pseudo divergence free element free galerkin method for incompressible fluid flow abstract incompressible modeling in finite elements has been a major concern since its early developments and has been extensively studied however incompressibility in mesh free methods is still an open topic thus instabilities or locking can preclude the use of mesh free approximations in such problems here a novel mesh free formulation is proposed for incompressible flow it is based on defining a pseudo divergence free interpolation space that is the finite dimensional interpolation space approaches a divergence free space when the discretization is refined note that such an interpolation does not include any overhead in the computations the numerical evaluations are performed using the inf sup numerical test and two well known benchmark examples for stokes flow

solution to nonsingular h 2 optimal control problem with unstable weights abstract in this paper we propose an approach that treats the synthesis of servo systems as well as the estimation of unstable plants as h 2 control problems with unstable weights this approach is based on the notion of comprehensive stability and the parameterization of comprehensively stabilizing controllers the complete result for the nonsingular case is obtained this provides an h 2 optimal synthesis method for general linear servo problems and estimation problems of unstable plants

lmi relaxation to riccati equations in structured control in this paper we discuss structured control methods for large scale interconnected systems based on a relaxation of riccati equations we derive some linear matrix inequality lmi conditions for sub optimal controllers in which information structure can be imposed in particular we derive controllers by solving low dimensional lmis which are decentralized except for the sharing information between neighbours as determined by the plant interconnection also we optimize a performance bound for each of the derived controllers

technical communique h optimal terminal control for linear systems with delayed states and controls in this paper we consider a linear time varying system with state and control delay terms both lumped and distributed subject to unknown square integrable disturbances using a differential games approach we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the h norm of the operator mapping the disturbance to the weighted control and terminal state

lmi based h optimal control with transients in this article the worst case norm of the regulated output over all exogenous signals and initial states as a performance measure of the system is characterised in terms of linear matrix inequalities lmis optimal time invariant state and output feedback controllers are synthesised as minimising this performance measure the essential role in this synthesis plays a weighting matrix reflecting the relative importance of the uncertainty in the initial state contrary to the uncertainty in the exogenous signal h optimal control with transients is shown to be actually a trade off between h control being optimal under unknown exogenous disturbances and zero initial state and control being optimal under zero exogenous signal and unknown initial conditions if and only if the weighting matrix satisfies a fundamental inequality if this inequality is met the performance measure is achieved and the explicit formulae for the worst case disturbance and initial state are provided if this inequality fa

h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

scheduled control for robust attenuation of non stationary sinusoidal disturbances with measurable frequencies attenuation of sinusoidal disturbances with uncertain yet online measurable frequencies is considered the disturbances are modeled as the outputs of an undisturbed parameter dependent exogenous system with a skew symmetric system matrix obtained in response to nonzero initial conditions the problem is formulated for a parameter dependent plant as the synthesis of a parameter dependent controller in a way to ensure internal stability as well as a desired level of steady state disturbance attenuation in the face of all admissible parameter variations the solvability of this problem is first related to the existence of bounded solutions to a matrix differential regulator equation subject to an asymptotic norm constraint reformulating this as a parameter dependent state feedback like synthesis based on which suitable solutions to the differential regulator equation can be obtained online tractable solvability conditions are then provided in the form of parameter dependent matrix inequalities controllers that solve the generalized asymptotic regulation problem are also parameterized in terms of the suitable solutions of the differential regulator equation and some free parameter dependent matrices that are to be designed off line to ensure stability a procedure is then developed to design the free parameters in a way to achieve desirable transient behavior the use of the developed synthesis procedure is illustrated on a simplified version of the course control problem in ship steering

generalized l sub 2 synthesis introduces a general framework for control design which can be used to solve several open problems in robust and optimal control these include systems subject to independently norm bounded disturbances robust stability for systems subject to element by element bounded structured uncertainty certain classes of robust performance problems and systems subject to deterministic white noise disturbances this is achieved by combining concepts such as h infinity optimization linear matrix inequalities and integral quadratic constraints necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive finite dimensional linear matrix inequality

