exact boundary controllability of vibrating non classical euler bernoulli micro scale beams abstract this study investigates the exact controllability problem for a vibrating non classical euler bernoulli micro beam whose governing partial differential equation pde of motion is derived based on the non classical continuum mechanics in this paper it is proved that via boundary controls it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time this control objective is achieved based on the pde model of the system which causes that spillover instabilities do not occur

fredholm transform and local rapid stabilization for a kuramoto sivashinsky equation this paper is devoted to the study of the local rapid exponential stabilization problem for a controlled kuramoto sivashinsky equation on a bounded interval we build a feedback control law to force the solution of the closed loop system to decay exponentially to zero with arbitrarily prescribed decay rates provided that the initial datum is small enough our approach uses a method we introduced for the rapid stabilization of a korteweg de vries equation it relies on the construction of a suitable integral transform and can be applied to many other equations

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

disturbance estimator based output feedback exponential stabilization for euler bernoulli beam equation with boundary control in this paper we are concerned with the output feedback exponential stabilization problem for a system plant described by a one dimensional euler bernoulli beam equation the measurements are only the displacement and the angular velocity at the right end an infinite dimensional estimator is designed to estimate the disturbance with the estimated disturbance we propose a state observer that is exponentially convergent to the original system then design two different kinds of stabilizing controllers one is based on the velocity feedback the other is based on the angular velocity feedback in both cases by adopting the riesz basis approach the exponential stability of the closed loop systems is built with guaranteeing that all internal systems are uniformly bounded the numerical experiments are carried out to illustrate the theoretical results

geometry of w algebras from the affine lie algebra point of view to classify the classical field theories with w symmetry one has to classify the symplectic leaves of the corresponding w algebra which are the intersection of the defining constraint and the coadjoint orbit of the affine lie algebra if the w algebra in question is obtained by reducing a wess zumino novikov witten wznw model the fields that survive the reduction will obey nonlinear poisson bracket or commutator relations in general for example the toda models are well known theories which possess such a nonlinear w symmetry and many features of these models can only be understood if one investigates the reduction procedure in this paper we analyse the sl n case from which the so called wn algebras can be obtained one advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the w algebra for the n 2 case corresponding to the coadjoint orbits of the virasoro algebra and for the n 3 case which gives rise to the zamolodchikov algebra our method in principle is capable of constructing explicit representatives on each leaf another attractive feature of this approach is the fact that the global nature of the w transformations can be explicitly described the reduction method also enables one to determine the classical highest weight hw states which are the stable minima of the energy on a w leaf these are important as only to those leaves can a hw representation space of the w algebra be associated which contains a classical hw state

stability of the rosenbrock methods for the neutral delay differential algebraic equations this paper develops the rosenbrock methods for the neutral delay differential algebraic equations nddaes and proves that the rosenbrock methods equipped with suitable interpolation are gp stable under proper assumption for the linear neutral delay differential algebraic equations with constant coefficients furthermore the gp stability of the runge kutta methods is also considered the discussions are supported by the numerical experiments

on spectrum and riesz basis assignment of infinite dimensional linear systems by bounded linear feedbacks this paper deals with spectrum and riesz basis assignability of infinite dimensional linear systems via bounded linear feedbacks the necessary and sufficient condition of sun siam j control optim 19 1981 pp 730 743 is generalized to a large class of boundary control systems two typical examples are presented to illustrate the application of our results the results obtained in this paper may have potential applications in nondissipative spectral systems

stabilization and gevrey regularity of a schrodinger equation in boundary feedback with a heat equation we study stability of a schrodinger equation with a collocated boundary feedback compensator in the form of a heat equation with a collocated input output pair remarkably exponential stability is achieved for both positive and negative gains namely as long as the gain is non zero we show that the spectrum of the closed loop system consists only of two branches along two parabolas which are asymptotically symmetric relative to the line re im the 135 line in the second quadrant the asymptotic expressions of both eigenvalues and eigenfunctions are obtained the riesz basis property and exponential stability of the system are then proved finally we show that the semigroup generated by the system operator is of gevrey class 2 a numerical computation is presented for the distributions of the spectrum of the closed loop system

