lq optimal control for a class of pulse width modulated systems we consider linear quadratic optimal control for a class of pulse width modulated systems the problem is motivated from a practical application digital control of switching power converters the control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account

the projective method for solving linear matrix inequalities numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities lmi since solving an lmi amounts to a convex optimization problem such formulations are known to be numerically tractable however the interest in lmi based design techniques has really surged with the introduction of efficient interior point methods for solving lmis with a polynomial time complexity this paper describes one particular method called the projective method simple geometrical arguments are used to clarify the strategy and convergence mechanism of the projective algorithm a complexity analysis is provided and applications to two generic lmi problems feasibility and linear objective minimization are discussed

three dimensional contour fdtd modeling of scattering from single and multiple bodies this paper introduces a generalization of the three dimensional finite difference time domain fdtd method the three dimensional contour fdtd cfdtd method is introduced the fdtd method represents curved media boundaries as stepped edges through the use of subcell modeling the cfdtd method conformably models bodies with curved surfaces yet retains the ability to model corners and edges electromagnetic scattering from single and multiple bodies is presented

hodge integrals and tau symmetric integrable hierarchies of hamiltonian evolutionary pdes for an arbitrary semisimple frobenius manifold we construct hodge integrable hierarchy of hamiltonian partial differential equations in the particular case of quantum cohomology the tau function of a solution to the hierarchy generates the intersection numbers of the gromov witten classes and their descendents along with the characteristic classes of hodge bundles on the moduli spaces of stable maps for the one dimensional frobenius manifold the hodge hierarchy is a deformation of the korteweg de vries hierarchy depending on an infinite number of parameters conjecturally this hierarchy is a universal object in the class of scalar hamiltonian integrable hierarchies possessing tau functions mathematics subject classication 2010 primary 53d45 secondary 37k10

a general integral quadratic constraints theorem with applications to a class of sampled data systems in the framework of integral quadratic constraints a more general stability theorem is derived by relaxing the assumptions on the uncertainty in contrast to existing results input output relations are only required to hold on a subspace of the full signal space this result is employed to incorporate uncertainties exhibiting sampling behavior into the framework of integral quadratic constraints the arising infinite dimensional stability test is exactly reduced to a finite dimensional linear matrix inequality advantages of this approach are illustrated for the specific case of an interconnection including a pulse width modulator

computation of open gromov witten invariants for toric calabi yau 3 folds by topological recursion a proof of the bkmp conjecture the bkmp conjecture 2006 2008 proposed a new method to compute closed and open gromov witten invariants for every toric calabi yau 3 folds through a topological recursion based on mirror symmetry so far this conjecture has been verified to low genus for several toric cy3folds and proved to all genus only for mathbb c 3 in this article we prove the general case our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs on the a model side this is the localization formula and on the b model side the graphs encode the recursive algorithm of the topological recursion

a new 3 d conformal pec fdtd scheme with user defined geometric precision and derived stability criterion a new conformal finite difference time domain cfdtd updating scheme for metallic surfaces nonaligned in the grid is presented in this paper in contrast to existing conformal models the new model can be formulated with the original yee fdtd update equation therefore the proposed scheme can be easily added in standard fdtd codes even if the codes are already parallelized or hardware accelerated in addition based on the commonly used conventional stability criterion a derivation of the stability is presented and based on the conformal geometric information a time step reduction formula is presented the time step reduction is used as a user defined parameter to tradeoff speed versus accuracy the achievable geometric precision is optimized to a given time step therefore even with the conventional time step no reduction the presented scheme profits from the conformal discretization to show the performance and the robustness of the proposed scheme canonical validations and two real world applications were investigated a broadband low profile circular antenna was successfully simulated showing the benefit of the conformal fdtd method compared to the conventional scheme furthermore a cad based mobile phone was conformally discretized and successfully simulated showing that the proposed scheme is highly suited for the simulation of advanced engineering problems

hodge gue correspondence and the discrete kdv equation we prove the conjectural relationship recently proposed in dubrovin and yang commun number theory phys 11 311 336 2017 between certain special cubic hodge integrals of the gopakumar marino vafa type gopakumar and vafa in adv theor math phys 5 1415 1443 1999 marino and vafa in contemp math 310 185 204 2002 and gue correlators and the conjecture proposed in dubrovin et al adv math 293 382 435 2016 that the partition function of these hodge integrals is a tau function of the discrete kdv hierarchy