revisited lq output feedback control minimax controller for a set of initial states a minimax linear quadratic lq output feedback controller is introduced which minimises the maximal value of the performance index over all initial states belonging to some set separated out a priori if the set is an ellipsoid or a polygon such controllers are synthesised in terms of linear matrix inequalities lmis in particular case when a size of this set tends to zero tightening to a point the minimax lq controller approaches the optimal lq output feedback controller for the given initial state while in another extreme case when this size tends to infinity we have the worst case lq output feedback controller numerical results for an inverted pendulum are presented

formulas on preview and delayed h infty control a generalized hinfin control problem which covers preview and delayed control strategies is discussed based on a state space approach by introducing a hamiltonian matrix which is associated with a delay free generalized plant the analytic solution to the corresponding operator riccati equation is newly established based on the result obtained here the hinfin control problem is solved and for typical control problems e g hinfin and linear quadratic lq control for multiple input delay systems hinfin preview control some interpretations are provided on the resulting control system

an extended pressure finite element space for two phase incompressible flows with surface tension we consider a standard model for incompressible two phase flows in which a localized force at the interface describes the effect of surface tension if a level set or vof method is applied then the interface which is implicitly given by the zero level of the level set function is in general not aligned with the triangulation that is used in the discretization of the flow problem this non alignment causes severe difficulties w r t the discretization of the localized surface tension force and the discretization of the flow variables in cases with large surface tension forces the pressure has a large jump across the interface in standard finite element spaces due to the non alignment the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure in many simulations these effects cause large oscillations of the velocity close to the interface so called spurious velocities in this paper for a simplified model problem we give an analysis that explains why known standard methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities in the paper s grosz a reusken finite element discretization error analysis of a surface tension force in two phase incompressible flows preprint 262 igpm rwth aachen siam j numer anal accepted for publication we introduce a new and accurate method for approximation of the surface tension force in the present paper we use the extended finite element space xfem presented in n moes j dolbow t belytschko a finite element method for crack growth without remeshing int j numer meth eng 46 1999 131 150 t belytschko n moes s usui c parimi arbitrary discontinuities in finite elements int j numer meth eng 50 2001 993 1013 for the discretization of the pressure we show that the size of spurious velocities is reduced substantially provided we use both the new treatment of the surface tension force and the extended pressure finite element space

computing cox rings we consider modifications for example blow ups of mori dream spaces and provide algorithms for investigating the effect on the cox ring e g testing finite generation or computing an explicit presentation in terms of generators and relations as a first application we compute the cox rings of all gorenstein log del pezzo surfaces of picard number one moreover we show computationally that all smooth rational surfaces of picard number at most six are mori dream surfaces and we provide explicit presentations of the cox ring for those not admitting a torus action finally we provide the cox rings of projective spaces blown up at a certain special point configurations

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

brief a parametric optimization approach to h and h2 strong stabilization this paper presents an approach for designing stable mimo h and h 2 controllers by directly computing the norm constrained stable transfer matrices q in the h and h 2 suboptimal controller parameterizations this is done by first converting the h 2 and h strong stabilization problems into some nonlinear unconstrained optimization problems through explicit parameterization of the norm constrained q s for any fixed order then a two stage numerical search is carried out by using a combination of a genetic algorithm and a quasi newton algorithm in order to reach an optimal solution the effectiveness of the proposed algorithms is illustrated through some benchmark numerical examples

the cox ring of an algebraic variety with torus action abstract we investigate the cox ring of a normal complete variety x with algebraic torus action our first results relate the cox ring of x to that of a maximal geometric quotient of x as a consequence we obtain a complete description of the cox ring in terms of generators and relations for varieties with torus action of complexity one moreover we provide a combinatorial approach to the cox ring using the language of polyhedral divisors applied to smooth k surfaces our results give a description of the cox ring in terms of orlik wagreich graphs as examples we explicitly compute the cox rings of all gorenstein del pezzo k surfaces with picard number at most two and the cox rings of projectivizations of rank two vector bundles as well as cotangent bundles over toric varieties in terms of klyachko s description

the h control problem with zeros on the boundary of the stability domain in this paper we study the discrete and continuous time h control problems without any assumptions on the system parameters our approach yields necessary and sufficient conditions for the existence of a suitable controller

