pointwise boundary stabilizability of hyperbolic evolution equations two dimensional hybrid elastic structures abstract a two dimensional hybrid elastic structure of a rectangular membrane linked with two rib strings on the boundary sides that have rigid bodies and pointwise controllers attached at the corner points is modelled as an abstract hyperbolic evolution equation by an analysis of energy decay and limit sets with a dissipative feedback the following necessary and sufficient condition for stabilizability in the energy space is obtained v i 2 v j 2 2n l 2 2 for any positive integer n and for any i j where v0 0 and vi i 1 2 are the increasing positive roots of the transcendental equation cot l 1 1 2 a a in which a 0 is a structural constant l1 l2 is the size of the region if this condition is satisfied then the stabilization is achieved by a pointwise boundary damping feedback otherwise the stabilization can be achieved by combining an additional boundary damping feedback controller locally distributed in the interior of one boundary string

exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain abstract here we are concerned about the stability of the solution of internally damped wave equation y y y with small damping constant 0 in a bounded domain in r n under mixed undamped boundary conditions a uniform exponential energy decay rate e t me t e 0 where m 1 and 0 0 being a quadratic function of is proved for the solution of this type of boundary value problem earlier authors have considered the undamped wave equation with certain forms of damped boundary conditions proving similar and faster energy decay rates

how well does the owa operator represent real preferences we present the results of an empirical study in which we analyze the ability of the ordered weighted average owa operator to model actual preferences in a multi attribute ranking task we compare the owa to a competing model simple additive weighting saw and we also study whether its characteristic feature the ability to represent different attitudes toward compensation among attributes is reflected in the preferences provided by subjects we find that in general the owa model fits slightly less well to empirical data subjects whose preferences are better explained by the saw model are also more consistent in their choice behavior our results furthermore indicate that preferences of most subjects are not fully compensatory thus the ability of the owa operator to represent different attitudes toward compensation can be a useful feature in modeling actual preferences the structure of the weights estimated for the owa operator also suggests that it might provide a good approximation to certain types of decision heuristics

stabilization of second order evolution equations with unbounded feedback with time dependent delay we consider abstract second order evolution equations with unbounded feedback with time varying delay existence results are obtained under some realistic assumptions we prove the exponential decay under some conditions by introducing an abstract lyapunov functional our abstract framework is applied to the wave to the beam and to the plate equations with boundary delays

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

an analytic approach for obtaining maximal entropy owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem in this paper using the method of lagrange multipliers we shall solve this constrained optimization problem analytically and derive a polynomial equation which is then solved to determine the optimal weighting vector

hesitant analytic hierarchy process abstract in traditional analytic hierarch process ahp decision makers dms are required to provide crisp judgments over paired comparisons of objectives to construct comparison matrices to enhance the modeling ability of traditional ahp we propose hesitant ahp h ahp that can consider the hesitancy experienced by the dms in decision h ahp is characterized by hesitant judgments where each hesitant judgment can be represented by several possible values different probability distributions can be used to further describe hesitant judgments according to the dms preferences based on a hesitant comparison matrix hcm that consists of hesitant judgments we define two indices to measure the consistency degree and the consensus degree of the hcm respectively from a stochastic point of view a new prioritization method is developed to derive priorities from hcms where the results are with probability interpretations we provide a step by step procedure for h ahp and demonstrate this new method with a real life decision making problem

well posedness of systems of linear elasticity with dirichlet boundary control and observation an open loop system of linear elasticity with dirichlet boundary control and collocated observation is considered the main result we obtained states that this system is well posed in the sense of salamon the result deduces the exponential stability of the closed loop system under proportional output feedback hence it answers positively an open question proposed by liu and krstic ima j appl math 65 2000 pp 109 121 moreover the well posedness together with the regularity of the open loop system in the sense of weiss that was obtained in our separate paper s g chai and b z guo feedthrough operator for linear elasticity system with boundary control and observation preprint school of computational and applied mathematics university of the witwatersrand south africa 2008 makes this infinite dimensional system parallel in many ways to a linear finite dimensional system in the framework of well posed and regular linear infinite dimensional systems

the cubic fourth order schrodinger equation fourth order schrodinger equations have been introduced by karpman and shagalov to take into account the role of small fourth order dispersion terms in the propagation of intense laser beams in a bulk medium with kerr nonlinearity in this paper we investigate the cubic defocusing fourth order schrodinger equation i tu 2u u 2u 0 in arbitrary space dimension rn for arbitrary initial data we prove that the equation is globally well posed when n 8 and ill posed when n 9 with the additional important information that scattering holds true when 5 n 8

