a new linear adaptive controller design analysis and performance the certainty equivalence and polynomial approach widely used for designing adaptive controllers leads to simple adaptive control designs that guarantee stability asymptotic error convergence and robustness but not necessarily good transient performance backstepping and tuning functions techniques on the other hand are used to design adaptive controllers that guarantee stability and good transient performance at the expense of a highly nonlinear controller in this paper we use elements from both design approaches to develop a new certainty equivalence based adaptive controller by combining backstepping based control law with a normalized adaptive law the new adaptive controller guarantees stability and performance as well as parametric robustness for the nonadaptive controller that are comparable with the tuning functions scheme without the use of higher order nonlinearities

collocation software for boundary value differential algebraic equations we describe the methods and implementation of a general purpose code coldae this code can solve boundary value problems for nonlinear systems of semi explicit differential algebraic equations daes of index at most 2 fully implicit index 1 boundary value dae problems can be handled as well the code coldae is an extension of the package colnew colsys for solving boundary value odes the implemented method is piecewise polynomial collocation at gaussian points extended as needed by the projection method of ascher petzold for general semi explicit index 2 problems as well as for fully implicit index 1 problems we define a em selective projected collocation method and demonstrate its use the mesh selection procedure of colsys is modified for the case of index 2 constraints we also discuss shooting for initial guesses the power and generality of the code are demonstrated by examples

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

on the numerical solution of differential algebraic equations by pade series in this paper the solution for a differential algebraic equation dae can be expanded up to arbitrary order using maple computer algebra systems frank maple v crc press boca raton fl 1996 first we calculate power series of the given equations system then transform it into pade series form which gives an arbitrary order for solving dae numerically

a shooting method for fully implicit index 2 differential algebraic equations a shooting method for two point boundary value problems bvps for fully implicit index 1 and index 2 differential algebraic equations daes is presented a combination of the shooting equations with a method of the calculation of consistent initial values leads to a system of nonlinear algebraic equations with a nonsingular jacobian matrix examples are given

on morse s new adaptive controller parameter convergence and transient performance some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by a s morse proc us italy joint seminar syst models feedback 1992 it is proved that the l sub 2 norm of the tracking error is uniformly bounded by the initial parameter estimation error further if the initial conditions are sufficiently small it is shown that the l sub infinity norm of the tracking error is uniformly bounded by the l sub m2 norm of the reference signal these transient bounds are independent of the signals richness and the adaptation gain making them arguably the strongest transient results available in the literature second excitation conditions for exponential stability a property which is well known to insure some local performance measures are given to this end it is shown that modulo a signal dependent time scale change morse s estimator is equivalent to a normalized gradient plus filtering identifier

robustness of discrete time direct adaptive controllers the problem of preserving stability of discrete time adaptive controllers in spite of reduced order modeling and output disturbances is addressed in this paper conditions for global stability convergence of the tracking error with bounded signals are derived for a discrete time pole zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals following an input output perpective the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors respectively and its stability is studied using the sector stability and passivity theorems first the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure in this l 2 framework it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed loop transfer function verifies certain conicity conditions the convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed the results are further extended to a broader class of l infty disturbances and reference inputs

the ordinary successive approximations method and pade approximants for solving a differential equation with variant retarded argument the aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument x t a t x t t t f t x t f t l 0 0 0

non linear dynamics in adaptive control chaotic and periodic stabilization abstract in this paper the non linear features of adaptive control algorithms are highlighted using a simple linear discrete time example based on classical design it is demonstrated that in the presence of undermodelling errors non linear phenomena in the feedback gain such as limit cycles and even chaos arise despite these complicated dynamics robust stabilization of the plant can still occur for the class of undermodelling errors considered the set of plants stabilizable by this adaptive controller is completely characterized

brief robust high order tuner of simplified structure recently morse has proposed a new adaptation scheme so called high order tuner which generates as outputs not only tuned parameters but also their time derivatives up to a certain order in this paper a robustified variant of the high order tuner is introduced to adaptively stabilize a siso linear plant subjected to external disturbances in comparison with morse s tuner the proposed one has essentially simplified structure namely the total order of time varying auxiliary filters is reduced 2n times where n is the order of the plant to be controlled

a well posed shooting method for transferable dae s consider a tpbvp for transferable nonlinear dae s in general the shooting equation has a singular jacobian a multiple shooting method which has a nonsingular jacobian and also produces consistent initial values for the integration is presented the estimation of the condition of the jacobian shows the well posedness of the method some illustrative examples are given

