stability and higher integrability of derivatives of solutions in double obstacle problems abstract higher integrability of the derivatives of solutions to double obstacle problems associated with the second order quasilinear elliptic differential equation a x u 0 is obtained under natural assumptions on obstacles this result is used to prove a stability result for solutions to double obstacle problems for varying equations

well posedness for nonlinear schrodinger equations with boundary forces in low dimensions by strichartz estimates abstract in this paper we study the well posedness of solutions for nonlinear schrodinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of dirichlet or neumann force we first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the strichartz estimates on domains secondly we obtain conditional uniqueness and local stability then we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory regarding subquadratic sources we appeal to classical methods and trudinger s inequality to prove the uniqueness which combined with the existence of weak energy solutions mass and energy inequalities eventually implies the continuity of solutions in time

nonlinear schrodinger equation with inhomogeneous dirichlet boundary data in this article we study the following nonlinear schrodinger equation iut u g u p 1u in a domain rn with initial condition u x 0 x and the dirichlet boundary condition u x t q x t on where q are given smooth functions the nonlinear term contributes a negative term to the energy i e g 0 we present the existence theorem for a global solution of finite energy when p 1 2 n

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

well posedness of feedback systems insights into exact robustness analysis and approximate computations this paper establishes a framework for robust stability analysis of linear time invariant uncertain systems the uncertainty is assumed to belong to an arbitrary subset of complex matrices the concept used here is well posedness of feedback systems leading to necessary and sufficient conditions for robust stability based on this concept some insights into exact robust stability conditions are given in particular frequency domain and state space conditions for well posedness are provided in terms of hermitian form inequalities it is shown that these inequalities can be interpreted as small gain conditions with a generalized class of scalings given by linear fractional transformations lft using the lft scaled small gain condition in the state space setting the duality is established between the h sub spl infin norm condition with frequency dependent scalings and the parameter dependent lyapunov condition connections to the existing results including the structured singular value and the integral quadratic constraints are also discussed finally we show that our well posedness conditions can be used to give a less conservative yet computable bound on the real structured singular value this result is illustrated by numerical examples

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

monotonicity method applied to the complex ginzburg landau and related equations abstract global existence of unique strong solutions is established for the complex ginzburg landau equation tu i u i u p 1u u 0 where 0 0 r p 1 and 1 2 p p 1 the key is a new inequality in monotonicity methods it is based on the sectorial estimates of in lp 1 and the nonlinear operator u u p 1u appearing in the equation the key inequality also yields the global existence of unique strong solutions of the nonlinear schrodinger type equation with monotone nonlinearity tu i u u p 1u 0 for all p 1

on the synthesis of boundary control laws for distributed port hamiltonian systems this paper is concerned with the energy shaping of 1 d linear boundary controlled port hamiltonian systems the energy casimir method is first proposed to deal with power preserving systems it is shown how to use finite dimensional dynamic boundary controllers and closed loop structural invariants to partially shape the closed loop energy function and how such controller finally reduces to a state feedback when dissipative port hamiltonian systems are considered the casimir functions do not exist anymore dissipation obstacle and the immersion via a dynamic controller reduction through invariants method cannot be applied the main contribution of this paper is to show how to use the same ideas and state functions to shape the closed loop energy function of dissipative systems through direct state feedback i e without relying on a dynamic controller and a reduction step in both cases the existence of solution and the asymptotic stability by additional damping injection of the closed loop system are proven the general theory and achievable closed loop performances are illustrated with the help of a concluding example the boundary stabilization of a longitudinal beam vibrations

global yield curve dynamics and interactions a dynamic nelson siegel approach the popular nelson siegel 1987 yield curve is routinely fit to cross sections of intra country bond yields and diebold and li 2006 have recently proposed a dynamized version in this paper we extend diebold li to a global context modeling a potentially large set of country yield curves in a framework that allows for both global and country specific factors in an empirical analysis of term structures of government bond yields for the germany japan the u k and the u s we find that global yield factors do indeed exist and are economically important generally explaining significant fractions of country yield curve dynamics with interesting differences across countries