feedthrough operator for linear elasticity system with boundary control and observation we are concerned with the feedthrough operator for the open loop system of linear elasticity with dirichlet boundary control and collocated observation this system has been known to be regular in the sense of g weiss in this paper the analytic expression of the corresponding feedthrough operator is presented by means of differential geometry and fourier transform methods

simultaneous exact approximate boundary controllability of thermo elastic plates with variable thermal coefficient and moment control abstract we study a controllability problem exact in the mechanical variables w w t and simultaneously approximate in the thermal variable of thermo elastic plates by means of boundary controls in the hinged dirichlet bc case when the thermal expansion term is variable in space

stabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedback we consider the stabilization of the wave equation with variable coefficients and a delay in the dissipative boundary feedback by virtue of the riemannian geometry methods the energy perturbed approach and the multiplier skills we establish the uniform stability of the energy of the closed loop system

regularity of a schrodinger equation with dirichlet control and colocated observation this paper studies the basic properties of the schrodinger equation defined on a bounded domain of r n n 2 with partial dirichlet control and colocated observation it is shown that the system is not only wellposed in the sense of d salamon but also regular in the sense of g weiss it is also shown that the corresponding feedthrough operator is zero 2005 elsevier b v all rights reserved

well posedness without semicontinuity for parametric quasiequilibria and quasioptimization abstract we consider quasiequilibrium and quasioptimization problems a relaxed level closedness notion is proposed and used together with pseudocontinuity to establish sufficient conditions for parametric well posedness and well posedness without semicontinuity assumptions we prove them in general formulations though such relaxations allow us to improve some existing results even in simple cases of r 1 several new well posedness results are also obtained for topological settings we use sensitivity analysis while for problems on metric spaces we argue on diameters and kuratowski s and hausdorff s measures of noncompactness of approximate solution sets

a boundary condition with memory for kirchhoff plates equations in this paper we study the stability of solutions for kirchhoff plates equations with a memory condition working at the boundary we show that such dissipation is strong enough to produce exponential decay to the solution provided the relaxation functions also decays exponentially when the relaxation functions decays polynomially we show that the solution decays polynomially and with the same rate

a dynamic control law for the wave equation abstract we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper we then show that if the transfer function of the controller is strictly proper then the resulting closed loop system is asymptotically stable and if proper but not strictly proper then the resulting closed loop system is exponentially stable

stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions abstract sufficient conditions for the local exponential stabilizability of abstract systems described by an arbitrary co semigroup with nonlinear unbounded perturbations are formulated applications to parabolic and in particular hyperbolic problems with nonlinearity appearing in the boundary conditions are given

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

on the issue of obtaining owa operator weights we first investigate the issue of obtaining the weights associated with the owa aggregation in the situation when we have observed data on the arguments and the aggregated value we next introduce a family of owa operators called exponential owa operators finally we look at a simple procedure for generating the weights given a required degree of orness

choosing owa operator weights in the field of social choice one of the most important issues in the theory of owa operators is the determination of associated weights this matter is essential in order to use the best suited owa operator in each aggregation process given that some aggregation processes can be seen as extensions of majority rules to the field of gradual preferences it is possible to determine the owa operator weights by taking into account the class of majority rule that we want to obtain when individuals do not grade their pairwise preferences however a difficulty with this approach is that the same majority rule can be obtained through a wide variety of owa operators for this reason a model for selecting the best suited owa operators is proposed in this paper

on obtaining minimal variability owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem another consideration that may be of interest to a decision maker involves the variability associated with a weighting vector in particular a decision maker may desire low variability associated with a chosen weighting vector in this paper using the kuhn tucker second order sufficiency conditions for optimality we shall analytically derive the minimal variability weighting vector for any level of orness