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

fast computation of achievable feedback performance in mixed sensitivity h design the computational bottleneck of the h infty design has been recognized to be the e iteration a computationally demanding direct search of the minimum achievable h infty performance verma and jonckheere showed that the optimal h infty performance can be characterized as the spectral radius of the so called toeplitz plus hankel operator even before the appearance of the toeplitz plus hankel operator in the h infty setting the same operator had already been shown to play a crucial role in the spectral theory of the linear quadratic problem developed by jonckheere and silverman in this paper we exploit this common toeplitz plus hankel operator structure shared by the seemingly unrelated linear quadratic and h infty problems and we construct fast state space algorithms for evaluating the spectral radius of the toeplitz plus hankel operator the salient feature of the algorithm is that the spectral radius can be evaluated with an accuracy predicted by an identifiable error bound from the antistabilizing solution of the algebraic riccati equation of the linear quadratic problem associated with the h infty design

variational formulations for surface tension capillarity and wetting the interest in the simulation of flows with significant surface tension effects has grown significantly in recent years this has been driven by the substantial advances made in the measurement and manufacturing of microscopic systems since at small length scales surface phenomena are dominant in this article surface tension capillarity and wetting effects are discussed in terms of the virtual work principle and shape sensitivity starting from first principles and arriving at variational formulations that are adequate for numerical treatment by finite elements for example to make the exposition self contained some elements of differential geometry are recalled using a formulation that is fully in cartesian coordinates and may thus be more friendly to readers not familiar with covariant derivatives all necessary results are proved in this cartesian formulation several numerical examples computed with a finite element level set formulation are used to illustrate this challenging physical problem

linear quadratic suboptimal control with static output feedback abstract this paper considers the design of a stabilizing static output feedback gain which keeps linear quadratic lq performance index less than a specified number we call this an lq suboptimal controller existence of such a controller is shown to be equivalent to the existence of a positive definite matrix p such that p satisfies two linear matrix inequalities lmis while p 1 satisfies another lmi all lq suboptimal controllers are explicitly parametrized by the freedom in the choice of the positive definite matrix p satisfying the lmis and an arbitrary positive scalar and an arbitrary matrix of fixed dimension with a norm bound a modified version of the min max algorithm is given to find a positive definite solution p to the lmis

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

the singular h 2 control problem in this paper we discuss the standard h2 control problem for linear finite dimensional time invariant systems without any assumptions on the system parameters we give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

on spurious velocities in incompressible flow problems with interfaces we show that a non physical velocity may appear in the finite element calculation of incompressible two phase flows subjected to an external local force there are different sources responsible for this phenomenon approximation of the incompressibility constraint the interface and the local external force furthermore we demonstrate that this non physical velocity does not vanish with the expected order of convergence we evaluate different concepts and give recommendations for a proper handling of this phenomenon

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

robust regulation with h 2 performance abstract we consider the problem of minimizing the h 2 norm of a feedback system subject to the constraint that the controller robustly regulate against constants and sinusoids we show that for any 0 there exists a controller that both achieves robust regulation and renders the closed loop h 2 norm within of the optimal norm the norm achievable without the robust regulation constraint we also provide conditions that are both necessary and sufficient for there to exist a robustly regulating controller that achieves the optimal h 2 norm all proofs are constructive

numerical assessment of stability of interface discontinuous finite element pressure spaces abstract the stability of two recently developed pressure spaces has been assessed numerically the space proposed by ausas et al r f ausas f s sousa g c buscaglia an improved finite element space for discontinuous pressures comput methods appl mech engrg 199 2010 1019 1031 which is capable of representing discontinuous pressures and the space proposed by coppola owen and codina a h coppola owen r codina improving eulerian two phase flow finite element approximation with discontinuous gradient pressure shape functions int j numer methods fluids 49 2005 1287 1304 which can represent discontinuities in pressure gradients we assess the stability of these spaces by numerically computing the inf sup constants of several meshes the inf sup constant results as the solution of a generalized eigenvalue problems both spaces are in this way confirmed to be stable in their original form an application of the same numerical assessment tool to the stabilized equal order p 1 p 1 formulation is then reported an interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation s stability an analogous result is also reported for the mini element p 1 p 1 when the velocity bubbles are removed in an arbitrary band of elements

