unknown time varying input delay compensation for uncertain nonlinear systems abstract a tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time varying input delay and additive disturbances a novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval the maximum tolerable error between unknown time varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin the controller development is based on an approach which uses lyapunov krasovskii functionals to analyze the effects of unknown sufficiently slowly time varying input delays a stability analysis is provided to prove ultimate boundedness of the tracking error signals numerical simulation results illustrate the performance of the developed robust controller

approximation orders and shape preserving properties of the multiquadric trigonometric b spline quasi interpolant the purpose of the paper is to derive some properties of the multiquadric trigonometric b spline quasi interpolant firstly the paper captures its approximation orders for high order derivatives based on the error estimate one can choose the shape parameter properly such that the quasi interpolant gives optimal approximations to high order derivatives moreover the approximation orders also show that from the theoretical point of view the considered quasi interpolant can be applied when the approximation of high order derivatives is needed i e numerical solution of some pdes construction of lyapunov function etc secondly the paper derives some shape preserving properties of the quasi interpolant these properties suggest that the quasi interpolant may be used in the geometric modeling cad cam for instance that requires shape preservation finally to illustrate the validity of the results some numerical examples are presented both theoretical and numerical results demonstrate that the quasi interpolant cannot only provide excellent approximations to high order derivatives but also preserve the shapes well

adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature we provide adaptive controllers for curve tracking in the plane under unknown curvatures and control uncertainty which is a central problem in robotics the system dynamics include a nonlinear dependence on the curvature and are coupled with an estimator for the unknown curvature to form the augmented error dynamics we prove input to state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty when the uncertainty is zero this gives tracking of the curve and convergence of the curvature estimate to the unknown curvature our curvature identification result is a significant improvement over earlier results which do not ensure parameter identification or which identify the control gain but not the curvature

generating positive and stable solutions through delayed state feedback for time varying forward complete nonlinear systems with delay in the input a new reduction model approach is proposed it presents three advantages first the corresponding control laws do not include distributed terms second it yields closed loop systems with positive solutions that can be easily derived finally the stabilized systems possess some robustness properties that can be estimated

global adaptive controller for linear systems with unknown input delay in this note a switching type delay adaptive predictor feedback controller is proposed to globally stabilize linear systems with unknown input delay the idea of our method is to take advantage of the robustness of feedback laws to delay estimate error that is sufficiently small we first prove that when the delay estimate is sufficiently close to the true delay there is a lyapunov krasovskii functional that is strictly decreasing and asymptotic regulation is achievable then with the help of the lyapunov krasovskii functional as a supervisor the switching logic plays the role of adjusting the estimated delay online to make it sufficiently close to the true delay the result of this note shows that global adaptive stabilization of linear systems with unknown input delay is achievable with a logic based switching control law

a quasi radial basis functions method for american options pricing abstract based on the idea of quasi interpolation and radial basis functions approximation a fast and accurate numerical method is developed for solving the black scholes equation for valuation of american options prices since the method does not require solving a resultant full matrix the ill conditioning problem resulting from using the radial basis functions as a global interpolant can be avoided the method has been shown to be effective in solving problems with free boundary condition as indicated in the numerical computation for the american option pricing an excellent approximation of the solution as well as the free optimal exercise boundary can be obtained

comment on the letter a new efficient method for calculating perturbation energies using functions which are not quadratically integrable by l skala and j cizek we suggest that the recent numerical integration perturbative approach to bound states as proposed by skala and cizek may be generalized via its renormalizations

non coercive lyapunov functions for infinite dimensional systems abstract we show that the existence of a non coercive lyapunov function is sufficient for uniform global asymptotic stability ugas of infinite dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied for evolution equations in banach spaces with lipschitz continuous nonlinearities these additional assumptions become especially simple the results encompass some recent results on linear switched systems on banach spaces finally we derive new non coercive converse lyapunov theorems and give some examples showing the necessity of our assumptions