exact controllability of the euler bernoulli equation with controls in the dirichlet and neumann boundary conditions a nonconservative case this paper considers the euler bernoulli problem 1 1a d with boundary controls g 1 g 2 in the dirichiet and neumann boundary conditions respectively several exact controllability results are shown including the following problem 1 1a d is exactly controllable in an arbitrarily short time t 0 in the space of maximal regularity h 1 omega times v v as in 1 4 i with boundary controls g 1 in l 2 sigma g 2 equiv 0 under some geometrical conditions on omega ii with boundary controls g 1 in l 2 sigma and g 2 in l 2 0 t h 1 gamma without geometrical conditions on omega a direct approach is given based on an operator model for problem 1 la d and on multiplier techniques an additional difficulty of the particular boundary conditions is due to the fact that in the natural norms for the solution arising in the application of multiplier techniques the corresponding homogeneous problem is not conservative this difficulty is overco

global exact controllability of a class of quasilinear hyperbolic systems in this paper we consider a distributed parameter boundary control system described by a reducible quasilinear hyperbolic system formula posed on the domain 0 x 1 with the nonlinear boundary conditions formula in the case that the system islinear degenerate we show that it isgloballyexactly boundary controllable

stabilization of wave and plate like equations with nonlinear dissipation on the boundary abstract in this paper we consider second order in time equations of petrovsky type wave and plate like with nonlinear dissipative boundary conditions under certain geometric conditions imposed on the domain the results on asymptotic behavior of the solutions are established

a variational principle for problems with functional constraints in this paper we show that in several important classes of optimization problems like mathematical programming with k smooth data quadratic programming in a hilbert space convex programming in a banach space semi infinite programming and optimal control of linear systems with quadratic cost most of the problems in the baire category sense are well posed this is derived from a general variational principle for problems with functional constraints

indicators for the characterization of discrete choquet integrals ordered weighted averaging owa operators and their extensions are powerful tools used in numerous decision making problems this class of operator belongs to a more general family of aggregation operators where each operator of this family is understood as a discrete choquet integral aggregation operators are usually characterized by indicators in this article four indicators usually associated with the owa operator are extended to the discrete choquet integral namely the degree of balance the divergence the variance indicator and renyi entropies all of these indicators are considered from a local and a global perspective linearity of indicators for linear combinations of capacities is investigated and to illustrate the usefulness of results indicators of the probabilistic ordered weighted averaging powa operator are derived finally a numerical example is provided to discuss the results in a specific context

stabilization of the wave equation with finite range dirichlet boundary feedback abstract we consider the wave equation defined on a smooth bounded domain with a one dimensional range non local feedback operator applied to the dirichlet boundary conditions and acting on the velocity the analysis is carried out on the space of optimal regularity of the problem which is l 2 h 1 under suitable assumptions it is shown that the feedback system is strongly stable for dim 1 but cannot be uniformly stable unless dim 1

uniform stabilization of the dynamic elastica by boundary feedback it is proved that the dynamic elastica which is a nonlinear model describing the large deflecting motion of an inextensible beam can be uniformly exponentially stabilized by boundary velocity feedback

exact controllability of the euler bernoulli equation with boundary controls for displacement and moment abstract we consider the euler bernoulli problem 1 1 in the solution w t with boundary controls g1 and g2 acting in the dirichlet traces for w and w respectively we show two main exact controllability results both in the spaces of maximal regularity of the solution at t t see i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 and both without geometrical conditions on the open bounded domain except for smoothness of its boundary one with g1 l2 0 t l2 and g2 h1 0 t l2 for any t 0 arbitrarily short and one with g1 h01 0 t l2 and g2 l2 0 t l2 for all t 0 sufficiently large an interpolation result between these two cases is also presented a direct approach is given based on two main steps first by means of an operator model i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 for problem 1 1 and a functional analytic approach the question of exact controllability is shown to be equivalent to an a priori inequality for the corresponding homogeneous problem next this a priori inequality is proved to hold true by means of multiplier techniques these are inspired by recent progress on the maximal regularity exact controllability and uniform stabilization questions for second order hyperbolic equations

on the kirchhoff plates equations with thermal effects and memory boundary conditions in this paper we study the existence of weak and strong global solutions and uniform decay of the energy to the kirchhoff plates equations with thermal effect and memory conditions working at the boundary we show that the dissipation produced by the memory effect not depend on the present values of temperature gradient that is we show that the dissipation produced by memory effect is strong enough to produce exponential decay of the solution provided the relaxation functions also decays exponentially when the relaxation functions decays polynomially we show that the solution decays polynomially with the same rate

asymptotic stability for intermittently controlled second order evolution equations motivated by several works on ordinary differential equations we are interested in the asymptotic stability of intermittently controlled partial differential equations we give a condition of asymptotic stability for second order evolution equations uniformly damped by an on off feedback this result extends to the case of partial differential equations a previous result of r a smith concerning ordinary differential equations