a duality based approach to the multiobjective h 2 h optimisation problem in this article a duality approach to multiobjective h 2 h problems is pursued in which real rational para hermitian multipliers and real valued ones are associated to h and as usual h 2 constraints respectively it is shown that the maximisation of a dual functional over all such multipliers yields the optimal value of the original multiobjective h 2 h problem to compute lower bounds on the latter and the corresponding approximate solutions to the original problem the maximisation of the dual functional over linearly parameterised finite dimensional classes of real rational multipliers is shown to be equivalent to semi definite linear programming problems once the optimal multipliers in such a class are obtained the corresponding approximate solutions can be computed from an unconstrained h 2 problem iterative modification of such classes is discussed to obtain increasing sequences of lower bounds on the optimal value of the original problem this is done on the basis of locally incr

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

brief robust h minimum entropy static output feedback control of singularly perturbed systems the problem of designing static output feedback e independent controllers for linear time invariant singularly perturbed systems is considered the controller is required to satisfy a prescribed h norm bound and to minimize the closed loop entropy at s for all small enough e the optimal controller gain is designed on the basis of generalized riccati and lyapunov equations with symmetric block 2 2 that are coupled via a projection this gain is either purely fast purely slow or a composite one depending on the structure of the output coupling matrix a well posed problem with a finite value of entropy for e 0 is obtained by assuming that the entropy of the fast subproblem is zero or by scaling the matrices of the system in the first case the optimal controller is the one that minimizes the entropy of the corresponding descriptor system

risk sensitive control with hara utility a control methodology based on the hyperbolic absolute risk averse hara utility function is presented as an alternative to the exponential of an integral approach to finding robust controllers the work is inspired by the intuition that hara controllers while being robust may give better performance than exponential controllers in normal situations the hara problem is shown to be equivalent to a certain differential game and the asymptotic properties of the hara problem and this differential game are studied as an example a linear quadratic hara problem is studied where the problem of finding a robust hara controller is proved to be equivalent to solving a standard linear quadratic problem for a system with a higher noise intensity this reveals an interesting relationship between robustness and uncertainty

distributed control of systems over discrete groups this paper discusses distributed controller design and analysis for distributed systems with arbitrary discrete symmetry groups we show how recent results for designing controllers for spatially interconnected systems based on semidefinite programming are applicable to a much larger class of interconnection topologies we also show how to exploit the structure of the symmetry group to produce a hierarchy of decreasingly conservative analysis and synthesis conditions

sampled data h optimal control of time varying systems the sampled data h optimal control problem is studied for time varying systems the problem consists of finding all sampled data controllers with a piece wise constant control signal for which the l2 induced norm from the continuous time disturbance to the continuous time output is less than a specified bound a game theoretic approach is used to obtain a complete solution to the problem in the finite horizon time varying case the solution involves a mixed discrete continuous riccati equation and a variable transformation which takes the problem to a standard discrete finite dimensional h filtering problem

lmi solution to general suboptimal control problems abstract in this paper we derive an lmi solution to general h 2 suboptimal control problems without any unnecessary assumptions necessary and sufficient conditions for the h 2 norm of the closed loop transfer matrix to be bounded by a given number is given by 4 coupled lmis a suboptimal controller is also obtained the obtained solution applies to both nonsingular and singular cases

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

lmi characterization of reduced order h controllers via invariant zero structure abstract in this paper we clarify a new relationship between invariant zeros of a generalized plant and the order reduction of h controllers by using linear matrix inequalities in both continuous time and discrete time cases in contrast with our recent paper where a relationship between an unstable transmission zero structure and the h controller order reduction is initiated in a fundamental manner results obtained in this paper are more flexible in two senses assumptions that are made for the generalized plant are relaxed and stable as well as unstable invariant zeros are characterized to obtain a reduced order h controller