a quick perturbative method for schrodinger equations within the framework of perturbation theory we propose firstly an iterative method which may serve as a source of optimal unperturbed solutions in both one and more dimensions it combines the runge kutta and newton algorithm and its efficiency is illustrated on a few quartic oscillators secondly admitting also an arbitrary perturbation of potentials we generalize the existing runge kutta one dimensional rayleigh schrodinger constructions of energies and wavefunctions to more dimensions

a multiquadric quasi interpolation with linear reproducing and preserving monotonicity in this paper we develop a multiquadric mq quasi interpolation which has the properties of linear reproducing and preserving monotonicity moreover we give its approximation error by theoretic analysis and illustrate the effect by means of two examples one of the examples is to approach the linear combination of two sine functions with different frequencies another is to approximate a function with discontinuity from the results of the examples we believe that the present mq quasi interpolation is feasible

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

a relaxed condition for stability of nonlinear observer based controllers we study certainty equivalence design of observer based controllers and present a new stability condition that exploits state dependent convergence properties of observers this result eliminates the conservatism of treating the observer error as an exogeneous disturbance as an application we show that the reduced order variant of the class of observers in automatica 37 2001 9231 preserves global asymptotic stability in a certainty equivalence implementation in another application we study a nonminimum phase system which cannot be stabilized with the existing output feedback designs

global existence of solutions of differential inclusions abstract in this paper we consider sufficient conditions for global existence of solutions to a differential inclusion dx dt f t x assuming existence of local solutions to it by means of lyapunov s second method our theorem includes as special cases s w seah s theorems 1982 j math anal appl 89 648 663

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

input to state stability and inverse optimality of predictor feedback for multi input linear systems for the exact predictor feedback control design recently introduced by tsubakino krstic and oliveira for multi input linear systems with distinct input delays we establish input to state stability with respect to additive plant disturbances as well as robustness to constant multiplicative uncertainties affecting the inputs we also show that the exact predictor feedback controller is inverse optimal with respect to a meaningful differential game problem our proofs capitalize on the availability of a backstepping transformation which is formulated appropriately in a recursive manner an example computed numerically is provided to illustrate the validity of the developed results

numerical integration based on a multilevel quartic quasi interpolation operator quasi interpolation is very important in the study of the scattered data approximation numerical integration and numerical solutions of differential equations in this paper we proposed a multilevel quasi interpolation scheme by using b spline basis functions on quartic spline space moreover the proposed scheme is applied to the numerical integration of two dimensional singular integrals some numerical results with contrast to the existing methods are provided

feedback stabilization of a 1 d linear reaction diffusion equation with delay boundary control the goal of this paper is to design a stabilizing feedback boundary control for a reaction diffusion partial differential equation pde where the boundary control is subject to a constant delay while the equation may be unstable without any control for this system which is equivalent to a parabolic equation coupled with a transport equation a prediction based control is explicitly computed by splitting the infinite dimensional system into two parts a finite dimensional unstable part and a stable infinite dimensional part a finite dimensional delayed controller is computed for the unstable part and it is shown that this controller stabilizes the whole pde the proof is based on an explicit expression of the classical artstein transformation combined with an adequately designed lyapunov function a numerical simulation illustrates the constructive feedback design method

nonlinear predictor feedback for input affine systems with distributed input delays prediction based transformation is applied to control affine systems with distributed input delays transformed system state is calculated as a prediction of the system s future response to the past input with future input set to zero stabilization of the new system leads to lyapunov krasovskii proven stabilization of the original one conditions on the original system are smooth linearly bounded open loop vector field and smooth uniformly bounded input vectors about the transformed system which turns out to be affine in the undelayed input but with input vectors dependent on the input history and system state we assume existence of a linearly bounded stabilizing feedback and quadratically bounded control lyapunov function if all assumptions hold globally then achieved exponential stability is global otherwise local analytical and numerical control design examples are provided

