stabilization of an axially moving web via regulation of axial velocity in this paper a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented the principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly the optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method the galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations odes for control design purposes these odes are rewritten into state space equations the vibration energy of the axially moving beam is represented by the quadratic form of the state variables in the optimal control problem the cost function modified from the vibration energy function is subjected to the constraints on the state variables and the axial transport velocity is considered as a control input numerical simulations are performed to confirm the effectiveness of the proposed control algorithm

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

oscillatory and asymptotic behavior of certain functional differential equations some new criteria for the oscillatory and asymptotic behavior of odd order functional equations of the form x n t p t x n 1 t q t f x g t are established

stabilization and disturbance rejection for the beam equation we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is a proper rational function of the complex variable and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis provided that the residues corresponding to these poles are nonnegative the rest of the transfer function is required to be a strictly positive real function we then show that depending on the location of the pole on the imaginary axis the closed loop system is asymptotically stable we also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately we also present some numerical simulation results which support this argument

oscillations in a class of difference equations a class of linear difference equations is considered and a necessary and sufficient condition for the oscillation of solutions is established this condition is referred to the roots of the associated characteristic equation

asymptotic stabilization of a nonlinear axially moving string by adaptive boundary control in this paper a robust adaptive boundary control for an axially moving string that shows nonlinear behavior resulting from spatially varying tension is investigated a hydraulic actuator equipped with a damper is used as the control actuator at the right boundary of the string the lyapunov redesign method is employed to derive a robust control algorithm employing adaptation laws that estimate three unknown system parameters mass per unit length of string lumped mass of hydraulic actuator and damping coefficient of damper and an unknown boundary disturbance the uniform asymptotic stability when the three parameters are all unknown the exponential stability when they are known and the uniform ultimate boundedness with a bounded boundary disturbance of the closed loop system are investigated the convergence of the parameter estimates to the true values is shown numerical simulations are performed to demonstrate the effectiveness of the proposed robust adaptive boundary control

boundary control design for extensible marine risers in three dimensional space abstract a design of boundary controllers is proposed for practical exponential stabilization of extensible marine risers in three dimensional 3d space under sea loads the design removes flaws in existing works two lyapunov type theorems are developed for study of existence and uniqueness and stability of nonlinear evolution systems in hilbert space these theorems have their potential use in control design and stability analysis for flexible systems including marine risers

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

oscillation theorems for certain functional differential equations abstract some new criteria for the oscillation of functional differential equations with a middle term of the form x n t p t x n 1 t h h t x g t are presented

robust boundary control of an axially moving string by using a pr transfer function in this note a scheme for the vibration suppression of a translating string using a positive real pr transfer function is investigated the transverse vibration of the string is controlled by hydraulic touch rolls located at the right end of the string the mathematical model of the system which consists of a hyperbolic partial differential equation pde describing the dynamics of the moving string and an ordinary differential equation ode for the actuator dynamics is derived by using hamilton s principle for translating continua the transfer function of the proposed boundary controller is a nonproper but pr function the asymptotic stability of the closed loop system in the presence of output disturbance is proved

oscillation theorems for forced neutral difference equations abstract some oscillation criteria are established for forced neutral difference equations of the form x n px n k q n x n f n and 2 x n px n k q n x n f n the results remain valid even when f n 0

a second order nonlinear difference equation oscillation and asymptotic behavior discrete analogues are investigated for well known results on oscillation growth and asymptotic behavior of solutions of y q t y 0 for q t 0 and for q t 0 the analogue of atkinson s oscillation criterion is shown to be true for 2yn 1 qn yn 0 but the analogue for atkinson s nonoscillation criterion is shown to be false

explicit conditions for the oscillation of difference equations we obtain sufficient conditions for the oscillation of all solutions of the difference equation an 1 an i 1mpian ki 0 n 0 1 2 where the pi s are real numbers and the ki s are integers the conditions are given explicitly in terms of the pi s and the ki s

adaptive vibration isolation for axially moving strings theory and experiment high speed transport of continuous materials such as belts webs filaments or bands can cause unwanted vibration vibration control for these systems often focuses on restricting the response resulting from external disturbances e g support roller eccentricity or aerodynamic excitation to areas not requiring high precision positioning this paper introduces vibration controllers for an axially moving string system consisting of a controlled span coupled to a disturbed span via an actuator the system model includes a partial differential equation for the two spans and an ordinary differential equation for the actuator exact model knowledge and adaptive isolation controllers based on lyapunov theory regulate the controlled span from bounded disturbances in the adjacent uncontrolled span assuming distributed damping in the uncontrolled span the exact model knowledge and adaptive controllers exponentially and asymptotically drive the controlled span displacement to zero respectively while ensuring bounded uncontrolled span displacement and control force experiments demonstrate the effectiveness of the proposed controller in isolating the controlled span from disturbances and damping the controlled span displacement

robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension in this paper a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated the lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension the axially moving string system is divided into two spans i e a controlled span and an uncontrolled span by a hydraulic touch roll actuator which is located in the middle section of the string the transverse vibration of the controlled span part of the string is controlled by the hydraulic touch roll actuator and the position of the actuator is considered as the right boundary of the controlled span part the mathematical model of the system which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics is derived by using the hamilton s principle the lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part the asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory simulation results verify the effectiveness of the robust adaptive boundary controller proposed

adaptive output feedback stabilisation for wave equations with dynamic boundary condition and corrupted boundary measurement this paper is devoted to the output feedback stabilisation for a class of wave equations remarkably only one boundary measurement corrupted by disturbance is available for feedback and the bound

oscillation theorems for certain neutral functional differential equations in this paper we shall offer sufficient conditions for the oscillation of all solutions to neutral functional differential equations of mixed type of the form dndtn x t ax t bx t q t x t g p t x t h 0 1 here p and q are periodic functions

oscillation theorems for second order neutral difference equations abstract oscillation criteria for the second order difference equations of the form 2xn qnf xn r 0 and the neutral difference equation 2 xn pxn k qnf xn r 0 are established here xn xn 1 xn is the forward difference operator 1 p is a real number and k are nonnegative integers qn is a sequence of nonnegtive real numbers and f r r is continuous

some iterative methods for finding fixed points and for solving constrained convex minimization problems the present paper is divided into two parts in the first part we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real hilbert space we establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping such a fixed point is also a solution of a variational inequality defined on the set of fixed points in the second part we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping the results of this paper extend and improve several results presented in the literature in the recent past