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

an improved ilmi method for static output feedback control with application to multivariable pid control an improved iterative linear matrix inequality ilmi algorithm for static output feedback sof stabilization problem without introducing any additional variables is proposed in this note the proposed ilmi algorithm is also extended to solve the sof hinfin controller design problem they are applied to the multivariable pid controllers numerical examples show that the proposed algorithms yield better results and faster convergence than the existing ones

an improved finite element space for discontinuous pressures abstract we consider incompressible stokes flow with an internal interface at which the pressure is discontinuous as happens for example in problems involving surface tension we assume that the mesh does not follow the interface which makes classical interpolation spaces to yield suboptimal convergence rates typically the interpolation error in the l 2 norm is of order h 1 2 we propose a modification of the p 1 conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system the unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element so that the implementation of the proposed space into existing codes is straightforward with this modification numerical tests show that the interpolation order improves to o h 3 2 the new pressure space is implemented for the stable p 1 p 1 mini element discretization and for the stabilized equal order p 1 p 1 discretization assessment is carried out for poiseuille flow with a forcing surface and for a static bubble in all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard p 1 space in addition two navier stokes simulations with moving interfaces rayleigh taylor instability and merging bubbles are reported to show that the proposed space is robust enough to carry out realistic simulations

an lmi approach to h synthesis subject to almost asymptotic regulation constraints a multi objective controller synthesis problem is considered in which an output is to be regulated approximately by assuring a bound on the steady state peak amplification in response to an infinite energy disturbance while also guaranteeing a desired level of performance measured in terms of the worst case energy gain from a finite energy input to a performance output relying on a characterization of the controllers with which almost asymptotic regulation is accomplished the problem of guaranteeing the desired level of performance is reduced to solving a system of linear matrix inequalities subject to a set of linear equality constraints based on the solution of this system a procedure is outlined for the construction of a suitable controller whose order is equal to the order of the plant plus the order of the exogenous system

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

performance with regulation constraints we study the problem where we have a regulation asymptotic tracking requirement together with a performance requirement for continuous time systems typically we measure performance by the h 2 or h norm of a chosen transfer function matrix although any other norm such as the l 1 norm could be used in the case when the performance is measured by the h 2 norm there is no loss in performance due to the regulation constraint on the other hand when the performance is measured by the h norm there exists in general certain loss of performance due to the regulation constraint and we explicitly characterize such a loss determining suitable controllers for a given system with both regulation and performance constraints requires solving only an unconstrained optimization problem for an auxiliary system which is explicitly constructed here

h control for semilinear systems in hilbert spaces abstract this paper considers the h controlled with state feedback for semilinear infinite dimensional systems in a hilbert space necessary and sufficient conditions for the existence of a suboptimal h controller are derived in terms of a hamilton jacobi equation

brief extended h control h control with unstable weights this paper presents a complete solution to an extended h control problem for a generalized plant comprising a physical system cascaded with weights containing poles in the closed right half plane necessary and sufficient conditions for a solution to exist are obtained which guarantee closed loop stability of the physical system and controller as well as achieving the h norm constraint on the closed loop of the transfer function matrix of the generalized plant and controller interconnection the set of all feasible controllers is characterized conditions for solvability are a minimal variation on those appearing in the standard h control problem

lmi based minimax estimation and filtering under unknown covariances in this paper we consider a minimax approach to the estimation and filtering problems in the stochastic framework where covariances of the random factors are completely unknown the term random factors refers either to unknown parameters and measurement noise in the estimation problem or to disturbance process and the initial state of a linear discrete time dynamic system in the filtering problem we introduce a notion of the attenuation level of random factors as a performance measure for both a linear unbiased estimate and a filter this is the worst case variance of the estimation error normalised by the sum of variances of all random factors over all nonzero covariance matrices it is shown that this performance measure is equal to the spectral norm of the transfer matrix and therefore the minimax estimate and filter can be computed in terms of linear matrix inequalities lmis moreover the explicit formulae for both the minimax estimate and the minimal value of the attenuation level are prese

robust regulation in the presence of norm bounded uncertainty we consider robust regulation against steps and sinusoids in the presence of unstructured uncertainty the unstructured uncertainty is norm bounded by a constant that is given a priori this problem is equivalent to a certain multiobjective problem where one objective is robust regulation and the other is the standard objective of h sub spl infin suboptimal control it is shown that a solution to this problem exists if and only if the standard h sub spl infin problem admits a solution and certain matrix inequalities are satisfied these solvability conditions are readily computable controller synthesis is also addressed

an optimization algorithm for checking feasibility of robust h infinity control problem for linear time varying uncertain systems an algorithm for checking feasibility of the robust h control problem for systems with time varying norm bounded uncertainty is suggested this algorithm is an iterative procedure on each step of