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

well posedness of boundary controlled and observed stochastic port hamiltonian systems in this article stochastic port hamiltonian systems sphs on infinite dimensional spaces governed by ito stochastic differential equations sdes are introduced and some properties of this new class of systems are studied they are an extension of sphss defined on a finite dimensional state space the concept of well posedness in the sense of weiss and salamon is generalized to the stochastic context under this extended definition sphss are shown to be well posed the theory is illustrated on an example of a vibrating string subject to a hilbert space valued gaussian white noise process

continuous dependence on obstacles for the double obstacle problem on metric spaces let x be a complete metric space equipped with a doubling borel measure supporting a p poincare inequality we obtain various convergence results for solutions of double obstacle problems on open subsets of x in particular we consider a sequence of double obstacle problems with converging obstacles and show that the corresponding solutions converge as well we use the convergence properties to define and study a generalized solution of the double obstacle problem

a small gain condition for interconnections of iss systems with mixed iss characterizations we consider interconnected nonlinear systems with external inputs where each of the subsystems is assumed to be input to state stable iss sufficient conditions of small gain type are provided guaranteeing that the interconnection is iss with respect to the external input to this end we extend recently obtained small gain theorems to a more general type of interconnections the small gain theorem provided here is applicable to situations where the iss conditions are formulated differently for each subsystem and are either given in the maximization or the summation sense furthermore it is shown that the conditions are compatible in the sense that it is always possible to transform sum formulations to maximum formulations without destroying a given small gain condition an example shows the advantages of our results in comparison with the known ones

the macroeconomy and the yield curve a dynamic latent factor approach we estimate a model that summarizes the yield curve using latent factors specifically level slope and curvature and also includes observable macroeconomic variables specifically real activity inflation and the monetary policy instrument our goal is to provide a characterization of the dynamic interactions between the macroeconomy and the yield curve we find strong evidence of the effects of macro variables on future movements in the yield curve and evidence for a reverse influence as well we also relate our results to the expectations hypothesis

on global leader following consensus of identical linear dynamic systems subject to actuator saturation abstract this paper studies the leader following consensus problem for a group of agents with identical linear systems subject to control input saturation we focus on two classes of linear systems neutrally stable systems and double integrator systems for neurally stable systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with proper choices of relative potential functions global consensus can also be achieved over a switching communication topology for double integrator systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with the help of a simple saturation function in the local feedback laws global consensus can also be achieved over a switching communication topology simulation results illustrate the theoretical results

dirac structures and boundary control systems associated with skew symmetric differential operators associated with a skew symmetric linear operator on the spatial domain a b we define a dirac structure which includes the port variables on the boundary of this spatial domain this dirac structure is a subspace of a hilbert space naturally associated with this dirac structure is an infinite dimensional system we parameterize the boundary port variables for which the c 0 semigroup associated with this system is contractive or unitary furthermore this parameterization is used to split the boundary port variables into inputs and outputs similarly we define a linear port controlled hamiltonian system associated with the previously defined dirac structure and a symmetric positive operator defining the energy of the system we illustrate this theory on the example of the timoshenko beam

robust stability of feedback systems a geometric approach using the gap metric a geometric framework for robust stabilization of infinite dimensional time varying linear systems is presented the uncertainty of a system is described by perturbations of its graph and is measured in the gap metric necessary and sufficient conditions for robust stability are generalized from the time invariant case an example is given to highlight an important difference between the obstructions which limit the size of a stabilizable gap ball in the time varying and time invariant cases several results on the gap metric and the gap topology are established that are central in a geometric treatment of the robust stabilizability problem in the gap in particular the concept of a graphable subspace is introduced in the paper subspaces that fail to be graphable are characterized by an index condition on a certain semi fredholm operator

weak form of stokes dirac structures and geometric discretization of port hamiltonian systems we present the mixed galerkin discretization of distributed parameter port hamiltonian systems due to the inherent definition of boundary interconnection ports this system representation is particularly useful for the modeling of interconnected multi physics systems and control at the prototypical example of a system of two conservation laws in arbitrary spatial dimension we derive the main contributions i a weak formulation of the underlying geometric stokes dirac structure ii its geometric approximation by a finite dimensional dirac structure using a mixed galerkin approach and power preserving maps on the space of discrete power variables and iii the approximation of the hamiltonian to obtain finite dimensional port hamiltonian state space models the power preserving maps on the discrete bond space offer design degrees of freedom for the discretization which is illustrated at the example whitney finite elements on a 2d simplicial triangulation the resulting schemes can be considered as trade offs between centered approximations and upwinding

global existence and open loop exponential stabilization of weak solutions for nonlinear schrodinger equations with localized external neumann manipulation abstract in this paper we consider the nonlinear schrodinger equations nls with focusing defocusing interior source and possibly nonlinear damping on a bounded regular domain in the euclidean space moreover it is assumed that the solutions are subject to external neumann boundary manipulation on one portion of the boundary our aim is to obtain global existence of the weak solutions under various assumptions on the sign of the source and powers of the nonlinearities in the case of a linear damping we also prove that solutions decay exponentially under the assumption that the neumann type control at the boundary decays in a similar manner

