robust adaptive boundary control of a flexible marine riser with vessel dynamics in this paper robust adaptive boundary control for a flexible marine riser with vessel dynamics is developed to suppress the riser s vibration to provide an accurate and concise representation of the riser s dynamic behavior the flexible marine riser with vessel dynamics is described by a distributed parameter system with a partial differential equation pde and four ordinary differential equations odes boundary control is proposed at the top boundary of the riser based on lyapunov s direct method to regulate the riser s vibration adaptive control is designed when the system parametric uncertainty exists with the proposed robust adaptive boundary control uniform boundedness under the ocean current disturbance can be achieved the proposed control is implementable with actual instrumentation since all the required signals in the control can be measured by sensors or calculated by a backward difference algorithm the state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters simulations are provided to illustrate the applicability and effectiveness of the proposed control

boundary optimal lq control of coupled hyperbolic pdes and odes this contribution addresses the development of a linear quadratic lq regulator for a set of hyperbolic pdes coupled with a set of odes through the boundary the approach is based on an infinite dimensional hilbert state space description of the system and the well known operator riccati equation ore in order to solve the optimal control problem the ore is converted to a set of matrix riccati equations the feedback operator is found by solving the resulting matrix riccati equations the performance of the designed control policy is assessed by applying it to a system of interconnected continuous stirred tank reactor cstr and a plug flow reactor pfr through a numerical simulation

h_ infty fuzzy control for a class of nonlinear coupled ode pde systems with input constraint this paper deals with the problem of h infty fuzzy control design with an input constraint for a class of coupled systems which consist of an n dimensional nonlinear subsystem of ordinary differential equations odes and a scalar linear parabolic subsystem of partial differential equation pde connected in feedback initially the nonlinear coupled system is represented by a takagi sugeno t s fuzzy coupled ode pde model then based on the fuzzy model and parallel distributed compensation scheme a fuzzy state feedback control design is developed via lyapunov s direct method such that the resulting closed loop fuzzy coupled system is exponentially stable and a prescribed h infty performance of disturbance attenuation is satisfied the existing condition of the proposed h infty fuzzy controllers is given in terms of linear matrix inequalities lmis moreover in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude a suboptimal h infty constrained fuzzy control problem is also addressed which is formulated as an lmi optimization problem finally the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness

iterated differentiation followed by composition from bloch type spaces to weighted bmoa spaces abstract let be a holomorphic self map of the open unit disk d and h d the class of holomorphic functions on d for n n 0 define an operator by c d n f f n f h d we characterize the boundedness and compactness of operator c d n from bloch type spaces to weighted bmoa spaces

on a product type operator from bloch spaces to weighted type spaces on the unit ball we characterize the boundedness and compactness of a product of radial derivative composition and multiplication operators from bloch spaces to weighted type spaces on the unit ball

boundary observer design for hyperbolic pde ode cascade systems the paper presents an observer design for a class of hyperbolic pde ode cascade systems with a boundary measurement the cascade systems consist of coupled pdes featuring one rightward and one leftward convecting first order transport pdes and a set of odes which enter the pdes through the left boundary of the systems the design which is based on the volterra integral transformation relies only on a single sensor at the right boundary of the system the observer consists of a copy of the plant plus output injection terms both in the pdes and the odes the observer is constructed in a collocated setup which means both sensing and actuation are located at the same boundary the observer gains are computed analytically by solving goursat type pdes in terms of bessel function of the first kind the observer design is tested against a field scale flow loop test experiment in stavanger by statoil oil company the results show that the observer converges to the actual values and that the design can be used as a process monitoring tool in oil well drilling

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

disturbance rejection fuzzy control for nonlinear parabolic pde systems via multiple observers a design method of low dimensional disturbance rejection fuzzy control drfc via multiple observers is proposed for a class of nonlinear parabolic partial differential equation pde systems where the disturbance is modeled by an exosystem of ordinary differential equations odes and enters into the pde system through the control channel in the proposed scheme the modal decomposition technique is initially applied to the pde system to derive a slow subsystem of low dimensional nonlinear odes which accurately captures the dominant dynamics of the pde system the resulting nonlinear slow subsystem is subsequently represented by a takagi sugeno t s fuzzy model from the t s fuzzy model and the exosystem a fuzzy slow mode observer and a fuzzy disturbance observer are constructed to estimate the slow mode and the disturbance respectively furthermore a nonlinear observation spillover observer is proposed to compensate the effect of observation spillover then based on these observers a low dimensional drfc design is developed in terms of linear matrix inequalities to guarantee the exponential stability of the closed loop pde system in the presence of the disturbance finally the effectiveness of the proposed design method is demonstrated on the control of one dimensional burgers kpp fisher diffusion reaction system and the temperature profile of a catalytic rod