exponential stability for a class of boundary conditions on a euler bernoulli beam subject to disturbances via boundary control abstract this paper outlines the procedure for applying a sliding mode backstepping boundary control technique to a euler bernoulli beam subject to unknown bounded disturbances on the boundary for four different types of boundary conditions referred to in this paper as a class of boundary conditions these boundary conditions include all combinations of pinned and sliding types with control and disturbances on one boundary i e pinned pinned pinned sliding sliding pinned and sliding sliding with input on the second boundary the technique was developed for the specific case of a pinned pinned beam in the literature and in this paper the technique is generalized to the degree that it is possible to cover all four of the aforementioned cases furthermore a proof of the fully arbitrary exponential stability of the closed loop system is provided in this paper to this point only asymptotic stability was shown for the closed loop system for one case the technique outlined in this paper provides for a class of boundary conditions a controller that exponentially stabilizes the vibrations in a beam in the presence of bounded unknown disturbances the beam displacement returns to the origin and its decay is bounded by a known exponential decay function after a known finite time reaching phase

the gpl stability of rosenbrock methods for delay differential equation this paper deals with the stability analysis of the rosenbrock method for the numerical solution of delay differential equation the stability behavior of rosenbrock method is analyzed for the solutions of linear test equation we will give that the rosenbrock method is gpl stable if and only if it is l stable

vibration control of an euler bernoulli beam under unknown spatiotemporally varying disturbance in this article the vibration suppression of an euler bernoulli beam system is considered by using the adaptive boundary control technique the dynamics of the beam are represented by a partial differential equation and four ordinary differential equations involving functions of both space and time by using lyapunov synthesis the robust boundary control with a disturbance observer is first proposed to suppress the vibration and attenuate the effect of the external disturbances to compensate for both the system parametric uncertainties and the disturbances uncertainties the adaptive boundary control is developed with the proposed boundary control the state of the beam system is proven to be uniformly ultimately bounded and converge to a small neighbourhood of zero by appropriately choosing the design parameters the effectiveness of the proposed control is successfully verified by numerical simulations

rapid boundary stabilization of linear distributed systems we prove that under rather general assumptions an exactly controllable problem is uniformly stabilizable with arbitrarily prescribed decay rates our approach is direct and constructive and avoids many of the technical difficulties associated with the usual methods based on riccati equations we give several applications for the wave equation and for petrovsky systems

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

rapid exponential feedback stabilization with unbounded control operators we study the wellposedness and the main features of a class of feedback control systems the involved control system is composed of the generator of a strongly continuous group for the free part and of an unbounded control operator so that the results can be applied to boundary or point control problems for partial differential equations of hyperbolic or petrowski type the feedback operator is explicit and one can achieve an arbitrary large decay rate for the closed loop system these results are proved under a controllability assumption and the proofs rely on general results about the algebraic riccati equation associated with the linear quadratic regulator problem

output feedback stabilization of a one dimensional schrodinger equation by boundary observation with time delay in this article we are concerned with the stabilization of a 1 d schrodinger equation with boundary control and observation the boundary observation is suffered from an arbitrary given time delay we first show that the proportional output feedback control that stabilizes exponentially the time delay free system can not stabilize the corresponding time delay system anymore we then use the observer and predictor to solve the stabilization problem of time delay system the state is estimated in the time span where the observation is available and the state is predicted in the time interval when the observation is not available it is shown that the estimated state feedback stabilizes exponentially the time delay system the numerical simulation is presented to illustrate the effect of the stabilizing controller