multivariate quasi interpolation schemes for dimension splitting multiquadric in this paper we extend the multilevel univariate quasi interpolation formula proposed in a univariate quasi multiquadric interpolation with better smoothness comput math appl in press to multidimensions using the dimension splitting multiquadric dsmq basis function approach our multivariate scheme is readily preformed on parallel computers we show that the cost of finding the coefficient of the quasi interpolant is 3dn on r d and the work of direct evaluation of the quasi interpolant can be reduced from 11n 2 in 2d and 16n 2 in 3d to 2n a boundary padding technique can be employed to improve accuracy numerical results in 2d and 3d are both given

nonsmooth feedback control of time delay nonlinear systems a dynamic gain based approach this technical note addresses the problem of global control for a class of time delay nonlinear systems under a smoothness condition on the system nonlinearities a delay independent non smooth dynamic state compensator is constructed by developing a dynamic gain based design method with the help of appropriate lyapunov krasovskii functionals it is shown that all the states of the time delay nonlinear system can be regulated to the origin while maintaining boundedness of the closed loop system a benchmark example is given to illustrate the effectiveness of the proposed non smooth feedback controller

numerical solution of one dimensional sine gordon equation using high accuracy multiquadric quasi interpolation abstract in this paper we propose a numerical scheme to solve one dimensional sine gordon equation related to many scientific research topics by using high accuracy multiquadric quasi interpolation we use the derivatives of a multiquadric quasi interpolant to approximate the spatial derivatives and a finite difference to approximate the temporal derivative the advantages of the scheme are that it is meshfree and in each time step only a multiquadric quasi interpolant is employed so that the algorithm is very easy to implement the accuracy of our scheme is demonstrated by some test problems

solving time dependent differential equations by multiquadric trigonometric quasi interpolation multiquadric mq quasi interpolation is a popular method for the numerical solution of differential equations however mq quasi interpolation is not well suited for the equations with periodic solutions this is mainly due to the fact that its kernel the mq function is not a periodic function a reasonable way of overcoming the difficulty is to use a quasi interpolant whose kernel itself is also periodic in these cases the paper constructs such a quasi interpolant error estimates of the quasi interpolant are also provided the quasi interpolant possesses many fair properties of the mq quasi interpolant i e simplicity efficiency stability etc moreover it is more suitable than the mq quasi interpolant for periodic problems since the quasi interpolant as well as its derivatives are periodic examples of solving both linear and nonlinear partial differential equations whose solutions are periodic by the quasi interpolant and the mq quasi interpolant are compared at the end of the paper numerical results show that the quasi interpolant outperforms the mq quasi interpolant for periodic problems

delay adaptive control for nonlinear systems we present a systematic delay adaptive prediction based control design for nonlinear systems with unknown long actuator delay our approach is based on the representation of the constant actuator delay as a transport partial differential equation pde in which the convective speed is inversely proportional to the unknown delay we study two different frameworks assuming first that the actuator state is measured and relaxing afterward for the full state feedback case we prove global asymptotic convergence of the proposed adaptive controller while in the second case replacing the actuator state by its adaptive estimate we prove local regulation the relevance of the obtained results are illustrated by simulations of a biological activator repressor system

a univariate quasi multiquadric interpolationwith better smoothness in this paper we propose a multilevel univariate quasi interpolation scheme usingmultiquadric basis it is practical as it does not require derivative values of the function being interpolated it has a higher degree of smoothness than the original level 0 formula as it allows a shape parameter c o h our level 1 quasi interpolation costs o email protected n flops to set up it preserves strict convexity and monotonicity when c o h we prove the proposed scheme converges with a rate of o h 2 email protected h furthermore if both a and are relatively small compared with email protected the convergence rate will increase we verify numerically that c h is a good shape parameter to use for our method hence we need not find the optimal parameter for all test functions both convergence speed and error are optimized for c between 0 5h and 1 5h our method can be generalized to a multilevel scheme we include the numerical results for the level 2 scheme the shape parameter of the level 2 scheme can be chosen between 2h to 3h