the basic successive substitute approximations method and pade approximations to solve the elasticity problem of settled of the wronkler ground with variable coefficients in this paper we have given numerical solution of the elasticity problem of settled on the wronkler ground with variable coefficient first we calculate the basic successive substitute approximation of the given boundary value problem then transform it into pade series form which give an arbitrary order for solving differential equation numerically we applied these methods to an example which is the elasticity problem of unit length homogeny beam which is a special form of boundary value problem

limitations of adaptive mesh refinement techniques for singularly perturbed problems with a moving interior layer in a composed domain on an axis r with the moving interface boundary between two subdomains we consider an initial value problem for a singularly perturbed parabolic reaction diffusion equation in the presence of a concentrated source on the interface boundary monotone classical difference schemes for problems from this class converge only when e n 1 n0 1 where e is the perturbation parameter n and n0 define the number of mesh points with respect to x on segments of unit length and t therefore in the case of such problems with moving interior layers it is necessary to develop special numerical methods whose errors depend rather weakly on the parameter e and in particular are independent of e i e e uniformly convergent methods in this paper we study schemes on adaptive meshes which are locally condensing in a neighbourhood of the set that is the trajectory of the moving source it turns out that in the class of difference schemes consisting of a standard finite difference operator on rectangular meshes which are a priori or a posteriori locally condensing in x and t there are no schemes that converge e uniformly and in particular even under the condition e n 2 n0 2 if the total number of the mesh points between the cross sections x0 and x0 1 for any x0 r has order of nn0 thus the adaptive mesh refinement techniques used directly do not allow us to widen essentially the convergence range of classical numerical methods on the other hand the use of condensing meshes but in a local coordinate system fitted to the set makes it possible to construct schemes which converge e uniformly for n n0 such a scheme converges at the rate o n 1 ln n n0 1

on the numerical solution of chemical differential algebraic equations by pade series in this paper the solution of chemical differential algebraic equation model of general type f y y x 0 has been done using the method the example including a model of an absorption tower is given to illustrate the utility of the method using maple computer algebra systems

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

a singularly perturbed convectiondiffusion problem with a moving pulse a singularly perturbed parabolic equation of convectiondiffusion type is examined initially the solution approximates a concentrated source this causes an interior layer to form within the domain for all future times using a suitable transformation a layer adapted mesh is constructed to track the movement of the centre of the interior layer a parameter uniform numerical method is then defined by combining the backward euler method and a simple upwinded finite difference operator with this layer adapted mesh numerical results are presented to illustrate the theoretical error bounds established

boundary value methods for the solution of differential algebraic equations boundary value techniques for the solution of initial value problems of odes despite their apparent higher cost present some important advantages over initial value methods among them there is the possibility to have greater accuracy to control the global error and to have an efficient parallel implementation in this paper the same techniques are applied to the solution of linear initial value problems of daes we have considered three term numerical methods midpoint simpson and an adams type method in order to obtain a block tridiagonal linear system as a discrete problem convergence results are stated in the case of constant coefficients and numerical examples are given on linear time varying problems

on the solution of the abel equation of the second kind by the shifted chebyshev polynomials abstract this paper presents a new approximate method of abel differential equation by using the shifted chebyshev expansion of the unknown function abel differential equation is approximately transformed to a system of nonlinear equations for the unknown coefficients a desired solution can be determined by solving the resulting nonlinear system this method gives a simple and closed form of approximate solution of abel differential equation the solution is calculated in the form of a series with easily computable components the numerical results show the effectiveness of the method for this type of equation comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

asymptotically optimal adaptive control with consistent parameter estimates for the discrete time linear stochastic systems with unknown coefficients we give an adaptive control by which both strong consistency of the parameter estimates and asymptotic optimality for the tracking system are achieved simultaneously this is done by disturbing the signal that is to be tracked and the disturbance consists of a sequence of random vectors with covariance matrices tending to zero the main result is essentially based on some criteria for consistency of parameter estimate for the system without monitoring which are also demonstrated in the paper the existence of adaptive control is also discussed

numerical solution of differential algebraic equations and computation of consistent initial boundary conditions boundary value methods for the solution of differential algebraic equations are described we consider both initial and boundary value problems and derive an algorithm that does not require additional information from the user but only the initial or boundary conditions needed in theory to obtain a unique solution

the successive approximation method and pade approximants for solutions the non linear boundary value problem in this paper we suggested an successive approximation method and pade approximants method for the solution of the non linear differential equation first we calculate power series of the given equation system then transform it into pade approximants series form which give an arbitrary order for solving differential equation numerically we compare our results with the result obtained by successive method for the non linear equation

