time discretization of an integro differential equation of parabolic type the stability and convergence properties of two time discretizations of an integro differential equation of parabolic type are studied the methods reduce to the backward euler and crank nicolson methods if the integral term is absent the integral term is approximated in each case by a quadrature rule with relatively high order truncation error so that a relatively large time step can be used for the quadrature in order to reduce the memory and computational requirements of the method

a robust algorithm for random parameter tracking an algorithm for tracking time varying parameters is studied it is shown to be exponentially stable independently of the choice of algorithm parameters we derive some useful nonasymptotic estimates for the tracking error and develop the asymptotically optimal version of the method

unconditionally stable numerical method for a nonlinear partial integro differential equation the paper presents an unconditionally stable numerical scheme to solve a nonlinear integro differential equation which arises in mathematical modeling of the penetration of a magnetic field into a substance if the temperature is kept constant throughout the material numerical scheme comprises of the galerkin finite element method jangveladze and kiguradze 2011 for the spatial discretization followed by an implicit finite difference scheme for the time stepping we extended the results for stability estimates to a non homogeneous problem and derived optimal order error estimates for the semidiscretized and fully discretized equations using h 0 1 projection further to show the efficiency the proposed numerical method is demonstrated via numerical example

persistency of excitation in possible unstable continuous time systems identification and indirect adaptive control the author proves persistency of excitation of the output of an output reachable possibly unstable linear system under certain input conditions and applies this result to adaptive identification and indirect adaptive control in adaptive identification he proves exponential parameter convergence regardless of stability of the identified plant in indirect adaptive control he proves exponential parameter convergence along with asymptotic time invariance and global experimental stability of the controlled closed loop system

finite difference approximation of a nonlinear integro differential system finite difference approximation of the nonlinear integro differential system associated with the penetration of a magnetic field into a substance is studied the convergence of the finite difference scheme is proved the rate of convergence of the discrete scheme is given the decay of the numerical solution is compared with the analytical results proven earlier

linearly localized difference schemes for the nonlinear maxwell model of a magnetic field into a substance abstract a linearly localized difference scheme with the first order time approximation is proposed for solving a nonlinear maxwell model associated with the penetration of a magnetic field into a substance the new scheme is computationally efficient since the resulting algebra equations are linear and can be computed by the fast thomas algorithm without any newton type inner iterations it is also local in time that is only numerical solutions in one previous time level are necessary to update the current solutions such that it requires much less storage compared with the fully implicit method furthermore the exponential decaying behavior of difference solution which is analogous to that of the continuous solution is obtained to improve the time accuracy we apply the crank nicolson type time discretization to construct a second order linearly localized method numerical examples are presented to support our theoretical results

sufficiency of excitation in the context of adaptive identification and adaptive control of linear systems the concept of a sufficiently exciting input play a key role in this note necessary and sufficient conditions are presented for an input function of a single input linear stationary system to be sufficiently exciting these conditions are independent of the stability properties of the linear system

on fully discrete galerkin approximations for partial integro differential equations of parabolic type the subject of this work is the application of fully discrete galerkin finite element methods to initial boundary value problems for linear partial integro differential equations of parabolic type we investigate numerical schemes based on the pade discretization with respect to time and associated with certain quadrature formulas to approximate the integral term a preliminary error estimate is established which contains a term related to the quadrature rule to be specified in particular we consider quadrature rules with sparse quadrature points so as to limit the storage requirements without sacrificing the order of overall convergence for the backward euler scheme the crank nicolson scheme and a third order pade type scheme the specific quadrature rules analyzed are based on the rectangular the trapezoidal and simpson s rule for all the schemes studied optimal order error estimates are obtained in the case that the solution of the problem is smooth enough since this is important for our error analysis we also discuss the regularity of the exact solutions of our equations high order regularity results with respect to both space and time are given for the solution of problems with smooth enough data 17 refs

nonasymptotic results for finite memory wls filters a nonasymptotic analysis of properties of weighted least squares wls adaptive filters used for identification of time varying systems is presented it is shown that the problem of mean square boundedness of wls estimates is closely related to the problem of invertibility in the mean sense of the corresponding regression matrix necessary and sufficient conditions are discussed for such invertibility to hold based on that a number of results are derived paralleling those already obtained for least mean square lms filters and the problem of statistical robustness of the wls estimator is briefly discussed