riesz basis approach to the stabilization of a flexible beam with a tip mass using an abstract condition of riesz basis generation of discrete operators in the hilbert spaces we show in this paper that a sequence of generalized eigenfunctions of an euler bernoulli beam equation with a tip mass under boundary linear feedback control forms a riesz basis for the state hilbert space in the meanwhile an asymptotic expression of eigenvalues and the exponential stability are readily obtained the main results of siam j control optim 36 1998 pp 1962 1986 are concluded as a special case and the additional conditions imposed there are removed

lyapunov approach to output feedback stabilization for the euler bernoulli beam equation with boundary input disturbance we propose a boundary output feedback control law for a one dimensional euler bernoulli beam equation with general external disturbance entering the control end a galerkin approximation scheme is constructed to show the existence of solution to the closed loop system the exponential stability of the closed loop system is obtained by the lyapunov functional method numerical simulations are presented for illustration

well posedness of boundary control systems continuity of the input output map for boundary control systems is shown through the system transfer function our approach transforms the question of continuity of the input output map of a boundary control system to uniform boundedness of the solution to a related elliptic problem this is shown for a class of boundary control systems with dirichlet neumann or robin boundary control

rapid stabilisation of an euler bernoulli beam with the internal delay control in this paper we are concerned with rapid stabilisation of an euler bernoulli beam with internal delayed control herein we introduce a new approach of the feedback control design from the system

spectral assignability for distributed parameter systems with unbounded scalar control this article studies a class of control systems in a hilbert space h given dot x t ax t bu t where a generates a holomorphic semigroup on h u t is a scalar control and the control input b is possibly unbounded many systems with boundary or point control can be represented in this form the author considers the question of what eigenvalues alpha k k in i the closed loop system can have when u t is a feedback control shun hua sun s condition on alpha k k in i siam j control optim 19 1981 pp 730 743 is generalized to the case where b is unbounded but satisfies an admissibility criterion this condition is generalized further when unbounded feedback elements are allowed these results are applied to a structurally damped elastic beam with a single point actuator similar techniques also prove a spectral assignability result for a damped elastic beam with a moment control force at one end even though the associated input element is not admissible in

arbitrary decay rate for euler bernoulli beam by backstepping boundary feedback we consider a problem of stabilization of the euler bernoulli beam the beam is controlled at one end using position and moment actuators and has the ldquoslidingrdquo boundary condition at the opposite end we design the controllers that achieve any prescribed decay rate of the closed loop system removing a long standing limitation of classical ldquoboundary damperrdquo controllers the idea of the control design is to use the well known representation of the euler bernoulli beam model through the schrodinger equation and then adapt recently developed backstepping designs for the latter in order to stabilize the beam we derive the explicit integral transformation and its inverse of the closed loop system into an exponentially stable target system the transformation is of a novel volterra fredholm type the design is illustrated with simulations

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

coadjoint orbits of the virasoro group the coadjoint orbits of the virasoro group which have been investigated by lazutkin and pankratova and by segal should according to the kirillov kostant theory be related to the unitary representations of the virasoro group in this paper the classification of orbits is reconsidered with an explicit description of the possible centralizers of coadjoint orbits the possible orbits are diff s1 itself diff s1 s1 and diff s1 sl n 2 r withsl n 2 r a certain discrete series of embeddings ofsl 2 r in diff s1 and diffs1 t wheret may be any of certain rather special one parameter subgroups of diffs1 an attempt is made to clarify the relation between orbits and representations it appears that quantization of diffs1 s1 is related to unitary representations with nondegenerate kac determinant unitary verma modules while quantization of diffs1 sl n 2 r is seemingly related to unitary representations with null vectors in leveln a better understanding of how to quantize the relevant orbits might lead to a better geometrical understanding of virasoro representation theory in the process of investigating virasoro coadjoint orbits we observe the existence of left invariant symplectic structures on the virasoro group manifold as is described in an appendix these give rise to lie bialgebra structures with the virasoro algebra as the underlying lie algebra