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

reduced order controllers for the h control problem with unstable invariant zeros this paper addresses the existence and design methods of reduced order controllers for the h control problem with unstable invariant zeros in the state space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output where the realization is induced from a stabilizable and detectable realization of the generalized plant this paper presents a new controller degree bound for the h control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region when the unstable invariant zero exists this paper shows that reduced order controllers with orders strictly less than that of the generalized plant exist if the h control problem is solvable moreover this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality based design methods algorithms for constructing the reduced order controllers the results developed in this paper are valid both for the continuous and discrete time h control problems

adaptive h control in finite frequency domain for uncertain linear systems this paper is concerned with the problem of adaptive h controller design in finite frequency domains for uncertain linear systems the uncertainties are assumed to be time invariant unknown but bounded which appear affinely in the matrices of system models an adaptive mechanism is introduced to construct a novel finite frequency h controller with time varying gains by using lyapunov theory and parseval s theorem the controller design conditions are given in terms of a set of linear matrix inequalities lmis it is shown that the proposed finite frequency controller with time varying gains can achieve better h performance than the traditional ones with fixed gains finally a numerical example of the f 18 aircraft model is given to illustrate the presented theoretical results

lyapunov characterization of forced oscillations this paper develops a lyapunov approach to the analysis of input output characteristics for systems under the excitation of a class of oscillatory inputs apart from sinusoidal signals the class of oscillatory inputs include multi tone signals and periodic signals which can be described as the output of an autonomous system the lyapunov approach is developed for linear systems homogeneous systems differential inclusions and nonlinear systems differential inclusions respectively in particular it is established that the steady state gain can be arbitrarily closely characterized with lyapunov functions if the output response converges exponentially to the steady state other output measures that will be characterized include the peak of the transient response and the convergence rate tools based on linear matrix inequalities lmis are developed for the numerical analysis of linear differential inclusions ldis this paper s results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals guided by the numerical result for a second order ldi an interesting phenomenon is observed that the peak of the frequency response can be strictly larger than the l 2 gain

homogeneous coordinates for algebraic varieties abstract we associate to every divisorial e g smooth variety x with only constant invertible global functions and finitely generated picard group a pic x graded homogeneous coordinate ring this generalizes the usual homogeneous coordinate ring of the projective space and constructions of cox and kajiwara for smooth and divisorial toric varieties we show that the homogeneous coordinate ring defines in fact a fully faithful functor for normal complex varieties x with only constant global functions we even obtain an equivalence of categories finally the homogeneous coordinate ring of a locally factorial complete irreducible variety with free finitely generated picard group turns out to be a krull ring admitting unique factorization

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

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

sensitivity minimization in an h norm parametrization of all suboptimal solutions a number of problems in the control of linear feedback systems can be reduced to the following we are given three stable rational matrix functions k of sizes p 1 x q 1 p 1 x q 2 and p 2 x q 1 respectively and seek a stable rational q 2 x p 2 matrix function s so as to minimize k s we assume that p 1 q 2 p 2 q 1 and that and have maximal rank q 2 and p 2 respectively on the j axis given a tolerance level sufficiently large we obtain a linear fractional map g f 0 11 g 0 12 0 13 0 21 g 0 22 0 23 1 such that f k s with s stable and f if and only if g is a stable q 2 x p 2 matrix function with g 1 the computation of 0 0 ij 1 i 2 1 j 3 reduces to solving a pair of symmetric wiener hopf factorization problems for the special case where i q2 0 t i p2 0 and k not necessarily stable to which the general case can be reduced we provide explicit state space formulae for 0 in terms of a state space realization of k and the