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

well posedness and energy decay estimates in the cauchy problem for the damped defocusing schrodinger equation abstract in this paper we study the existence at the h 1 level as well as the stability for the damped defocusing schrodinger equation in r d the considered damping coefficient is time dependent and may vanish at infinity to prove the existence we employ the method devised by ozsari kalantarov and lasiecka 27 which is based on monotone operators theory in particular when d 1 or d 2 we obtain the uniqueness decay estimates for the l 2 level and h 1 l p 2 level energies are established with the help of direct multipliers method coupled with refined energy estimates and a lower semi continuity argument

bayes inference in regression models with arma p q errors we develop practical and exact methods of analyzing arma p 4 regression error models in a bayesian framework by using the gibbs sampling and metropolis hastings algorithms and we prove that the kernel of the proposed markov chain sampler converges to the true density the procedures can be applied to pure arma time series models and to determine features of the likelihood function by choosing appropriate diffuse priors our results are unconditional on the initial observations we also show how the algorithm can be further simplified for the important special cases of stationary ar p and invertible ma q models recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation examples with simulated and actual economic data are presented kpj ourls gibbs sampling metropolis hastings algorithm data augmentation time series arma processes markov chain bayesian statistics

forecasting the term structure of government bond yields despite powerful advances in yield curve modeling in the last 20 years comparatively little attention has been paid to the key practical problem of forecasting the yield curve in this paper we do so we use neither the no arbitrage approach nor the equilibrium approach instead we use variations on the nelson siegel exponential components framework to model the entire yield curve period by period as a three dimensional parameter evolving dynamically we show that the three time varying parameters may be interpreted as factors corresponding to level slope and curvature and that they may be estimated with high efficiency we propose and estimate autoregressive models for the factors and we show that our models are consistent with a variety of stylized facts regarding the yield curve we use our models to produce term structure forecasts at both short and long horizons with encouraging results in particular our forecasts appear much more accurate at long horizons than various standard benchmark forecasts r 2005 published by elsevier b v

fractional schrodinger equation solvability and connection with classical schrodinger equation abstract we consider the dirichlet boundary problem for semilinear fractional schrodinger equation with subcritical nonlinear term local and global in time solvability and regularity properties of solutions are discussed but our main task is to describe the connections of the fractional equation with the classical nonlinear schrodinger equation including convergence of the linear semigroups and continuity of the nonlinear semigroups when the fractional exponent approaches 1

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

conditions for the equivalence between iqc and graph separation stability results abstractthis paper provides a link between time domain and frequency domain stability results in the literature specifically we focus on the comparison between stability results for a feedback in

non linear systems stabilization and coprimeness a theory of coprimeness is developed for non linear systems with the intention of constructing analytic tools for the solution of the problem of stabilizing a non linear system through the application of additive non linear feedback the qualitative features of the resulting theory are strikingly similar to the situation in the linear case

singular perturbations and input to state stability this paper establishes a type of total stability for the input to state stability property with respect to singular perturbations in particular if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input to state stable with respect to disturbances then these properties continue to hold up to an arbitrarily small offset for initial conditions disturbances and their derivatives in an arbitrarily large compact set as long as the singular perturbation parameter is sufficiently small

energy based lyapunov functions for forced hamiltonian systems with dissipation in this paper we propose a constructive procedure to modify the hamiltonian function of forced hamiltonian systems with dissipation in order to generate lyapunov functions for nonzero equilibria a key step in the procedure which is motivated from energy balance considerations standard in network modeling of physical systems is to embed the system into a larger hamiltonian system for which a series of casimir functions can be easily constructed interestingly enough for linear systems the resulting lyapunov function is the incremental energy thus our derivations provide a physical explanation to it an easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given some examples that illustrate the method are given

coprime fractional representations and stability of non linear feedback systems fractional representation methods for finite dimensional linear time invariant fdlti systems have been developed in an algebraic framework of principal ideal domains the concept of coprime fractional representations has been generalized to discrete time non linear systems by hammer 1985 1987 by viewing the bezout identity as the basis of the definition of coprimeness in this paper we view the role of right coprime fractional representation in representing the set of all stable input output pairs of a possibly unstable non linear system this notion of coprimeness is shown to be equivalent to that of fdlti systems using coprime fractional representations of non linear systems we obtain a characterization of the stability of non linear feedback systems this characterization is similar to that obtained in the case of fdlti systems we also obtain a parameterization of all non linear and time varying stabilizing controllers for linear possibly time varying plants which has the same form as t