minimum phase infinite dimensional second order systems in general better performance can be achieved with a controlled minimum phase system than a controlled nonminimum phase system we show that a wide class of second order infinite dimensional systems with either velocity or position measurements are minimum phase the results are illustrated by two examples

owa operators with maximal renyi entropy this paper lays bare a parametric class of ordered weighted averaging owa operators with maximal renyi entropy owa weights for any level of orness in particular we shall formulate an extended approach to decision making with owa operators by introducing considerations of maximizing information content in the aggregation according to a general parametric class of dispersion measures

models to determine parameterized ordered weighted averaging operators using optimization criteria this paper proposes a general optimization model for determining ordered weighted averaging owa operators and three specific models for generating monotonic and symmetric owa operators as well as those with any function shape in these models entropy and variance concepts are generalized as general dispersion indices for use in the objective functions while the ordinary orness level constraints are used in the constraint equations as a special case we define an orness function for monotonic owa operators which measures the closeness of the aggregation value to the maximum value and a medianness function for symmetric owa operators which measures the closeness of the aggregation value to the median value we also extend the commonly used models for determining owa operators under given orness values to determine monotonic owa operators with given orness function values and symmetric owa operators with given medianness function values analytical solutions and properties of these models are discussed we also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values by setting different forms of the objective function and constraints the parameterized owa operator family elements can achieve various distributions in any desired shape two examples are given to show the owa operator elements distributed in quadratic and gaussian distribution function shapes

inverse observability estimates for second order hyperbolic equations with variable coefficients abstract we consider a general second order hyperbolic equation defined on an open bounded domain r n with variable coefficients in both the elliptic principal part and in the first order terms as well at first no boundary conditions b c are imposed our main result theorem 3 5 is a reconstruction or inverse estimate for solutions w under checkable conditions on the coefficients of the principal part the h1 l2 energy at time t t or at time t 0 is dominated by the l2 norms of the boundary traces w a and wt modulo an interior lower order term once homogeneous b c are imposed our results yield under a uniqueness theorem needed to absorb the lower order term continuous observability estimates for both the dirichlet and neumann case with an explicit sharp observability time hence by duality exact controllability results moreover no artificial geometrical conditions are imposed on the controlled part of the boundary in the neumann case in contrast with existing literature the first step of our method employs a riemann geometry approach to reduce the original variable coefficient principal part problem in r n to a problem on an appropriate riemann manifold determined by the coefficients of the principal part where the principal part is the laplacian in our second step we employ explicit carleman estimates at the differential level to take care of the variable first order energy level terms in our third step we employ micro local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the neumann case

exponential decay rates for the solutions of euler bernoulli equations with boundary dissipation occurring in the moments only abstract we shall derive uniform decay rates for the total energy of the solutions to the euler bernoulli equations wherein energy dissipation occurs on the boundary the main feature which distinguishes this paper from other related works is the fact that the boundary feedback is acting through the moments only the key technical element responsible for the proof of the main result is a new regularity estimate for the solutions to the nonhomogeneous schrodinger equation

a preemptive goal programming method for aggregating owa operator weights in group decision making this paper reveals that owa operator weights cannot be aggregated by the weighted arithmetic or geometric average method in group decision making a preemptive goal programming method pgpm is proposed for aggregating owa operator weights which is an extension of the minimax disparity approach developed earlier by the same authors the effectiveness of pgpm is illustrated with a numerical example

necessary conditions for exponential stabilizability of distributed parameter systems with infinite dimensional unbounded feedback abstract in this paper we consider distributed parameter control systems of the form x t ax t bu t where x t is in the state space x u t is in an infinite dimensional control space u and b is an unbounded input operator which is admissible in a standard sense we find necessary conditions for there to exist a compact operator k x u such that a bk generates a c 0 semigroup which is of exponential growth type in particular for every a must have at most finitely many eigenvalues of finite multiplicity in re z furthermore the part of a corresponding to the remaining spectrum must generate a semigroup with type at most we apply this to a model for a clamped euler bernoulli plate with dirichlet control applied to the entire boundary we show that a compact state feedback cannot exponentially stabilize the plate in the state space of maximum regularity

a note on the boundary stabilization of the wave equation we study the energy decay rates of the wave equation in a domain where boundary damping is present we generalize the geometrical conditions obtained earlier in j math purer appl 58 1979 pp 249 273 by using some more general multipliers of strauss comm pure appl math 28 1975 pp 265 278 the interaction between distributed damping and boundary damping is discussed a regulator problem is also formally discussed by the synthesis method