h control problem with jω axis zeros abstract in this paper we discuss the so called one block h control problem in the case where the plant has j axis including infinity poles and zeros first we derive a necessary and sufficient condition for the h model matching problem to have a solution in the transfer function setting second we give a solvability condition which enables us to check the solvability by i examining matrix norm conditions related to j axis zeros and ii solving two generalized riccati equations finally we extend our result to the standard h problem

factorially graded rings and cox rings abstract cox rings of normal prevarieties are factorially graded i e homogeneous elements allow a unique decomposition into homogeneous factors we study this property from an algebraic point of view and give a criterion which in a sense reduces it to factoriality this will allow us to detect and construct cox rings in a purely algebraic manner

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

wiener hopf design of the general two degree of freedom controllers and the connection to state space formulas h 2 design of the two degree of freedom controller configuration is treated for the generalized plant in both the frequency and state space domains a frequency domain wiener hopf formula is derived first under a set of compact assumptions that gives the entire class of controllers for which the feedback control system is stable and a quadratic cost functional is finite the h 2 design method suggested in this paper allows the reference inputs to include the persistent signals such as step or ramp functions and the class of persistent reference inputs that can be tracked with zero steady state error is characterized explicitly to circumvent the computational difficulties of the wiener hopf formulas the corresponding state space domain formulas are derived by rationalizing the polynomial fractional descriptions it is shown that the well known standard time domain assumptions for the h 2 design problem have the corresponding equivalent frequency domain conditions and this equivalence relationship is show

the xy centring algorithm for the dual lmi problem a new approach to fixed order control design many fixed order suboptimal control problems with stability performance and robustness specifications can be reduced to a search for a matrix x 0 satisfying a linear matrix inequality lmi while x 1 satisfies another lmi this paper defines a certain class of these problems we shall call the dual lmi problem and a computational algorithm to solve our dual lmi problem is given properties and limitations of the algorithm are discussed in comparison with the existing algorithm the min max algorithm an extension to optimal control problems is provided numerical examples for the fixed order stabilization problem and the static output feedback linear quadratic optimal control problem demonstrate the applicability of the proposed algorithm

on optimal output regulation for linear systems the classical output regulation problem formulation for linear systems has a number of shortcomings among them a primary one is that it does not take into account the transient response although this problem has been studied since the 1970s a complete picture has not emerged yet we formulate and study here a number of output regulation problems which incorporate the notion of transient performance into them by defining a performance index that involves transient response we define optimal and suboptimal control problems which are constrained by the steady state output regulation requirement such constrained optimal and suboptimal control problems for a given system are studied by transforming them to unconstrained optimal and suboptimal control problems for certain auxiliary systems several issues such as obtaining expressions for the infimal performance measure solvability conditions regulator construction are studied in detail both state and measurement feedback controllers are considered

reduced order controllers for continuous and discrete time singular h control problems based on lmi this paper describes a method for constructing a petri net controller for a discrete event system modeled by a petri net the controller consists only of places and arcs and is computed based on the concept of petri net place invariants the size of the controller is proportional to the number of constraints that must be satisfied this method is computationally efficient and can accommodate constraints written as boolean logic formulas in the conjunctive normal form or algebraic inequalities that contain elements of the marking and or the firing vectors

low order controller design for siso systems using coprime factors and lmi this paper develops a low order controller design method for linear continuous time invariant single input single output systems requiring only the solution of a convex optimization problem the technique integrates several well known results in control theory an important step is the use of coprime factors so that based on strictly positive real functions feedback stabilization using low order controllers becomes a zero placement problem which is convex from this result we develop algorithms to solve two optimal control problems