stochastic nonlinear schrodinger equation on an upper right quarter plane with dirichlet random boundary in this paper we study the nonhomogeneous stochastic initial boundary value problem for the nonlinear schrodinger equation on an upper right quarter plane with random dirichlet boundary conditions the main novelty of this work is a convenient framework for the analysis of such equations excited by the wiener additive noise on the boundary our approach allows us to show the local existence and uniqueness of solutions in the space h2 the basic properties of the solutions such as the continuity and the boundary layer behavior are also studied using the ito calculus despite several technical difficulties we believe that the approach developed in this paper can be applied to the case of a large class of noise including fractional wiener space time white noise homogeneous noise and levy noise

exponential stability of a class of boundary control systems we study a class of partial differential equations with variable coefficients on a one dimensional spatial domain with control and observation at the boundary for this class of systems we provide simple tools to check exponential stability this class is general enough to include models of flexible structures traveling waves heat exchangers and bioreactors among others the result is based on the use of a generating function the energy for physical systems and an inequality condition at the boundary furthermore based on the port hamiltonian approach we give a constructive method to reduce this inequality to a simple matrix inequality

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

weakly damped focusing nonlinear schrodinger equations with dirichlet control abstract in this article we consider the weakly damped focusing nonlinear schrodinger equations on bounded domains at the natural h 1 energy level with dirichlet control acting on a portion of the boundary we introduce the dynamic extension method for homogenizing the inhomogeneous boundary input then we construct approximate solutions using monotone operator theory a hidden trace regularity is proved to control the norm of the solutions in a global sense this allows the use of compactness techniques by which we prove the existence of weak solutions finally using multiplier techniques we prove the exponential decay of solutions under the assumption that the boundary control also decays in a similar fashion

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

exponential stabilization of port hamiltonian boundary control systems via energy shaping this article is concerned with the exponential stabilization of a class of linear boundary control systems bcss in port hamiltonian form through energy shaping starting from a first feedback loop that is in charge of modifying the hamiltonian function of the plant a second control loop that guarantees exponential convergence to the equilibrium is designed in this way a major limitation of standard energy shaping plus damping injection control laws applied to linear port hamiltonian bcss namely the fact that only asymptotic convergence is assured has been removed

a bayesian multivariate functional dynamic linear model abstractwe present a bayesian approach for modeling multivariate dependent functional data to account for the three dominant structural features in the data functional time dependent and multivariate components we extend hierarchical dynamic linear models for multivariate time series to the functional data setting we also develop bayesian spline theory in a more general constrained optimization framework the proposed methods identify a time invariant functional basis for the functional observations which is smooth and interpretable and can be made common across multivariate observations for additional information sharing the bayesian framework permits joint estimation of the model parameters provides exact inference up to mcmc error on specific parameters and allows generalized dependence structures sampling from the posterior distribution is accomplished with an efficient gibbs sampling algorithm we illustrate the proposed framework with two applications 1 multi economy yield curve data

stability analysis for high frequency networked control systems this note generalizes the stability analysis for a high frequency networked control system the high frequency networked control system is described by a delta operator system with a high frequency constraint stability conditions are given for the high frequency delta operator system furthermore by developing the generalized kalman yakubovic popov lemma improved stability conditions are also presented in terms of linear matrix inequalities some experiment results are presented to illustrate the effectiveness of the developed techniques

qualitative properties of solutions for nonlinear schrodinger equations with nonlinear boundary conditions on the half line in this paper we study the interaction between a nonlinear focusing robin type boundary source a nonlinear defocusing interior source and a weak damping term for nonlinear schrodinger equations posed on the infinite half line we construct solutions with negative initial energy satisfying a certain set of conditions which blow up in finite time in the h1 sense we obtain a sufficient condition relating the powers of nonlinearities present in the model which allows construction of blow up solutions in addition to the blow up property we also discuss the stabilization property and the critical exponent for this model

on very weak solutions to a class of double obstacle problems abstract we prove the uniqueness of very weak solutions by hodge decomposition and obtain the existence by an approximation argument moreover we prove that the solution quasiminimizes the r dirichlet integral in k r and finally the stability of very weak solutions is established for varying obstacle functions

pseudo spectral methods for the spatial symplectic reduction of open systems of conservation laws a reduction method is presented for systems of conservation laws with boundary energy flow it is stated as a generalized pseudo spectral method which performs exact differentiation by using simultaneously several approximation spaces generated by polynomials bases and suitable choices of port variables the symplecticity of this spatial reduction method is proved when used for the reduction of both closed and open systems of conservation laws for any choice of collocation points i e for any polynomial bases the symplecticity of some more usual collocation schemes is discussed and finally their accuracy on approximation of the spectrum on the example of the ideal transmission line is discussed in comparison with the suggested reduction scheme