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

comments on a new efficient method for calculating perturbation energies using functions which are not quadratically integrable the recently proposed method of calculating perturbation energies using a non normalizable wavefunction by skala and cizek is analysed and rigorously proved

a new efficient method for calculating perturbative energies using functions which are not square integrable regularization and justification the method recently proposed by skala and cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent even though this ratio comes out finite and gives the correct perturbation energies the calculational process must be regularized to be justified we examine one possible method of regularization and show that the proposed method gives traditional quantum mechanical results

perturbation theory using functions that are not quadratically integrable in previous work 0305 4470 29 19 031 skala l and cizek j 1996 j phys a math gen 29 l129 1996 j phys a math gen 29 6467 a new method of calculating perturbation energies for one dimensional problems based on the linear dependence of the perturbation wavefunctions on the perturbation energies has been suggested it is shown in this letter that this method can be extended to multi dimensional problems and the linearity can be used not only at a boundary point but also at an arbitrary point inside the integration region degenerate eigenvalues are also discussed the resulting perturbation theory is very simple and can be used at large orders

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs

multilevel compact radial functions based computational schemes for some elliptic problems abstract compactly supported radial basis functions cs rbfs have been recently introduced in the context of the dual reciprocity method as a possible cure of dense matrices and ill conditioning problems when using the classical radial basis functions however the support scaling factor and slow convergence rate of the cs rbfs have also raised issues on the effectiveness of the cs rbfs in this paper two multilevel schemes have been proposed to alleviate these problems

numerical solution of nonlinear burgers equation using high accuracy multi quadric quasi interpolation in this paper a numerical method is presented to approximate the solution to nonlinear burgers equation which is related to many scientific research topics a numerical scheme by using high accuracy multi quadric quasi interpolation is presented in which a kind of multi quadric quasi interpolant is used to approximate the derivatives of the solution in spatial domain and finite difference is used to approximate the derivatives of the solution in temporal domain the advantage of the scheme is that it is mesh free and in each time step only a multi quadric quasi interpolant is employed so that the algorithm is easy to implement the numerical results of this scheme are also shown and compared with other numerical schemes

stabilization of discrete time linear systems with an unknown time varying delay by switched low gain feedback in this note we investigate the stabilization of discrete time linear systems with an unknown time varying delay existing literature on the stabilization of time delay systems require some knowledge such as an upper bound of the delay in this paper by proposing a switched low gain feedback control law we are able to achieve asymptotic stabilization of the system without any knowledge of the delay in addition the proposed switched low gain feedback law also significantly improves the closed loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design simulation study illustrates the effectiveness of our theoretical results

a shape preserving quasi interpolation operator satisfying quadratic polynomial reproduction property to scattered data abstract in this paper we construct a univariate quasi interpolation operator to non uniformly distributed data by cubic multiquadric functions this operator is practical as it does not require derivatives of the being approximated function at endpoints furthermore it possesses univariate quadratic polynomial reproduction property strict convexity preserving and shape preserving of order 3 properties and a higher convergence rate finally some numerical experiments are shown to compare the approximation capacity of our quasi interpolation operator with that of wu and schaback s quasi interpolation scheme

multistep scattered data interpolation using compactly supported radial basis functions a hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support a nested sequence of subsets of the data is computed efficiently using successive delaunay triangulations the scale of the basis function at each level is determined from the current density of the points using information from the triangulation the method is rotationally invariant and has good reproduction properties moreover the solution can be calculated and evaluated in acceptable computing time

the strong coupling expansion for anharmonic oscillators we accurately calculate the strong coupling expansion for anharmonic oscillators by means of a robust and stable numerical algorithm the method applies to any state and to any anharmonicity degree by means of the perturbation coefficients we estimate the location of the branch points that determine the convergence radius of the strong coupling expansion

observation and stabilization of ltv systems with time varying measurement delay abstract this work deals with observer based output feedback stabilization of linear time varying ltv systems with time varying measurement delay the delay is modeled by a first order hyperbolic partial differential equation pde whose boundary condition evolves according to an ordinary differential equation ode namely the plant the overall system is thus represented by an ode pde cascade which is also the structure of the proposed observer the exponential stability of the estimation error is established for arbitrarily large time varying delays an observer based controller is also introduced and the closed loop stability is proved the separation principle holds and the design of both the observer and controller gains can be done as if there was no delay some simulations illustrate the feasibility of this approach