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

stability condition for sampled data based control of linear continuous switched systems abstract most practical systems are continuous in nature but with discrete sampled feedback when digital control is utilized this paper investigates the stabilization problem of switched linear continuous time systems with sampled data based control for both known and unknown arbitrary switching processes on the basis of lyapunov stability theory a sufficient global exponential stability condition related to dwell time and sampling period is established for the latter case on line one step adaptive estimation algorithm is derived and integrated with sampled feedback for control design validation and verification of the established result are conducted through cruise control of train systems

convergence analysis for h1 galerkin mixed finite element approximation of one nonlinear integro differential model in this paper we investigate h 1 galerkin mixed finite element approximation of one nonlinear integro differential equation this method possesses some advantages such as approximating the unknown function and its gradient simultaneously as well as the finite element spaces being free of lbb condition a priori error estimates of the unknown function and its gradient are derived for both semi discrete and fully discrete schemes a numerical example is presented to illustrate the theoretical findings

recursive identification of overparametrized systems a recursive identification algorithm based on extended least squares is proposed to deal with the contingency of overparametrization the algorithm is relatively simple compared to those involving online order determination being based on adaptively introducing suitable excitation into the algorithm to avoid ill conditioning in the case of extended least squares based adaptive estimation then the regressors are appropriately stochastically perturbed the algorithm is shown to converge to a uniquely defined signal model with any pole zero cancellations at the origin

on parameter convergence in adaptive control it is well known that the parameter error as well as the model plant mismatch error in a model reference adaptive scheme tends exponentially to zero iff a certain sufficient richness condition holds for signals inside the time varying plant control loop in this paper we give conditions on the reference signal the exogenous input to the adaptive loop namely that it have as many spectral lines as there are unknown parameters in order to guarantee parameter convergence

large time behavior of solutions to a nonlinear integro differential system abstract asymptotic behavior of solutions as t to the nonlinear integro differential system associated with the penetration of a magnetic field into a substance is studied initial boundary value problems with two kinds of boundary data are considered the first with homogeneous conditions on whole boundary and the second with non homogeneous boundary data on one side of lateral boundary the rates of convergence are given too

long time numerical solution of a parabolic equation with memory long time stability and convergence properties of two time discreti zation methods for an integro differential equation of parabolic type are studied the methods are based on the standard backward euler and second order back ward differencing methods the memory term is approximated by a quadrature rule with emphasis on such rules with reduced computational memory require ments discretization of the spatial partial differential operators by the finite element method is also considered

a new collocation approach for solving systems of high order linear volterra integro differential equations with variable coefficients this paper contributes an efficient numerical approach for solving the systems of high order linear volterra integro differential equations with variable coefficients under the mixed conditions the method we have used consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations the obtained matrix equation is based on the matrix forms of fibonacci polynomials and their derivatives by means of collocations in addition the method is presented with error numerical results with comparisons are given to demonstrate the applicability efficiency and accuracy of the proposed method the results of the examples indicated that the method is simple and effective and could provide an approximate solution with high accuracy or exact solution of the system of high order linear volterra integro differential equations

periodic solutions of a nonlinear parabolic equation associated with the penetration of a magnetic field into a substance abstract we prove the existence and uniqueness of a t periodic weak solution of the nonlinear parabolic equation u t 1 r r a 0 t u r r s 2 ds r u r f u 0 r t 0 1 x o t u r 0 t u r 1 t h t u 1 t 0 in a sobolev space with weight in the proof the galerkin method is employed numerical results are given