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

brief paper generalized asymptotic regulation with guaranteed h2 performance an lmi solution a multi objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix the generalized regulation constraints are expressed as bounds on the state steady peak in response to disturbances generated by an anti stable autonomous exogenous system with nonzero initial states the controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices which are subject to convex constraints and an accompanying controller with which the feedback loop is to be stabilized formulating the design of the accompanying controller in a way to guarantee the additional performance objective the overall design is rendered tractable over a set of free variables in terms of which the synthesis of a suitable controller is also outlined the order of the controller is equal to the order of the plant plus the order of the exogenous system by an adaptation of the developed techniques a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

a finite element technique for multifluid incompressible flow using eulerian grids the paper presents a finite element method for 3d incompressible fluid flows with capillary free boundaries it uses a fixed eulerian grid of 10 nodes p2 p1 tetrahedra and tracks the free boundary using a six nodes p2 triangular surface grid in order to improve the mass conservation properties of the method a local enrichment of the finite element basis in the elements intersected by the free boundaries is employed in addition to the surface tracking it also advects a smooth indicator function for an easy identification of the fluid properties in the different parts of the domain the advective part of the navier stokes equations is split and integrated with a characteristic method the remaining generalized stokes problem is resolved by means of an inexact outer inner uzawa iteration with a properly chosen preconditioner the performance of this technique is evaluated on several problems involving droplets in viscous liquids

universal regulators for optimal tracking in discrete time systems affected by harmonic disturbances considers the problem of controlling a discrete time linear system by output feedback so as to have a second output z sub t track an observed reference signal r sub t the authors turn to an approach to the tracking problem which allows for damping of other system and control variables and this is our main result the measure of performance is given by a natural quadratic cost function the object is to design an optimal regulator which is universal in the sense that it does not depend on the unknown amplitudes and phases of r sub t and w sub t and is optimal for all choices of r sub t and w sub t the authors prove that an optimal universal regulator exists in a wide class of stabilizing and possibly nonlinear regulators under natural technical conditions and that this regulator is in fact linear provided that the second dimensionality condition above is satisfied on the other hand if it is not satisfied the existence of an optimal universal regulator is not a generic property so as a rule no optimal universal regulator exists

finite element discretization error analysis of a surface tension force in two phase incompressible flows we consider a standard model for a stationary two phase incompressible flow with surface tension in the variational formulation of the model a linear functional which describes the surface tension force occurs this functional depends on the location and the curvature of the interface in a finite element discretization method the functional has to be approximated for an approximation method based on a laplace beltrami representation of the curvature we derive sharp bounds for the approximation error a new modified approximation method with a significantly smaller error is introduced

a controller degree bound for h 0e control problems of the second kind this paper is a continuation of our work on mathcal h infty optimal control problems which may be embedded in the linear fractional configuration of fig 1 in two previous articles 19 20 a controller degree bound was established for problems in which both p 12 s and p 21 s are square problems of the first kind if the mcmillan degree of p s is n it was shown that there exist mathcal h infty optimal controllers with mcmillan degree no greater than n 1 here we switch our attention to problems of the second kind that is we allow p 12 s to have more rows than columns with p 21 s square or alternatively we allow p 21 s to have more columns than rows with p 12 s square our main result shows that the degree bound derived previously for problems of the first kind carries over to problems of the second kind without change in addition to the controller degree bound our analysis suggests a number of modifications which are easily made to cur

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

an analysis of the pole zero cancellations in h optimal control problems of the first kind the aim of this paper is to study the pole zero cancellations which occur in a class of h infty optimal control problems which may be embedded in the configuration of fig 1 h infty control problems are said to be of the first kind if both p 12 s and p 21 s are square but not necessarily of the same size it is primarily this class of problems which will concern us here a general bound on the mcmillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies bf mathcal r s infty leqq rho rho need not be optimal in the l infty norm sense is derived as illustrated in fig 1 bf mathcal r s is the transfer function relating y 1 s to u 1 s if the mcmillan degree of p s in fig 1 is n we show that in the single loop siso case the corresponding unique h infty optimal controller never requires more than n 1 states in the multivariable case there is a continuum of optimal controllers whose mcmil

a simple method for deriving j spectral factors a simple method is presented for deriving the j spectral factor of a transfer function matrix explicitly in terms of the parameters of this matrix this method provides closed form expressions for the j spectral factor and its inverse which only require a solution of a single linear sylvester equation this method can be easily applied in the solution of the h sub infinity optimal regulation problem and it provides useful geometric insight into the structure of the optimal regulator return difference matrix