dirac structures on hilbert spaces and boundary control of distributed port hamiltonian systems abstract aim of this paper is to show how the dirac structure properties can be exploited in the development of energy based boundary control laws for distributed port hamiltonian systems usually stabilization of non zero equilibria has been achieved by looking at or generating a set of structural invariants namely casimir functions in closed loop since this approach fails when an infinite amount of energy is required at the equilibrium dissipation obstacle this paper illustrates a novel approach that enlarges the class of stabilizing controllers the starting point is the parametrization of the dynamics provided by the image representation of the dirac structure that is able to show the effects of the boundary inputs on the state evolution in this way energy balancing and control by state modulated source methodologies are extended to the distributed parameter scenario and a geometric interpretation of these control techniques is provided the theoretical results are discussed with the help of a simple but illustrative example i e a transmission line with an rlc load in both serial and parallel configurations in the latter case energy balancing controllers are not able to stabilize non zero equilibria because of the dissipation obstacle the problem is solved thanks to a boundary state modulated source

boundary controllability for the semilinear schrodinger equations on riemannian manifolds we study the boundary exact controllability for the semilinear schrodinger equation defined on an open bounded connected set of a complete n dimensional riemannian manifold m with metric g we prove the locally exact controllability around the equilibria under some checkable geometrical conditions our results show that exact controllability is geometrical characters of a riemannian metric given by the coefficients and equilibria of the semilinear schrodinger equation we then establish the globally exact controllability in such a way that the state of the semilinear schrodinger equation moves from an equilibrium in one location to an equilibrium in another location

on representations and integrability of mathematical structures in energy conserving physical systems in the present paper we elaborate on the underlying hamiltonian structure of interconnected energy conserving physical systems it is shown that a power conserving interconnection of port controlled generalized hamiltonian systems leads to an implicit generalized hamiltonian system and a power conserving partial interconnection to an implicit port controlled hamiltonian system the crucial concept is the notion of a generalized dirac structure defined on the space of energy variables or on the product of the space of energy variables and the space of flow variables in the port controlled case three natural representations of generalized dirac structures are treated necessary and sufficient conditions for closedness or integrability of dirac structures in all three representations are obtained the theory is applied to implicit port controlled generalized hamiltonian systems and it is shown that the closedness condition for the dirac structure leads to strong conditions on the input vector fields

an input output based robust stabilization criterion for neural network control of nonlinear systems a stabilization method based on the input output conicity criterion is presented conventional learning algorithms are applied to adjust the controller dynamics and robust stability of the closed loop system is guaranteed by modifying the training patterns which yield unstable behavior the methodology developed expands the class of nonlinear systems to be controlled using neural control schemes so that the stabilization of a broad class of neural network based control systems even with unknown dynamics is assured straightforwardness in the application of this method is evident in contrast to the lyapunov function approach

local exact controllability and stabilizability of the nonlinear schrodinger equation on a bounded interval this paper studies the exact controllability and the stabilization of the cubic schrodinger equation posed on a bounded interval both internal and boundary controls are considered and the results are given first in a periodic setting and next with dirichlet resp neumann boundary conditions it is shown that the systems with either an internal control or a boundary control are locally exactly controllable in the classical sobolev space h s for any s geq0 it is also shown that the systems with an internal stabilization are locally exponentially stabilizable in h s for any s geq0

stability and passivity preserving petrov galerkin approximation of linear infinite dimensional systems this contribution presents two approximation methods for linear infinite dimensional systems that ensure the preservation of stability and passivity the first approach allows one to approximate internal source free infinite dimensional systems such that the resulting approximation is a port controlled hamiltonian system with dissipation the second method deals with the class of systems that are not required to have conjugated outputs but only a dissipative system operator it yields approximations with a dissipative system matrix for which bounds of their stability margin are provided both approaches are based on a state space formulation of the infinite dimensional system this makes it possible to use the petrov galerkin approximation whose free parameters are partly used for achieving the structure preservation since still free parameters remain further application specific objectives such as e g moment matching can be achieved both approaches are applied to the approximation of an euler bernoulli beam

dissipativity based boundary control of linear distributed port hamiltonian systems the main contribution of this paper is a general synthesis methodology of exponentially stabilising control laws for a class of boundary control systems in port hamiltonian form that are dissipative with respect to a quadratic supply rate being the total energy the storage function more precisely general conditions that a linear regulator has to satisfy to have at first a well posed and secondly an exponentially stable closed loop system are presented the methodology is illustrated with reference to two specific stabilisation scenarios namely when the distributed parameter plant is in impedance or in scattering form moreover it is also shown how these techniques can be employed in the analysis of more general systems that are described by coupled partial and ordinary differential equations in particular the repetitive control scheme is studied and conditions on the finite dimensional linear plant to have asymptotic tracking of generic periodic reference signals are determined