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

transfer functions of regular linear systems part i characterizations of regularity we recall the main facts about the representation of regular linear systems essentially that they can be described by equations of the form x t ax t bu t y t cx t du t like finite dimensional systems but now a b and c are in general unbounded operators regular linear systems are a subclass of abstract linear systems we define transfer functions of abstract linear systems via a generalization of a theorem of foures and segal we prove a formula for the transfer function of a regular linear system which is similar to the formula in finite dimensions the main result is a simple to state but hard to prove necessary and sufficient condition for an abstract linear system to be regular in terms of its transfer function other conditions equivalent to regularity are also obtained the main result is a consequence of a new tauberian theorem which is of independent interest

l p tauberian theorems and l p rates for energy decay abstract we prove l p analogues of the classical tauberian theorem of ingham and karamata and its variations giving rates of decay these results are applied to derive l p decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains by constructing some examples of critical behaviour we show that the l p rates of decay obtained in this way are best possible under our assumptions

riccati equations for hyperbolic partial differential equations with l 2 0 t l 2 γ dirichlet boundary terms this paper studies the quadratic optimal control problem for second order linear hyperbolic partial differential equations defined on a bounded domain omega subset r n with boundary gamma both the finite interval case 0 t t infty and the infinite interval case t infty regulator problem are considered the distinguishing feature of the paper which differentiates it from previous scarce literature on the subject is that the controls are only l 2 0 t l 2 gamma functions which act in the dirichlet b c and that the corresponding solutions are penalized in the l 2 0 t l 2 omega norm smoother controls particularly in space were taken in the few previous works on this subject the well posedness of this formulation stems from recent results by the authors about regularity of second order hyperbolic mixed problems l t 1 l t 3 under minimal assumptions the optimal control is synthesized in a pointwise feedback form through an operator which is s

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

stabilization of an abstract second order system with application to wave equations under non collocated control and observations abstract the objective of this paper is to deal with the stabilization of multi dimensional wave equations under non collocated control and observation with the following cases a locally internal distributed control and observation b internal distributed control and boundary observation c boundary control and internal distributed observation d locally internal distributed control and boundary observation we first discuss the stability of an abstract second order infinite dimensional system under the estimated state feedback control the well posedness in the sense of d salamon is specially emphasized the result is then applied to the multi dimensional wave equations with the aforementioned three different non collocated control and observations a c finally we prove the stabilizability of a wave equation with non collocated control and observation d by using the same idea although it cannot be cast into the abstract setting

variational principles and well posedness in optimization and calculus of variations the concluding result of the paper states that variational problems are generically solvable and even well posed in a strong sense without the convexity and growth conditions always present in individual existence theorems this and some other generic well posedness theorems are obtained as realizations of a general variational principle extending the variational principle of deville godefroy zizler

an analytic approach to obtain the least square deviation owa operator weights an important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one important approach suggested by wang luo and liu in 2007 determines a special class of owa operators with the least square deviation lsd of owa weights for a given orness level in this paper using the method of lagrange multipliers we solve this constrained optimization problem analytically and derive a polynomial equation to determine the optimal weighting vector numerical examples illustrate our proposed approach

generic optimality conditions for semialgebraic convex programs we consider linear optimization over a nonempty convex semialgebraic feasible region f semidefinite programming is an example if f is compact then for almost every linear objective there is a unique optimal solution lying on a unique active manifold around which f is partly smooth and the second order sufficient conditions hold perturbing the objective results in smooth variation of the optimal solution the active manifold consists locally of these perturbed optimal solutions it is independent of the representation of f and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes these results extend to unbounded sets f

the existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term abstract in this paper we consider a plate equation with a logarithmic nonlinearity in the presence of a frictional damping we prove for a suitably chosen initial data a global existence as well as a decay result