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

a singularly perturbed parabolic problem with a layer in the initial condition abstract singularly perturbed reaction diffusion parabolic problems with non smooth initial conditions are studied a finite difference method is constructed on a piecewise uniform mesh for a parabolic problem with an initial condition containing a layer the parameter uniform convergence of this numerical method is analyzed this numerical method is used to generate an approximation to the solution of a singularly perturbed parabolic problem with a discontinuous initial condition

adomian decomposition method for solution of nonlinear differential algebraic equations in m m hosseini adomian decomposition method with chebyshev polynomials appl math comput in press an efficient modification of the adomian decomposition method was presented by using chebyshev polynomials also in m m hosseini adomian decomposition method for solution of differential algebraic equations j comput appl math in press solution of linear differential algebraic equations was considered by adomian decomposition method in this paper standard and modified adomian decomposition methods are applied to non linear differential algebraic equations the schemes are tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

on the numerical solution of differential algebraic equations with index 2 in this paper numerical solution of differential algebraic equations daes with index 2 is considered an index reduction for dae with index 2 is suggested first index 2 system is reduced to index 1 system then we have applied the method for solving daes with index 2 numerically

numerical solutions of linear time varying descriptor systems via hybrid functions state analysis of linear time varying descriptor systems via hybrid functions are proposed in this paper based upon some useful properties of hybrid functions a special product matrix and a related coefficient matrix are applied to solve the descriptor systems the unknown coefficient matrix will be in generalized lyapunov equation form which is solved via the kronecker product method the advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems we propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions the high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples

transient bounds for adaptive control systems adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity in this note we consider how these theories may be applied to adaptive control to quantify transient response this involves the explicit description of the constants appearing in the passivity theorem and or the small gain theorem which characterize both system gains and initial condition effects the result is a fundamental connection between transient response bounds and uniform plant controllability which connects initial state conditions with the input output analysis applying these general theorems to adaptive control we are able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response the implication of these sufficient results is that without both bounds upon initial conditions and guarantees of excitation potentially extreme transient excursions of system variables are possible even though global convergence and asymptotic performance are guaranteed

a numerical solution of the elasticity problem of settled of the wronkler ground with variable coefficients in this paper we have given numerical solution of the elasticity problem of settled on the wronkler ground with variable coefficient the approximation solution of boundary value problem which is pertinent to this has been converted to integral equations and then by using the successive approximation methods has been reached in addition to this the approximation solution of the problem was put into pade series form we applied these methods to an example which is the elasticity problem of unit length homogeny beam which is a special form of boundary value problem first we calculate the successive approximation of the given boundary value problem then transform it into pade series form which give an arbitrary order for solving differential equation numerically

on the numerical solution of differential algebraic equations with index 3 in this study numerical solution of differential algebraic equations daes with index 3 has been presented by pade approximation an index reduction for differential algebraic equation with index 3 is suggested first index 3 system is reduced to index 1 system then we have applied the method for solving differential algebraic equations with index 3 numerically

non linear dynamics in adaptive control periodic and chaotic stabilization ii analysis abstract a particular non linear equation arising in an adaptive control problem is presented in the first part of this paper this equation displays vividly a wealth of non linear phenomena depending on the value of one crucial parameter characterizing the extent and presence of non design circumstances we demonstrate the existence of asymptotically periodic behaviour or chaotic dynamics in the feedback controller this paper contains the mathematical analysis associated with the earlier results and as such serves two main purposes to provide the theoretical proofs and support for these results and to demonstrate more fully the extraordinary complexity and difficulty of conducting a thorough global analysis of even this simplest of robust adaptive problems by performing this latter task we aim to delineate better what are reasonable objectives to be expected of robust adaptive control theory

numerical solution of differential algebraic equations with index 2 abstract in this paper numerical solution of differential algebraic equations daes with index 2 has been presented using pade approximation method an index reduction for differential algebraic equation with index 2 is suggested first index 2 system is reduced to index 1 system then we have applied the method for solving differential algebraic equations with index 2 numerically