a characterization of boundary conditions yielding maximal monotone operators abstract we provide a characterization for maximal monotone realizations for a certain class of nonlinear operators in terms of their corresponding boundary data spaces the operators under consideration naturally arise in the study of evolutionary problems in mathematical physics we apply our abstract characterization result to port hamiltonian systems and a class of frictional boundary conditions in the theory of contact problems in visco elasticity

ap weight and integrability of solutions in obstacle problems integrability of solutions to obstacle problems is obtained under assumption that the obstacles belong to the a p weight class this result is used to prove an existence result for a p weight problems c 2011 elsevier ltd all rights reserved

lossless and dissipative distributed systems this paper deals with linear shift invariant distributed systems by this we mean systems described by constant coefficient linear partial differential equations we define dissipativity with respect to a quadratic differential form i e a quadratic functional in the system variables and their partial derivatives the main result states the equivalence of dissipativity and the existence of a storage function or a dissipation rate the proof of this result involves the construction of the dissipation rate we show that this problem can be reduced to hilbert s 17th problem on the representation of a nonnegative rational function as a sum of squares of rational functions

an inhomogeneous boundary value problem for nonlinear schrodinger equations abstract we consider a nonlinear schrodinger equation in a domain r n with the inhomegeneous dirichlet boundary condition u q where q is a given smooth function the nonlinear term contributes a positive term to the energy we prove the existence of global solutions of finite energy

determination of zero coupon and spot rates from treasury data by maximum entropy methods abstract an interesting and important inverse problem in finance consists of the determination of spot rates or prices of the zero coupon bonds when the only information available consists of the prices of a few coupon bonds a variety of methods have been proposed to deal with this problem here we present variants of a non parametric method to treat with such problems which neither imposes an analytic form on the rates or bond prices nor imposes a model for the random evolution of the yields the procedure consists of transforming the problem of the determination of the prices of the zero coupon bonds into a linear inverse problem with convex constraints and then applying the method of maximum entropy in the mean this method is flexible enough to provide a possible solution to a mispricing problem

boundedness properties of nonlinear quasi dissipative systems boundedness results for feedback interconnections of quasi dissipative systems are presented a classical result due to hill and moylan is generalized to the case of finite power gain stability of feedback interconnection of quasi dissipative systems it is also shown that under the assumption of strong finite time detectability such an interconnection has uniformly ultimately bounded trajectories for any uniformly bounded input

energy shaping of distributed parameter port hamiltonian systems based on finite element approximation the main contribution of this paper is a procedure for the control by energy shaping via casimir generation of infinite dimensional port hamiltonian systems based on a particular finite element approximation the proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve casimir functions in the closed loop system when going from the distributed to the approximated lumped parameter system besides the intrinsic difficulties related to the large number of state variables the finite element model is generally given in terms of a dirac structure and is completely a causal which implies that the plant dynamics is not given in standard input state output form but as a set of daes consequently the classical energy casimir method has to be extended in order to deal with dynamical systems with constraints usually appearing in the form of lagrangian multipliers the general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line

inhomogeneous dirichlet boundary value problem for nonlinear schrodinger equations with a power nonlinearity on the upper half plane abstract we consider the inhomogeneous dirichlet boundary value problem for nonlinear schrodinger equations with a power nonlinearity in the upper half plane we present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the problem by using the classical energy method and factorization techniques

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

dirac structures and their composition on hilbert spaces dirac structures appear naturally in the study of certain classes of physical models described by partial differential equations and they can be regarded as the underlying power conserving structures we study these structures and their properties from an operator theoretic point of view in particular we find necessary and sufficient conditions for the composition of two dirac structures to be a dirac structure and we show that they can be seen as lagrangian hyper maximal neutral subspaces of krein spaces moreover special emphasis is laid on dirac structures associated with operator colligations it turns out that this class of dirac structures is linked to boundary triplets and that this class is closed under composition

a general boundedness result for interconnected nonlinear systems a general boundedness result is given for the feedback interconnection of two nonlinear stable systems using the same input output approach as in the standard small gain theorem the sufficient condition given here relaxes the finite gain stability assumption and does not require a boundedness result for all possible bounded exogenous inputs this condition has a simple graphical interpretation that utilizes graphs of bounding functions