tractor calculi for parabolic geometries parabolic geometries may be considered as curved analogues of the homogeneous spaces g p where g is a semisimple lie group and p c g a parabolic subgroup conformal geometries and cr geometries are examples of such structures we present a uniform description of a calculus called tractor calculus based on natural bundles with canonical linear connections for all parabolic geometries it is shown that from these bundles and connections one can recover the cartan bundle and the cartan connection in particular we characterize the normal cartan connection from this induced bundle connection perspective we construct explicitly a family of fundamental first order differential operators which are analogous to a covariant derivative iterable and defined on all natural vector bundles on parabolic geometries for an important subclass of parabolic geometries we explicitly and directly construct the tractor bundles their canonical linear connections and the machinery for explicitly calculating via the tractor calculus

on operator p g φ from the logarithmic bloch type space to the mixed norm space on the unit ball the boundedness and compactness of the following recently introduced by this author integral type operatorp f gf z email protected 0 1f f tz g tz dtt email protected b where f is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type spaces to mixed norm spaces on b are studied in this paper

higher symmetries of the conformal powers of the laplacian on conformally flat manifolds a r g gratefully acknowledges support from the royal society of new zealand via marsden grant nos 06 uoa 029 and 10 uoa 113 j s was supported by the max planck institute fur math ematik in bonn and by the grant agency of the czech republic under the grant no p201 12 g028

composition operators from the hardy space to the nth weighted type space on the unit disk and the half plane the boundedness of the composition operator c ff z f f z from the hardy space h p x p 0 where x is the upper half plane p z c imz 0 or the unit disk d z c z 1 in the complex plane c to the nth weighted type space where f is an analytic self map of x is characterized

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

products of volterra type operator and composition operator from h and bloch spaces to zygmund spaces the boundedness and compactness of the products of volterra type operators and composition operators from the space of bounded analytic functions and the bloch space to the zygmund space are discussed in this paper

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

conformally invariant powers of the laplacian q curvature and tractor calculus we describe an elementary algorithm for expressing as explicit formulae in tractor calculus the conformally invariant gjms operators due to c r graham et alia these differential operators have leading part a power of the laplacian conformal tractor calculus is the natural induced bundle calculus associated to the conformal cartan connection applications discussed include standard formulae for these operators in terms of the levi civita connection and its curvature and a direct definition and formula for t branson s so called q curvature which integrates to a global conformal invariant as well as generalisations of the operators and the q curvature among examples the operators of order 4 6 and 8 and the related q curvatures are treated explicitly the algorithm exploits the ambient metric construction of fefferman and graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions this is partly based on 12 where the relationship of the normal standard tractor bundle to the ambient construction is described

finite dimensional control of distributed parameter systems by galerkin approximation of infinite dimensional controllers the galerkin method is presented as a way to develop finite dimensional controllers for linear distributed parameter systems dps the direct approach approximates the open loop dps and then generates the controller from this approximation the indirect approach approximates the infinite dimensional stabilizing controller conditions under which they produce equivalent controllers in the sense of closed loop stability are presented the indirect approach is shown to converge to the stable closed loop system consisting of dps and infinite dimensional controller conditions are presented on the behavior of the galerkin method for the open loop dps which guarantee closed loop stability for large enough finite dimensional approximations

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

products of composition and differentiation operators from zygmund spaces to bloch spaces and bers spaces abstract the boundedness and compactness of the products of differentiation and composition operators from zygmund spaces to bloch spaces and bers spaces are discussed in this paper

on a new integral type operator from the bloch space to bloch type spaces on the unit ball abstract we introduce the following integral type operator on the space h b of all holomorphic functions on the unit ball b c n p g f z 0 1 f t z g t z d t t z b where g h b g 0 0 and is a holomorphic self map of b the boundedness and compactness of the operator from the bloch space b or the little bloch space b 0 to the bloch type space b or the little bloch type space b 0 are characterized in the main results we calculate the essential norm of the operators p g b or b 0 b or b 0 in an elegant way

weighted differentiation composition operators from h and bloch spaces to nth weighted type spaces on the unit disk we characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions the bloch space and the little bloch space to nth weighted type spaces on the unit disk