programming based owa operator weights with quadratic objective function yager s ordered weighted averaging owa operators are extensively employed to perform mean type aggregations their success heavily depends on proper determination of the associated weights that characterize the operators several methods have been established to determine the weights and thereby to support successful owa aggregation in this study the least square method which is one of the nonlinear programs with a quadratic objective function is reformulated by using the extreme points that correspond to its constraints and then solved by a few steps of matrix operations finally we present a new weighting method called the minimizing distances from the extreme points mdp wherein the owa operator weights that minimize the expected quadratic distance with respect to the set of extreme points are chosen a different attitudinal character leads to different extreme points and thus the mdp seeks to find the owa operator weights that are dynamically adjusted to be at the center of attitude dependent polytope

well posedness and exact controllability of fourth order schrodinger equation with boundary control and collocated observation in this paper we study the well posedness and exact controllability of a system described by a fourth order schrodinger equation on a bounded domain of mathbb r n n geqslant 2 with boundary control and collocated observation the neumann boundary control problem is first discussed it is shown that the system is well posed in the sense of d salamon this implies the exponential stability of the closed loop system under proportional output feedback control the well posedness result is then generalized to the dirichlet boundary control problem in particular in order to conclude feedback stabilization from well posedness we discuss the exact controllability with the dirichlet boundary control which is similar to the neumann boundary control case in addition we show that both systems are regular in the sense of g weiss and their feedthrough operators are zero

improving minimax disparity model to determine the owa operator weights determining the ordered weighted averaging owa operator weights is important in decision making applications several approaches have been proposed in the literature to obtain the associated weights this paper provides an alternative disparity model to identify the owa operator weights the proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct owa weights the proposed disparity model can be used for a preference ranking aggregation a numerical example in preference ranking and an application in search engines prove the usefulness of the generated owa weights

uniform exponential energy decay of wave equations in a bounded region with l2 0 l2 γ feedback control in the dirichlet boundary conditions etant donne un ouvert borne r n n 2 on considere l equation d onde w tt w dans o avec des conditions initiales w o x w o x l 2 w 1 o x w 1 x h 1 et des conditions aux limites non homogenes de type dirichlet w t u t sur o etant la frontiere de

exponential stabilization of the wave equation by dirichlet integral feedback we consider the problem of boundary feedback stabilization of a vibrating string that is fixed at one end and with control action at the other end in contrast to previous studies that have require

dirichlet feedback control for the stabilization of the wave equation a numerical approach abstract in j differential equations 66 1987 340 a uniform stabilization method of the wave equation by boundary control a la dirichlet has been discussed in this article we investigate the numerical implementation of the above stabilization process by a numerical scheme which mimics the energy decay properties of its continuous counterpart the practical implementation of that scheme leads to a biharmonic problem of a new type which is solved by a method directly inspired by some related work of glowinski and pironneau on the solution of the dirichlet problem for the biharmonic operator siam rev 21 2 1979 167 numerical experiments show that the decay properties of the energy are well preserved by our numerical methodology

boundary controllers and observers for the linearized schrodinger equation we consider a problem of stabilization of the linearized schrodinger equation using boundary actuation and measurements we propose two different control designs first a simple proportional collocated boundary controller is shown to exponentially stabilize the system how ever the decay rate of the closed loop system cannot be prescribed the second full state feedback boundary control design achieves an arbitrary decay rate we formally view the schrodinger equa tion as a heat equation in complex variables and apply the backstepping method recently developed for boundary control of reaction advection diffusion equations the resulting controller is then sup plied with the backstepping observer to obtain an output feedback compensator the designs are illustrated with simulations

dynamical boundary control of two dimensional wave equations vibrating membrane on general domain dynamical boundary control of a vibrating membrane with edge mass and of general shape is mathematically formulated as an abstract evolutionary system the approximate controllability and the strong stabilization by linear boundary damping feedback are established by an approach based on lasalle s invariance principle the mathematical model and the reduced system can be used to investigate some optimization problems

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

exponential stabilization of well posed systems by colocated feedback we consider well posed linear systems whose state trajectories satisfy dot x ax bu where u is the input and a is an essentially skew adjoint and dissipative operator on the hilbert space x this means that the domains of a and a are equal and a a q where q geq 0 is bounded on x the control operator b is possibly unbounded but admissible and the observation operator of the system is b such a description fits many wave and beam equations with colocated sensors and actuators and it has been shown for many particular cases that the feedback u ka y v with ka 0 stabilizes the system strongly or even exponentially here y is the output of the system and v is the new input we show by means of a counterexample that if b is sufficiently unbounded then such a feedback may be unsuitable the closed loop semigroup may even grow exponentially our counterexample is a simple regular system with feedthrough operator zero however we prove that if the original system is exactly controllable and observable and if ka is sufficiently small then the closed loop system is exponentially stable