galerkin finite element method for one nonlinear integro differential model galerkin finite element method for the approximation of a nonlinear integro differential equation associated with the penetration of a magnetic field into a substance is studied first type initial boundary value problem is investigated the convergence of the finite element scheme is proved the rate of convergence is given too the decay of the numerical solution is compared with the analytical results

finite difference scheme for one system of nonlinear partial integro differential equations abstract system of maxwell equations is considered reduction to the integro differential form is given existence uniqueness and large time behavior of solutions of the initial boundary value problem for integro differential model with two component and one dimensional case are studied finite difference scheme is investigated wider class of nonlinearity is studied than one has been investigated before freefem realization code and results of numerical experiments are given

nonlinear functionals of wavelet expansions adaptive reconstruction and fast evaluation summary this paper is concerned with the efficient evaluation of nonlinear expressions of wavelet expansions obtained through an adaptive process in particular evaluation covers here the computation of inner products of such expressions with wavelets which arise for instance in the context of galerkin or petrov galerkin schemes for the solution of differential equations the central objective is to develop schemes that facilitate such evaluations at a computational expense exceeding the complexity of the given expansion i e the number of nonzero wavelet coefficients as little as possible the following issues are addressed first motivated by previous treatments of the subject we discuss the type of regularity assumptions that are appropriate in this context and explain the relevance of besov norms the principal strategy is to relate the computation of inner products of wavelets with compositions to approximations of compositions in terms of possibly few dual wavelets the analysis of these approximations finally leads to a concrete evaluation scheme which is shown to be in a certain sense asymptotically optimal we conclude with a simple numerical example

persistence of excitation in linear systems abstract this paper develops output reachability characterizations of linear finite dimensional multivariate systems so as to translate excitation properties of system inputs to excitation properties of system outputs states or associated regression vectors such properties are of fundamental concern for convergence of algorithms involving on line identification adaptive state estimation prediction and control persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties

neural network based finite horizon optimal control of uncertain affine nonlinear discrete time systems in this paper the finite horizon optimal control design for nonlinear discrete time systems in affine form is presented in contrast with the traditional approximate dynamic programming methodology which requires at least partial knowledge of the system dynamics in this paper the complete system dynamics are relaxed utilizing a neural network nn based identifier to learn the control coefficient matrix the identifier is then used together with the actor critic based scheme to learn the time varying solution referred to as the value function of the hamilton jacobi bellman hjb equation in an online and forward in time manner since the solution of hjb is time varying nns with constant weights and time varying activation functions are considered to properly satisfy the terminal constraint an additional error term is incorporated in the novel update law such that the terminal constraint error is also minimized over time policy and or value iterations are not needed and the nn weights are updated once a sampling instant the uniform ultimate boundedness of the closed loop system is verified by standard lyapunov stability theory under nonautonomous analysis numerical examples are provided to illustrate the effectiveness of the proposed method

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

convergence rates of continuous time stochastic els parameter estimation discrete time convergence rates for extended least squares els algorithms are generalized to the continuous time case an essential difference in the estimation is the appropriate prefiltering while in the theory the existence of solutions of the stochastic equations is a concern

transfer function identification with filtering techniques this paper addresses the problem of identifying the transfer function of a plant with the aid of filtering techniques conditions for obtaining fair estimates of a transfer function are derived it is shown that to be able to reduce the effect of noise and other stochastic effects highly tuned filters are required it is also found that proper excitation signals are necessary for effective implementation of the proposed scheme some methods for designing the required highly tuned filters are proposed the relationship between the proposed scheme and existing methods is discussed it is shown that for some specific cases the proposed scheme is in effect a computationally efficient implementation of existing methods however for some other cases the proposed scheme gives more accurate results the theoretical predictions are substantiated with computer simulations

using the refinement equation for evaluating integrals of wavelets the wavelet galerkin method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets this paper studies the problem from the point of view of stationary subdivision schemes one of the main results is to identify these integrals as components of the unique solution of a certain eigenvector moment problem associated with the coefficients of the refinement equation asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach

