant systems subject to input nonlinearities the proposed control algorithm guarantees regional stability in the existence of input saturation and provides less conservative performance than most existing anti windup schemes moreover an explicit form of anti windup controller with its order no more than the order of the plant is derived an inverted pendulum example is used to demonstrate the advantages of the newly proposed anti windup control technique

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

a collocated isogeometric finite element method based on gauss lobatto lagrange extraction of splines generalizing the concept of bezier extraction we introduce an extraction operator that links c0c0 gauss lobatto lagrange functions with smooth splines this opens the door for collocated isogeometric analysis that combines the accuracy of the galerkin method with collocation type formation and assembly procedures we present the key ingredients of the technology i e integration by parts and the weighted residual form the interaction of gauss lobatto lagrange extraction with gauss lobatto quadrature and symmetrization with the ultra weak formulation we compare the new method with standard isogeometric galerkin and isogeometric point collocation methods for spline discretizations in three dimensions

pseudo hermitian hamiltonians indefinite inner product spaces and their symmetries we extend the definition of generalized parity p charge conjugation c and time reversal t operators to nondiagonalizable pseudo hermitian hamiltonians and use these generalized operators to describe the full set of symmetries of a pseudo hermitian hamiltonian according to a fourfold classification in particular we show that t p and ct p are the generators of the p antiunitary symmetries moreover a necessary and sufficient condition is provided for a pseudo hermitian hamiltonian h to admit a p reflecting symmetry which generates the p pseudounitary and the p pseudoantiunitary symmetries finally a physical example is considered and some hints on the p unitary evolution of a physical system are also given

brief paper simultaneous linear and anti windup controller synthesis using multiobjective convex optimization we present a method for the synthesis of a control law for input constrained linear systems that incorporates both a traditional linear output feedback controller as well as a static anti windup compensator unlike traditional two step anti windup controller designs in which the linear controller and anti windup compensator are designed sequentially our method synthesizes all controller parameters simultaneously this one step design retains the anti windup structure thus providing structurally a priori compensation for saturation we derive sufficient conditions for guaranteeing global quadratic stability and for satisfying multiple possibly conflicting performance objectives on the constrained and unconstrained closed loop dynamics the resulting synthesis problem is recast as an optimization over linear matrix inequalities lmis we demonstrate the proposed method on a benchmark problem

anti windup synthesis via sampled data piecewise affine optimal control discrete time receding horizon optimal control is employed in model based anti windup augmentation the optimal control formulation enables designs that minimize the mismatch between the unconstrained closed loop response with a given controller and the constrained closed loop response with anti windup augmentation recently developed techniques for off line computation of the constrained linear regulator s solution which is piecewise affine facilitate implementation the resulting sampled data anti windup closed loop system s properties are established and its performance is demonstrated on a simulation example

on the eigenproblems of pt symmetric oscillators we consider the non hermitian hamiltonian h d2 dx2 p x2 ix 2n 1 on the real line where p x is a polynomial of degree at most n 1 with all non negative real coefficients possibly p 0 it is proved that the eigenvalues must be in the sector arg 2n 3 also for the cubic case h d2 dx2 ix 3 we establish a zero free region of the eigenfunction u and its derivative u and we find some other interesting properties of eigenfunctions