remodeling the b model we propose a complete new formalism to compute unambiguously b model open and closed amplitudes in local calabi yau geometries including the mirrors of toric manifolds the formalism is based on the recursive solution of matrix models recently proposed by eynard and orantin the resulting amplitudes are non perturbative in both the closed and the open moduli the formalism can then be used to study stringy phase transitions in the open closed moduli space at large radius this formalism may be seen as a mirror formalism to the topological vertex but it is also valid in other phases in the moduli space we develop the formalism in general and provide an extensive number of checks including a test at the orbifold point of ap fibrations where the amplitudes compute the t hooft expansion of vevs of wilson loops in chern simons theory on lens spaces we also use our formalism to predict the disk amplitude for the orbifold mathbb c 3 mathbb z 3

topological open strings on orbifolds we use the remodeling approach to the b model topological string in terms of recursion relations to study open string amplitudes at orbifold points to this end we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest we exemplify this procedure for the mathbb c 3 mathbb z 3 orbifold point of local mathbb p 2 where we present results for topological string amplitudes for genus zero and up to three holes and for the one holed torus these amplitudes can be understood as generating functions for either open orbifold gromov witten invariants of mathbb c 3 mathbb z 3 or correlation functions in the orbifold cft involving insertions of both bulk and boundary operators

local absorbing boundary conditions for elliptical shaped boundaries we compare several local absorbing boundary conditions for solving the helmholtz equation by a finite difference or finite element method exterior to a general scatterer these boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface in order to compare the computational solution with an analytical solution we consider as an example scattering about an ellipse we solve the helmholtz equation with both finite differences and finite elements we also introduce a new boundary condition for an ellipse based on a modal expansion

an elliptical cylindrical fdtd algorithm for modeling conformal patch antenna an explicit finite difference time domain fdtd method is described using a uniform elliptical cylindrical spatial grid for time domain maxwell s equations to accurately and efficiently model conformal elliptical cylindrical line fed patch antennas and overcome stair casing errors such errors are encountered when a cartesian spatial grid is used for modeling curved surfaces in addition the method described in this paper obviates coding complexity encountered in modeling of curved surfaces which is manifest using cp fdtd or cfdtd techniques characterizing expressions representing the absorbing boundary condition and courant stability condition are presented and used to provide a highly effective algorithm to simulate conformal microstrip antennas the proposed fdtd algorithm is validated against hfss results showing excellent correlation

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

the topological vertex we construct a cubic field theory which provides all genus amplitudes of the topological a model for all non compact toric calabi yau threefolds the topology of a given feynman diagram encodes the topology of a fixed calabi yau with schwinger parameters playing the role of kahler classes of the threefold we interpret this result as an operatorial computation of the amplitudes in the b model mirror which is the quantum kodaira spencer theory the only degree of freedom of this theory is an unconventional chiral scalar on a riemann surface in this setup we identify the b branes on the mirror riemann surface as fermions related to the chiral boson by bosonization

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

a proof of a conjecture of marino vafa on hodge integrals where i c1 li is the first chern class of li and j cj e is the j th chern class of the hodge bundle hodge integrals arise in the calculations of gromov witten invariants by localization techniques 14 7 the explicit evaluation of hodge integrals is a difficult problem the hodge integrals involving only classes can be computed recursively by witten s conjecture 26 proven by kontsevich 13 algorithms of computing hodge integrals are described in 2 in 23 m marino and c vafa obtained a closed formula for a generating function of certain open gromov witten invariants some of which has been reduced to hodge integrals by localization techniques which are not fully clarified mathematically this leads to a conjectural formula of hodge integrals to state this formula we introduce some notation following 28 let

h robust servo problem with h norm constraint a robust servo problem with an h infinity norm constraint is investigated based on the lmi linear matrix inequality approach to the h infinity control problem the following results are obtained 1 a necessary and sufficient condition for the existence of an h infinity controller with robust tracking property is derived it consists of the following two indepent conditions i the existence of an h infinity controller ii a boundary constraint at the reference mode 2 if there exists an h infinity controller with robust tracking performance there exists one whose order equals the sum of an h infinity controller and the internal model