interpolation of besov spaces we investigate besov spaces and their connection with dyadic spline approximation in lp q 0 p oo our main results are the determination of the interpolation spaces between a pair of besov spaces an atomic decomposition for functions in a besov space the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines

finite element methods for parabolic and hyperbolic partial integro differential equations on formule plusieurs methodes de galerkin a temps discret pour des equations integrodifferentielles paraboliques

on an adaptive multigrid solver for convection dominated problems the objective of this paper is to develop and describe an adaptive multigrid scheme for the numerical solution of convection diffusion reaction equations with dominating convection or reaction term specifically we propose a systematic construction of problem and scale dependent restriction prolongation and smoothing operators in combination with an adaptive mesh refinement strategy in particular adaptivity is not only to reduce computational complexity but also to stabilize standard galerkin discretizations so that adding artificial viscosity can be avoided the approach is suited for any choice of underlying multiresolution sequences in particular for standard finite element discretizations on nested but possibly nonuniform meshes moreover all concepts are in principle independent of the spatial dimension and avoid any special flow dependent enumeration of unknowns the performance of the scheme is illustrated by various examples in one and two spatial dimensions they are chosen so as to exhibit possibly many types of adverse or singular behavior in connection with constant and varying convection or the interplay between convective and reactive terms in the light of these tests those issues are identified that require further research

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

central tendency adaptive pole assignment the concept of central tendency adaptive control for achieving minimum variance objectives proposed by the authors in a companion paper 1989 is applied to adaptive pole assignment at any iteration given plant parameter estimate and their uncertainty a controller is designed which is most likely to achieve the pole assignment objectives simulations show a factor of 100 improvement in transient response over certainty equivalent adaptive pole assignment schemes for one example

central tendency minimum variance adaptive control the authors propose designing indirect adaptive controllers using measures of central tendency of the a posteriori probability function of the control for parameters that is given a knowledge of plant uncertainty at each time instant from estimation algorithms and a controller design rule controller parameters are sought which maximize the likelihood of achieving the control objectives the particular case of adaptive minimum variance control is studied in detail

asymptotically optimal parameter estimation with scheduled measurements to reduce the communication cost of a sensor node this paper is concerned with an estimation framework with scheduled measurements for a linear system a scheduler is designed to control the transmission of measurements from sensor to estimator which results in that only a subset of measurements is transmitted to the estimator we propose an innovation based scheduler and derive an analytical expression for the cramer rao lower bound crlb for the given scheduling strategy under a communication constraint an adaptive scheduler and a corresponding recursive estimator are jointly designed to asymptotically attain the crlb the structure of the estimator bears close resemblance to the standard least square estimator lse with the full set of sensor measurements moreover we prove that the estimation performance in terms of mean square estimation error is comparable to the standard lse even under a moderate communication cost the theoretical results are verified by simulations

a universality advantage of stochastic excitation signals for adaptive control abstract adaptive control schemes usually depend on estimation of system parameters which in turn depends excitation of modes associated with these parameters such excitation is supplied by plant noise the adaptive control signal itself and any external excitation such as a reference signal in this note it is shown that there is a universality advantage for any externally applied signal to be stochastic rather than deterministic the crucial property of a stochastic signal exploited in this note is its unpredictability by any causal system such as an adaptive control scheme when such unpredictable signals excite an adaptive control scheme there is no need to deliberately constrain the adaptation to be slow or excitation maintaining to ensure adequate identification

on the local stability properties of adaptive parameter estimators with composite errors and split algorithms the stability characteristics of a generalized error system structure are examined for adaptive parameter estimation systems this error system form encompasses the structure of a number of particular applications of adaptive parameter estimation theory which fall outside the framework of more familiar error system models the consequences for error system stability which derive from the added generality are analyzed it is demonstrated that when using averaging theory techniques to analyze the error system stability conditions must be augmented for the basic error system in order to ensure stability for the generalized error system the inadequacy of regressor spectral restrictions and persistent spanning conditions to guarantee local error system stability of the generalized structure is rigorously established alternative conditions which will yield such local stability are demonstrated to illustrate the concepts involved the recursive identification of parameters is examined in a parallel form realization of a linear system