typical convex program is very well posed in this paper we consider the collection of convex programming problems with inequality and equality constraints in which every problem of the collection is obtained by linear perturbations of the cost function and right hand side perturbation of the constraints while the core cost function and the left hand side constraint functions are kept fixed the main result shows that the set of the problems which are not well posed is porous in a certain strong sense our results concern both the infinite and finite dimensional case in the last case the conclusions are significantly sharper

a physically motivated class of scattering passive linear systems we introduce a class of scattering passive linear systems motivated by examples from mathematical physics the state space of the system is x h oplus e where h and e are hilbert spaces we also have a hilbert space e 0 which is dense in e with continuous embedding and e 0 is the dual of e 0 with respect to the pivot space e the input space is the same as the output space and it is denoted by u the semigroup generator has the structure a big begin smallmatrix 0 l l g frac 1 2 k k end smallmatrix big where l in cal l e 0 h and k in cal l e 0 u are such that big begin smallmatrix l k end smallmatrix big with domain e 0 is closed as an unbounded operator from e to h oplus u the operator g in cal l e 0 e 0 is such that rm re langle gw 0 w 0 rangle leq 0 for all w 0 in e 0 the observation operator is c left begin matrix 0 k end matrix right the control operator is b c and the output equatio

generalized ordered weighted utility averaging hyperbolic absolute risk aversion operators and their applications to group decision making abstract this paper develops a new class of aggregation operator based on utility function which introduces the risk attitude of decision makers dms in the aggregation process first under the general framework of utility function we provide a new operator called the generalized ordered weighted utility averaging gowua operator and study its properties which are suitable for any utility function then under the hyperbolic absolute risk aversion hara utility function we propose another new operator named as the generalized ordered weighted utility averaging hyperbolic absolute risk aversion gowua hara operator and further investigate its families including a wide range of aggregation operators to determine the gowua hara operator weights we put forward an orness measure of the gowua hara operator and analyze its properties considering that different dms may have different opinions toward decision making and their opinions can be characterized by different orness measures we construct a new optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights furthermore based on the gowua hara operator a method for the multiple attribute group decision making magdm is developed finally an example is given to illustrate the application of the gowua hara operator to the magdm

well posedness of cauchy problem for the fourth order nonlinear schrodinger equations in multi dimensional spaces abstract we study the well posedness of cauchy problem for the fourth order nonlinear schrodinger equations i t u e u 2 u p x u 2 x u 2 t r x r n where e 1 0 1 n 2 denotes the spatial dimension and p is a polynomial excluding constant and linear terms

stability of solitons described by nonlinear schrodinger type equations with higher order dispersion abstract steady solitons described by the fourth order nonlinear schrodinger type equations in one two and three dimensions with power law nonlinearities are studied conditions of existence and stability of such solitons are found numerical results demonstrating soliton existence stability and instability are described they agree with the developed theory

nonlinear boundary feedback stabilization for a semilinear kirchhoff plate with dissipation acting only via moments limiting behavior abstract a semilinear kirchhoff plate with a nonlinear dissipation acting via moments only is considered it is shown that the plate is uniformly stabilizable with uniform energy decay rates with respect to the parameter 0 representing rotational forces assumed small moreover it is shown that the solutions of the kirchhoff plate converge to solutions of the semilinear euler bernoulli plate when 0 which is also uniformly stable in finite energy norm

dirichlet boundary stabilization of the wave equation with damping feedback of finite range abstract a closed loop system consisting of the wave equation with a feedback acting in the dirichlet boundary condition in the form of a nonlocal one dimensional range operator defined on the velocity vector damping is considered beside the well posedness question generation of a feedback c 0 semigroup the boundary feedback stabilization problem is studied while asymptotic decay to zero in the uniform operator norm can never occur for the considered class of closed loop systems however checkable sufficient conditions on the vectors in the boundary conditions are provided that guarantee asymptotic decay to zero in the strong norm of appropriate sobolev spaces these conditions include but are not limited to the standard case of dissipativity of the feedback system the starting point of this approach is a functional analytic model for the study of nonsmooth boundary input hyperbolic equations recently developed i lasiecka and r triggiani appl math optim 7 1 1981 35 93