the parallel projection operators of a nonlinear feedback system abstract this paper defines and studies a pair of nonlinear parallel projection operators associated with a nonlinear feedback system these operators have been seen to play an important role in the robustness and design of linear systems especially in the theory of the gap metric the use of weighted gaps in control system design and glover mcfarlane loop shaping we show that the input output l 2 stability of a feedback system amounts to a coordinatization of the input and output spaces which is also equivalent to the existence of a pair of nonlinear parallel projection operators onto the graph of the plant and the inverse graph of the controller respectively these projections are shown to have equal norms whenever one of the feedback elements is linear a bound on this norm is given in the case of passive systems with unity negative feedback

exponential stability for infinite dimensional non autonomous port hamiltonian systems abstract we study the non autonomous version of an infinite dimensional linear port hamiltonian system on an interval a b employing abstract results on evolution families we show c 1 well posedness of the corresponding cauchy problem and thereby existence and uniqueness of classical solutions for sufficiently regular initial data further we demonstrate that a dissipation condition in the style of the dissipation condition sufficient for uniform exponential stability in the autonomous case also leads to a uniform exponential decay rate of the energy in this non autonomous setting

neural network based distributed attitude coordination control for spacecraft formation flying with input saturation this brief considers the attitude coordination control problem for spacecraft formation flying when only a subset of the group members has access to the common reference attitude a quaternion based distributed attitude coordination control scheme is proposed with consideration of the input saturation and with the aid of the sliding mode observer separation principle theorem chebyshev neural networks smooth projection algorithm and robust control technique using graph theory and a lyapunov based approach it is shown that the distributed controller can guarantee the attitude of all spacecraft to converge to a common time varying reference attitude when the reference attitude is available only to a portion of the group of spacecraft numerical simulations are presented to demonstrate the performance of the proposed distributed controller

robustness analysis of nonlinear feedback systems an input output approach this paper presents an approach to robustness analysis for nonlinear feedback systems we pursue a notion of model uncertainty based on the closeness of input output trajectories which is not tied to a particular uncertainty representation such as additive parametric structured etc the basic viewpoint is to regard systems as operators on signal spaces we present two versions of a global theory where stability is captured by induced norms or by gain functions we also develop local approaches over bounded signal sets and give a treatment for systems with potential for finite time escape we compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations e g small time delays we also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations the paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection

uniform decay rate estimates for schrodinger and plate equations with nonlinear locally distributed damping on a compact n dimensional riemannian manifold m g we establish uniform decay rate estimates for the linear schrodinger and plate equations subject to an internal nonlinear damping locally distributed on the manifold our approach can be also employed for other equations provided that inverse inequality for the linear model occurs in the particular case of the wave equation where the well known geometric control condition gcc is equivalent to the observability inequality our method generalizes the results due to cavalcanti et al 2010 2009 9 10 regarding the optimal choice of dissipative regions

exact boundary controllability of the nonlinear schrodinger equation abstract this paper studies the exact boundary controllability of the semi linear schrodinger equation posed on a bounded domain r n with either the dirichlet boundary conditions or the neumann boundary conditions it is shown that if s n 2 or 0 s n 2 with 1 n 2 2 s or s 0 1 with n 2 then the systems are locally exactly controllable in the classical sobolev space h s around any smooth solution of the cubic schrodinger equation

on exploring the domain of attraction for bilateral teleoperator subject to interval delay and saturated p d control scheme the domain of attraction problem is investigated for networked teleoperation system subject to actuator saturation the forward and backward time varying communication delays are assumed to be interval and asymmetric which is the case for network based teleoperation system we propose a novel lyapunov krasovskii functional for the closed loop teleoperation system with the consideration of the interval values of the time delays the delay dependent estimation of the domain of attraction is presented using linear matrix inequality lmi technique the problem of designing mathrm p mathrm d control law such that the domain of attraction is enlarged is formulated and solved as an optimization problem with lmi constraints experiments are performed to verify the effectiveness of the proposed approach

stabilization of infinite dimensional port hamiltonian systems by nonlinear dynamic boundary control the conditions for existence of solutions and stability asymptotic and exponential of a large class of boundary controlled systems on a 1d spatial domain subject to nonlinear dynamic boundary actuation are given the consideration of such class of control systems is motivated by the use of actuators and sensors with nonlinear behavior in many engineering applications these nonlinearities are usually associated to large deformations or the use of smart materials such as piezo actuators and memory shape alloys including them in the controller model results in passive dynamic controllers with nonlinear potential energy function and or nonlinear damping forces first it is shown that under very natural assumptions the solutions of the partial differential equation with the nonlinear dynamic boundary conditions exist globally secondly when energy dissipation is present in the controller then it globally asymptotically stabilizes the partial differential equation finally it is shown that assuming some additional conditions on the interconnection and on the passivity properties of the controller consistent with physical applications global exponential stability of the closed loop system is achieved