boundary control of the linearized ginzburg landau model of vortex shedding in this paper we continue the development of state feedback boundary control laws based on the backstepping methodology for the stabilization of unstable parabolic partial differential equations we consider the linearized ginzburg landau equation which models for instance vortex shedding in bluff body flows asymptotic stabilization is achieved by means of boundary control via state feedback in the form of an integral operator the kernel of the operator is shown to be twice continuously differentiable and a series approximation for its solution is given under certain conditions on the parameters of the ginzburg landau equation compatible with vortex shedding modelling on a semi infinite domain the kernel is shown to have compact support resulting in partial state feedback simulations are provided in order to demonstrate the performance of the controller in summary the paper extends previous work in two ways 1 it deals with two coupled partial differential equations and 2 under certain circumstances handles equations defined on a semi infinite domain

on an integral type operator from logarithmic bloch type spaces to mixed norm spaces on the unit ball let h b denote the space of all holomorphic functions on the open unit ball b of c n and email protected h b we characterize the boundedness and compactness of the following integral type operator l gf z email protected 0 1rf tz g tz dtt email protected b where rf is the radial derivative of function f from logarithmic bloch type spaces to mixed norm spaces on the unit ball

weighted radial operator from the mixed norm space to the nth weighted type space on the unit ball abstract the boundedness and compactness of the weighted radial operator from the mixed norm space to the n th weighted type space on the unit ball are characterized

characterizations of composition followed by differentiation between bloch type spaces abstract some results on the boundedness and compactness of composition followed by differentiation between bloch type spaces are refined in this paper

a free boundary problem of a predator prey model with advection in heterogeneous environment this paper is concerned with a system of reaction diffusion advection equations with a free boundary which arises in a predator prey ecological model in heterogeneous environment the evolution of the free boundary problem is discussed precisely we prove a spreading vanishing dichotomy namely both prey and predator either survive and establish themselves successfully in the new environment or they fail to establish and vanishes eventually furthermore when spreading occurs we obtain an upper bound of the asymptotic spreading speed which is smaller than the minimal speed of the corresponding traveling wave problem

exponential stability analysis of sampled data ode pde systems and application to observer design a small gain approach is presented for analyzing exponential stability of a class of dynamical hybrid systems the systems considered in the paper are composed of finite dimensional dynamics represented by a linear ordinary differential equation ode and infinite dimensional dynamics described by a parabolic partial differential equation pde exponential stability is established under conditions involving the maximum allowable sampling period masp this new stability result is shown to be useful in the design of sampled output exponentially convergent observers for linear systems that are described by an ode pde cascade the new stability result also proves to be useful in designing practical approximate observers involving no pdes

distributed fuzzy control design of nonlinear hyperbolic pde systems with application to nonisothermal plug flow reactor this paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first order hyperbolic partial differential equations pdes where the control actuators are continuously distributed in space the goal of this paper is to develop a fuzzy state feedback control design methodology for these systems by employing a combination of pde theory and concepts from takagi sugeno t s fuzzy control first the t s fuzzy hyperbolic pde model is proposed to accurately represent the nonlinear first order hyperbolic pde system subsequently based on the t s fuzzy pde model a lyapunov technique is used to analyze the closed loop exponential stability with a given decay rate then a fuzzy state feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities sdlmis from the resulting stability conditions furthermore utilizing the finite difference approximation method with a backward difference for the spatial derivative a recursive algorithm is presented to solve the sdlmis via the existing lmi optimization techniques finally the developed design methodology is successfully applied to the control of a nonisothermal plug flow reactor

generalized composition operators from f p q s spaces to bloch type spaces abstract let h b denote the space of all holomorphic functions on the unit ball b of c n let be a holomorphic self map of b and g h b such that g 0 0 in this paper we investigate the boundedness and compactness of the generalized composition operator c g f z 0 1 r f tz g tz dt t which map from f p q s and f0 p q s to bloch type space b in the unit ball

stabilization of coupled linear heterodirectional hyperbolic pde ode systems we solve the problem of stabilizing a linear ode having a system of a linearly coupled hyperbolic pdes in the actuating and sensing paths the system is exponentially stabilized by mapping it to a target system with a cascade structure using a volterra transformation

on some integral type operators between a general space and bloch type spaces abstract the boundedness and compactness of the next integral operators p g f z 0 1 f tz g tz dt t and l g f z 0 1 r f tz g tz dt t between f p q s spaces and bloch type spaces on the unit ball of c n are studied among other results we solve some open problems and considerably extend results in the paper li and stevic compactness of riemann stieltjes operators between f p q s and bloch spaces publ math debrecen 72 1 2 2008 111 128

semiholonomic verma modules abstract verma modules arise geometrically through the jets of homogeneous vector bundles we consider in this article the modules that arise from the semiholonomic jets of a homogeneous vector bundle we are particularly concerned with the case of a sphere under mobius transformations in this case there are immediate applications in the theory of conformally invariant differential operators