error estimates for semidiscrete finite element methods for parabolic integro differential equations application des methodes d elements finis aux equations integro differentielles de type parabolique avec un noyau integral forme par un operateur aux derivees partielles d ordre 2

persistence of excitation in extended least squares in least squares parameter estimation schemes persistency of excitation conditions on the plant states are required for consistent estimation in the case of extended least squares the persistency conditions are on the state estimates here these persistency of excitation conditions are translated into sufficiently rich conditions on the plant noise and inputs in the case of adaptive minimum variance control schemes the sufficiently rich conditions are on the noise and specified output trajectory with sufficiently rich input signals guaranteed convergence rates of prediction errors improve and it is conjectured that the algorithms are consequently more robust

finite differences versus finite elements for solving nonlinear integro differential equations consider the nonlinear integro differential equation ut x t 0t a t x ux x d f x t 0 x 0 t t with appropriate initial and boundary conditions this problem serves as a model for one dimensional heat flow in materials with memory the numerical solution via finite elements was discussed in b neta j math anal appl 89 1982 598 611 in this paper we compare the results obtained there with finite difference approximation from the point of view of accuracy and computer storage it turns out that the finite difference method yields comparable results for the same mesh spacing using less computer storage

an integro differential formulation for magnetic induction in bounded domains boundary element finite volume method simulations of magnetohydrodynamic mhd flows in bounded domains using spectral methods suffer from a number of serious limitations alternative methods based on local discretization raise the problem of how to implement non local boundary conditions for the magnetic field we have developed a new strategy for the numerical solution of mhd problems in bounded domains which combines the flexibility of a local discretization with a rigorous formulation of magnetic boundary conditions next to an insulator in arbitrary geometries in accordance with the character of underlying equations we apply a global integral approach at the boundary and a differential approach inside the conducting domain the formulation of the boundary problem in terms of primitive variables allows us to combine these approaches and propose a mixed finite volume and boundary element method we illustrate its efficiency on magnetic diffusion problems in a sphere and in a finite cylinder

adaptive neural network based event triggered control of single input single output nonlinear discrete time systems this paper presents a novel adaptive neural network nn control of single input and single output uncertain nonlinear discrete time systems under event sampled nn inputs in this control scheme the feedback signals are transmitted and the nn weights are tuned in an aperiodic manner at the event sampled instants after reviewing the nn approximation property with event sampled inputs an adaptive state estimator se consisting of linearly parameterized nns is utilized to approximate the unknown system dynamics in an event sampled context the se is viewed as a model and its approximated dynamics and the state vector during any two events are utilized for the event triggered controller design an adaptive event trigger condition is derived by using both the estimated nn weights and a dead zone operator to determine the event sampling instants this condition both facilitates the nn approximation and reduces the transmission of feedback signals the ultimate boundedness of both the nn weight estimation error and the system state vector is demonstrated through the lyapunov approach as expected during an initial online learning phase events are observed more frequently over time with the convergence of the nn weights the inter event times increase thereby lowering the number of triggered events these claims are illustrated through the simulation results

numerical solution of a nonlinear integro differential equation abstract galerkin s method with appropriate discretization in time is considered for approximating the solution of the nonlinear integro differential equation u t x t 0 t a t x u x x d f x t 0 an error estimate in a suitable norm will be derived for the difference u uh between the exact solution u and the approximant uh it turns out that the rate of convergence of uh to u as h 0 is optimal this result was confirmed by the numerical experiments

finite element approximation of a parabolic integro differential equation with a weakly singular kernel we give error estimates for the numerical solution by means of the galerkin finite element method of an integro differential equation of parabolic type with a memory term containing a weakly singular kernel optimal order estimates are shown for spatially semidiscrete and completely discrete methods special attention is paid to the regularity of the exact solution