exponential stabilization of boundary controlled port hamiltonian systems with dynamic feedback it is shown that a strictly input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain this follows since the controller imposes exponential dissipation of the total energy the result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled pde s and ode s the result is specialized to port hamiltonian control systems and a simplified dna manipulation process is used to illustrate the result

dissipative extensions and port hamiltonian operators on networks abstract in this article we study port hamiltonian partial differential equations on certain one dimensional manifolds we classify those boundary conditions that give rise to contraction semigroups as an application we study port hamiltonian operators on networks whose edges can have finite or infinite length in particular we discuss possibly infinite networks in which the edge lengths can accumulate zero and port hamiltonian operators with hamiltonians that neither are bounded nor bounded away from zero we achieve this by first providing a new description for maximal dissipative extensions of skew symmetric operators the main technical tool used for this is the notion of boundary systems the latter generalizes the classical notion of boundary triple t s and allows to treat skew symmetric operators with unequal deficiency indices in order to deal with fairly general variable coefficients we develop a theory of possibly unbounded non negative injective weights on an abstract hilbert space

on relationships among passivity positive realness and dissipativity in linear systems the notions of passivity and positive realness are fundamental concepts in classical control theory but the use of the terms has varied for lti systems these two concepts capture the same essential property of dynamical systems that is a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment this paper summarizes the connection between these two concepts for continuous and discrete time lti systems beyond that relationships are provided between classes of strictly passive systems and classes of positive real systems the more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy based results the frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity after surveying relevant existing results some clarifying results are presented these involve connections between classes of passive systems and finite gain l2l2 stability as well as asymptotic stability additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results this paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts

a generalization of the scattering transformation for conic systems a generalized version of the scattering transformation is introduced which allows for rendering of the input output characteristics of a nonlinear conic system into an arbitrary prescribed conic sector the transformation is consequently applied to the problem of stabilization of conic systems interconnections the stability is achieved by rendering the input output characteristics of the subsystems into complementary cones such that the graph separation stability condition is satisfied in the presence of communication delays the scattering based technique for stabilization of feedback interconnections is generalized to the case of arbitrary conic subsystems

uniform decay rates for the energy of weakly damped defocusing semilinear schrodinger equations with inhomogeneous dirichlet boundary control abstract in this paper we study the open loop stabilization as well as the existence and regularity of solutions of the weakly damped defocusing semilinear schrodinger equation with an inhomogeneous dirichlet boundary control first of all we prove the global existence of weak solutions at the h 1 energy level together with the stabilization in the same sense it is then deduced that the decay rate of the boundary data controls the decay rate of the solutions up to an exponential rate secondly we prove some regularity and stabilization results for the strong solutions in h 2 sense the proof uses the direct multiplier method combined with monotonicity and compactness techniques the result for weak solutions is strong in the sense that it is independent of the dimension of the domain the power of the nonlinearity and the smallness of the initial data however the regularity and stabilization of strong solutions are obtained only in low dimensions with small initial and boundary data

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

on global solutions to the initial boundary value problem for the damped nonlinear schrodinger equations where a 0 and q is a bounded domain in rn with smooth boundary x when a 0 undamped case the global existence of smooth solutions to the initial boundary value problem l 3 has been proved only when n 2 and f lu12 w lulp with p 2 brezis and gallouet cl with 2 i p i3 m tsutsumi 9 higher dimensional cases are very difficult pribl s and remain unproved as far as the author knows if we add a linear damping term iau a 0 then the mass ilull iztr1 and the energy ivu x t l dx j f lu x t l dx decay exponentially as t cc as is seen below which may assert the global existence of small smooth solutions even if the nonlinear term f lul u does not have a proper sign it is our purpose to establish the global existence and decay estimates of smooth solutions of the problem l 3 with small data there are a number of works on the nonlinear evolution equations see 3 5 71 and their references in the following spirit energy and decay estimates give global existence of solutions if the damping term is not added there is no hope that the decay estimates of solutions in some f q p 2 2 can be obtained since

on graphs conic relations and input output stability of nonlinear feedback systems this paper presents necessary and sufficient conditions for the stability of general interconnected dynamical systems the results are expressed in terms of the graphs of the interconnection s subsystems conditions for robustness of stability for an interconnection with additive disturbances are also provided finally the paper gives sufficient conditions for stability using conic sector conditions that generalize earlier conditions and that incorporate a recent nonlinear small gain idea