the numerical solution of delay differential algebraic equations of retarded and neutral type in this paper we consider the numerical solution of initial value delay differential algebraic equations ddaes of retarded and neutral types with a structure corresponding to that of hessenberg daes we give conditions under which the ddae is well conditioned and show how the ddae is related to an underlying retarded or neutral delay ordinary differential equation dode we present convergence results for linear multistep and runge kutta methods applied to ddaes of index 1 and 2 and show how higher index hessenberg ddaes can be formulated in as stable a way as index 2 hessenberg ddaes we also comment on some practical aspects of the numerical solution of these problems

classical a n w geometry by analyzing theextrinsic geometry of two dimensional surfaces chirally embedded incp n thecp n w surface 1 we give exact treatments in various aspects of the classical w geometry in the conformal gauge first the basis of tangent and normal vectors are defined at regular points of the surface such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the conformal a n toda lax pair since the latter is known to be intrinsically related with the w symmetries this gives the geometrical meaning of thea n w algebra second w surfaces are put in one to one correspondence with solutions of the conformally reduced wznw model which is such that the toda fields give the cartan part in the gauss decomposition of its solutions third the additional variables of the toda hierarchy are used as coordinates ofcp n this allows us to show that w transformations may be extended as particular diffeomorphisms of this target space higher dimensional generalizations of the wznw equations are derived and related with the zakharov shabat equations of the toda hierarchy fourth singular points are studied from a global viewpoint using our earlier observation 1 that w surfaces may be regarded as instantons the global indices of the w geometry which are written in terms of the toda fields are shown to be the instanton numbers for associated mappings of w surfaces into the grassmannians the relation with the singularities of w surface is derived by combining the toda equations with the gauss bonnet theorem

stabilization of a system of n 1 coupled first order hyperbolic linear pdes with a single boundary input we solve the problem of stabilization of a class of linear first order hyperbolic systems featuring n rightward convecting transport pdes and one leftward convecting transport pde we design a controller which requires a single control input applied on the leftward convecting pde s right boundary and an observer which employs a single sensor on the same pde s left boundary we prove exponential stability of the origin of the resulting plant observer controller system in the spatial l2 sense

exponential decay of energy of the euler bernoulli beam with locally distributed kelvin voigt damping in this paper we consider the longitudinal and transversal vibrations of the euler bernoulli beam with kelvin voigt damping distributed locally on any subinterval of the region occupied by the beam we prove that the semigroup associated with the equation for the transversal motion of the beam is exponentially stable although the semigroup associated with the equation for the longitudinal motion of the beam is not exponentially stable due to the locally distributed and unbounded nature of the damping we use a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent we also show that the associated semigroups are not analytic

absolute stability of the kirchhoff string with sector boundary control this paper addresses the stability problem of the nonlinear kirchhoff string with nonlinear boundary control the nonlinear boundary control is the negative feedback of the transverse velocity of the string at one end which satisfies a sector constraint employing the integral type multiplier method we establish explicit absolute exponential stability of the kirchhoff string system

the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli beam equation with boundary input disturbance in this paper we are concerned with the boundary feedback stabilization of a one dimensional euler bernoulli beam equation with the external disturbance flowing to the control end the active disturbance rejection control adrc and sliding mode control smc are adopted in investigation by the adrc approach the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed loop it is shown that the external disturbance can be attenuated in the sense that the resulting closed loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity in the second part we use the smc to reject the disturbance by removing the condition in adrc that the derivative of the disturbance is supposed to be bounded the existence and uniqueness of the solution for the closed loop via smc are proved and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system the numerical simulations validate the effectiveness of both methods

characters and fusion rules for w algebras via quantized drinfeld sokolov reduction using the cohomological approach tow algebras we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the quantized drinfeld sokolov reduction

backstepping approach to the arbitrary decay rate for euler bernoulli beam under boundary feedback in this article we are concerned with the boundary stabilisation of the euler bernoulli beam equation for which all eigenvalues of the control free system are located on the imaginary axis of the complex plane the fourth order system in spacial variable is transformed into a coupled heat like system this enables us to make a natural backstepping transformation in vector form to transform the system into a target system which has arbitrary decay rate the state feedback is thus designed it is shown that the original closed loop system is exponentially stable with the given arbitrary decay rate