adaptive sinusoidal disturbance cancellation for unknown lti systems despite input delay solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays in this paper two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time invariant system in controllable canonical form despite input delay the design is based on three steps 1 parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters 2 representation of the delay as a transport pde 3 design of the adaptive controller by using the backstepping boundary control technique for pdes it is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t with perfect disturbance estimation the effectiveness of the controller is illustrated with a simulation example of a second order system

reply to comments on a new efficient method for calculating perturbation energies using functions which are not quadratically integrable in a previous paper sk la and c zek 1996 a new approach to calculating perturbation energies of bound states based on the use of functions which are not quadratically integrable was suggested this method has been analysed in a comment by guardiola and ros 1996 the present comment is the reply to this previous comment the aim is to give a simple and straightforward proof of the method and clarify some other points important for its application

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

large order behaviour of the strong coupling perturbation expansion for anharmonic oscillators a new formula describing the large order behaviour of the strong coupling perturbation coefficients for the anharmonic oscillators with the hamiltonian is suggested a new method for the accurate calculation of the square root branch points of the energy from the numerical values of the coefficients is also suggested the branch points and the related minimal values of the coupling constant for which the expansion converges are calculated for the ground state of the quartic sextic octic and decadic oscillators

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

a new efficient method for calculating perturbation energies using functions which are not quadratically integrable a new approach to calculating perturbation energies of bound states based on the use of functions which are not quadratically integrable is suggested the key to the method is one simple property of the perturbation equations which to our knowledge has not been noticed until know the use of the resolvent in this method is avoided and the energy spectrum of the unperturbed hamiltonian is not needed in the calculation the resulting method is very simple and straightforward and gives very accurate eigenvalues and wavefunctions

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

a kind of multiquadric quasi interpolation operator satisfying any degree polynomial reproduction property to scattered data in this paper by virtue of using the linear combinations of the shifts of f x to approximate the derivatives of f x and waldron s superposition idea 2009 we modify a multiquadric quasi interpolation with the property of linear reproducing to scattered data on one dimensional space such that a kind of quasi interpolation operator l r 1f has the property of r 1 email protected z r 0 degree polynomial reproducing and converges up to a rate of r 2 there is no demand for the derivatives of f in the proposed quasi interpolation l r 1f so it does not increase the orders of smoothness of f finally some numerical experiments are shown to compare the approximation capacity of our quasi interpolation operators with that of wu schaback s quasi interpolation scheme and feng li s quasi interpolation scheme

upper and lower bounds of the ground state energy of anharmonic oscillators using renormalized inner projection renormalization is a method often used to approximate the eigenvalues of a hamiltonian that cannot be solved exactly it consists of splitting the hamiltonian into a solvable part and a remainder which is then minimized the inner projection technique first introduced by lowdin in the sixties was developed to bracket the eigenvalues between lower and upper bounds combining renormalization and lowdin s inner projection yielded the so called renormalized inner projection technique in this study this method will be applied to the quartic sextic and octic anharmonic oscillators lower and upper energy bounds are obtained for finite values of the coupling constant as well as for the infinite case the relation between the renormalized inner projection and perturbation theory will also be discussed another feature of this study is the importance of symbolic computation in allowing us to manipulate expressions with unevaluated parameters and to perform calculations in rational arithmetics or high decimal precision thus lowdin s rational approximants can be expressed explicitly as rational fractions in terms of the coupling constant and values for the limit constant can be obtained with amazing high accuracy namely 62 33 and 21 decimal places for the quartic sextic and octic oscillator respectively

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy

a kind of improved univariate multiquadric quasi interpolation operators in this paper a kind of improved univariate multiquadric quasi interpolation operators is proposed by using hermite interpolating polynomials error analysis shows that the convergence rate of the operators depends heavily on the shape parameter c which indicates that our operators could provide the desired smoothness and precision by choosing a suitable value of c numerical examples show that the operators provide a high degree of accuracy moreover operators are applied to the fitting of discrete solutions of initial value problems