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

compensating the distributed effect of diffusion and counter convection in multi input and multi output lti systems compensation of infinite dimensional input or sensor dynamics in siso lti systems is achieved using the backstepping method for mimo lti systems with distributed input or sensor dynamics governed by diffusion with counter convection we develop a methodology for constructing control laws and observers that compensate the infinite dimensional actuator or sensor dynamics the explicit construction of the compensators are based on novel transformations which can be considered of backstepping forwarding type of the finite dimensional state of the plant and of the infinite dimensional actuator or sensor states based on these transformations we construct explicit lyapunov functionals which prove exponential stability of the closed loop system or convergence of the estimation error in the case of observer design finally we illustrate the effectiveness of our controller with a numerical example

higher symmetries of the laplacian we identify the symmetry algebra of the laplacian on euclidean space as an explicit quotient of the universal enveloping algebra of the lie algebra of conformal motions we construct analogues of these symmetries on a general conformal manifold

laplacian operators and q curvature on conformally einstein manifolds a new definition of canonical conformal differential operators p k k 1 2 with leading term a kth power of the laplacian is given for conformally einstein manifolds of any signature these act between density bundles and more generally between weighted tractor bundles of any rank by construction these factor into a power of a fundamental laplacian associated to einstein metrics there are natural conformal laplacian operators on density bundles due to graham jenne mason sparling gjms it is shown that on conformally einstein manifolds these agree with the p k operators and hence on einstein manifolds the gjms operators factor into a product of second order laplacian type operators in even dimension n the gjms operators are defined only for 1 k n 2 and so on conformally einstein manifolds the p k give an extension of this family of operators to operators of all even orders for n even and k n 2 the operators p k are each given by a natural formula in terms of an einstein metric but they are not natural conformally invariant operators in the usual sense they are shown to be nevertheless canonical objects on conformally einstein structures there are generalisations of these results to operators between weighted tractor bundles it is shown that on einstein manifolds the branson q curvature is constant and an explicit formula for the constant is given in terms of the scalar curvature as part of development conformally invariant tractor equations equivalent to the conformal killing equation are presented

bernstein gelfand gelfand sequences the bernstein gelfand gelfand sequences extend the complexes of homogeneous vector bundles to curved cartan geometries

fischer decomposition for the symplectic group we prove the fischer decomposition for the space of spinor valued polynomials defined on euclidean space of four fold dimension in terms of irreducible modules for the symplectic group consisting of so called osp 4 2 monogenics

fuzzy observer based control for nonlinear coupled hyperbolic pde ode systems in this work the fuzzy observer based control problem is investigated for a class of nonlinear coupled systems which consists of a hyperbolic partial differential equation pde containing nonlinearities and a nonlinear ordinary differential equation ode the nonlinear coupled system is represented as a takagi sugeno t s fuzzy coupled hyperbolic pde ode model based on the t s fuzzy model a novel lyapunov functional approach is proposed to design a fuzzy observer based control strategy more specifically a fuzzy observer is presented to estimate the state variables of the fuzzy coupled pde ode system with the measurements of the pde and the exponential convergence of the observer error is proved then a fuzzy controller is given utilizing the estimated states as feedback variables and it is proved that the evolution profiles of the pde and the trajectory of the ode in the closed loop fuzzy system converge exponentially to the desired values respectively the sufficient existence conditions of the fuzzy observer based controller are formulated in terms of a set of space differential linear matrix inequalities sdlmis a recursive algorithm based on the finite difference approximation and the linear matrix inequality techniques are provided to solve the sdlmis finally the results are applied to case study of a predator prey system and the simulations are performed to illustrate the effectiveness of the proposed observer based control law

equivariant quantizations for ahs structures abstract we construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles associated to irreducible representations for a so called ahs structure outside of a finite set of critical or resonant weights this procedure gives rise to a quantization which is intrinsic to this geometric structure in particular this provides projectively and conformally equivariant quantizations for arbitrary symbols on general curved projective and conformal structures

products of composition multiplication and radial derivative operators from logarithmic bloch spaces to weighted type spaces on the unit ball abstract let h b denote the space of all holomorphic functions on the unit ball b of c n h b and be a holomorphic self map of b let c m and r denote the composition multiplication and radial derivative operators respectively in this paper we characterize the boundedness and compactness of linear operators induced by products of these operators from logarithmic bloch spaces to weighted type spaces on the unit ball

products of multiplication composition and differentiation operators on weighted bergman spaces abstract let be a holomorphic function on the open unit disk d and a holomorphic self map of d let c m and d denote the composition multiplication and differentiation operator respectively we consider linear operators induced by products of these operators on weighted bergman spaces on d the boundedness is established by using carleson type measures