riesz basis property and exponential stability of controlled euler bernoulli beam equations with variable coefficients this paper studies the basis property and the stability of a distributed system described by a nonuniform euler bernoulli beam equation under linear boundary feedback control it is shown that there is a sequence of generalized eigenfunctions of the system which forms a riesz basis for the state hilbert space the asymptotic distribution of eigenvalues the spectrum determined growth condition and the exponential stability are concluded the results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam

sliding mode boundary control of an euler bernoulli beam subject to disturbances in this paper a control technique is presented for an undamped pinned pinned euler bernoulli beam with control inputs and bounded disturbances on one boundary the control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances this is achieved in two main steps first a backstepping transformation is used to convert the marginally stable euler bernoulli beam system to a new form that has an exponentially stable homogeneous form control inputs are needed to fully convert the system to this form however since they are distorted by unknown bounded disturbances the next step implements a sliding mode controller to account for them the proposed sliding manifolds require a combination of classical and second order techniques in order to avoid discontinuous chattering on the physical system therefore the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate and do so in the presence of unknown bounded disturbances on the boundary the main contributions of this paper with respect to previous backstepping designs for the euler bernoulli beam are that all three of the following goals are accomplished together i steady state position is the origin ii decay rate has no theoretical restrictions and iii is robust to bounded disturbances

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

brief paper arbitrary decay rate for two connected strings with joint anti damping by boundary output feedback in this paper we are concerned with the boundary stabilization of two connected strings with middle joint anti damping for which all eigenvalues of the control free system are located on the right complex plane we first design an explicit state feedback controller to achieve exponential stability for the closed loop system consequently we design the output feedback by using infinite dimensional observer the backstepping approach is adopted in investigation it is shown that by using one boundary stabilizer only the output feedback can make the closed loop system exponentially stable with arbitrary decay rate

exponentially stabilizing fuzzy controller design for a nonlinear ode beam cascaded system and its application to flexible air breathing hypersonic vehicle abstract this paper addresses fuzzy control design for a class of nonlinear systems which are described by nonlinear ordinary differential equations odes cascaded with an euler bernoulli beam ebb equation two design difficulties are involved in the control design addressed in this paper the first one is caused by the ebb equation whose spatiotemporal dynamics is affected by the output of the nonlinear ode subsystem through its differential equation rather than boundary conditions a state differential transformation is introduced for the ebb equation to bring the output of the ode subsystem in the differential equation to its boundary conditions the second one comes from the nonlinear ode subsystem to overcome this difficulty it is assumed that an exact takagi sugeno t s fuzzy ode model is utilized by the sector nonlinearity approach to describe the dynamics of nonlinear ode subsystem based on the t s fuzzy model a composite lyapunov function is constructed to develop a fuzzy controller via the ode state feedback and boundary feedback of transformed ebb equation to exponentially stabilize the nonlinear ode ebb cascaded system the design procedure is presented in terms of bilinear matrix inequalities bmis moreover a simple design method is also provided in terms of linear matrix inequalities lmis from the obtained design procedure finally numerical simulations on flight control with vibration suppression of a flexible air breathing hypersonic vehicle are given to illustrate the effectiveness of the proposed design method

disturbance estimator and servomechanism based performance output tracking for a 1 d euler bernoulli beam equation in this paper we consider performance output tracking for a one dimensional euler bernoulli beam equation with boundary moment control and unmatched internal uncertainty and external disturbance for such system the reference feng and guo 2017 firstly studied the active disturbance rejection control adrc problem we design an infinite dimensional disturbance estimator to estimate the total disturbance internal uncertainty and external disturbance and the system state simultaneously a servomechanism generated by the reference signal is designed based on the estimated total disturbance we design an output feedback control law such that the performance output signal tracks the reference signal and all the signals of closed loop system are bounded some illustrative simulations are presented