practical optimal state feedback control law for continuous time switched affine systems with cyclic steady state in this article a method for computing an optimal state feedback control law for continuous time switched affine systems exhibiting cyclic behaviour in steady state is presented the hybrid solutions are deduced from the fillipov solutions it is shown that the optimal trajectory synthesis implies to determine singular arcs algebraic conditions are given to obtain these particular arcs of the trajectory a numerical procedure is then proposed to generate optimal trajectories on a given state space area avoiding the classical two point boundary value problem occurring in optimal control synthesis the interpolation of the solutions set through a neural network yields a state feedback control law several examples in the power converters field show the feasibility and the efficiency of the method

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

simplifying the h theory via loop shifting matrix pencil and descriptor concepts the 2 riccati h controller formulae and derivations are simplified via various loop shifting transformations that are naturally expressed in terms of a degree one polynomial system matrix psm closely related to the luenberger descriptor form of a system the technique enables one without loss of generality to restrict attention to the simple case in which d 11 0 d 22 0 d t 12 0 l d 21 0 l d l 12 c1 0 and b 1 d t 21 0 matrix fraction descriptions mfds for the algebraic riccati equation solutions afford another change of variables which brings the 2 riccati h controller formulae into a cleaner more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the riccati solutions pi and q blow up and in cases where l qp is nearly singular numerical difficulties previously associated with verifying the existence conditions p 0 q 0 and maxlpar qp 1 are largely eliminated by e

simple maps hurwitz numbers and topological recursion we introduce the notion of fully simple maps which are maps with non self intersecting disjoint boundaries in contrast maps where such a restriction is not imposed are called ordinary we study in detail the combinatorics of fully simple maps with topology of a disk or a cylinder we show that the generating series of simple disks is given by the functional inversion of the generating series of ordinary disks we also obtain an elegant formula for cylinders these relations reproduce the relation between moments and higher order free cumulants established by collins et al 22 and implement the symplectic transformation x leftrightarrow y on the spectral curve in the context of topological recursion we conjecture that the generating series of fully simple maps are computed by the topological recursion after exchange of x and y we propose an argument to prove this statement conditionally to a mild version of the symplectic invariance for the 1 hermitian matrix model which is believed to be true but has not been proved yet our conjecture can be considered as a combinatorial interpretation of the property of symplectic invariance of the topological recursion our argument relies on an unconditional matrix model interpretation of fully simple maps via the formal hermitian matrix model with external field we also deduce a universal relation between generating series of fully simple maps and of ordinary maps which involves double monotone hurwitz numbers in particular ordinary maps without internal faces which are generated by the gaussian unitary ensemble and with boundary perimeters lambda 1 ldots lambda n are strictly monotone double hurwitz numbers with ramifications lambda above infty and 2 ldots 2 above 0 combining with a recent result of dubrovin et al 24 this implies an elsv like formula for these hurwitz numbers

a new method to avoid reduction of time step in the cp fdtd method a new cp wcs fdtd method is developed to avoid the time step reduction in the conformal path fdtd method the stability condition in this method is not related with the shape and size of the distorted cell and the time step size in this method is only determined by the space discretization perpendicular to the curved metal surface the cp wcs fdtd method has the same accuracy as that for the cp fdtd method and due to large time step size can be used the cp wcs fdtd has higher computation efficiency which is demonstrated by numerical examples

h optimization without assumptions on finite or infinite zeros explicit algebraic conditions are presented for the suboptimality of some parameter in the h infty optimization problem by output measurement control apart from two strict properness conditions no artificial assumptions restrict the underlying system in particular the plant may have zeros on the imaginary axis or at infinity these suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

virasoro symmetries of the extended toda hierarchy we prove that the extended toda hierarchy of 1 admits a nonabelian lie algebra of infinitesimal symmetries isomorphic to half of the virasoro algebra the generators lm m 1 of the lie algebra act by linear differential operators onto the tau function of the hierarchy we also prove that the tau function of a generic solution to the extended toda hierarchy is annihilated by a combination of the virasoro operators and the flows of the hierarchy as an application we show that the validity of the virasoro constraints for the cp1 gromov witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended toda hierarchy