on the effectiveness of high gain observer based residuals for a class of non linear control systems the design of a high gain observer based residual is considered for a class of non linear systems input output maps are derived for use in residual design to increase design flexibility an invest

on the solution of characteristic value problems arising in linear stability analysis semi analytical approach abstract the linear stability analysis is normally governed by equations that constitute an eigenvalue characteristic value problem in this paper for the first time two semi analytical algorithms 1 differential transform method dtm and 2 adomian decomposition method adm are examined for solving a characteristic value problem occurring in linear stability analysis in this paper the characteristic value problem of couette taylor flow is selected because its simple geometry continues to be a paradigm for theoretical studies of hydrodynamic stability the results show that dtm handles the solution conveniently and accurately however this paper limits the use of adm for solving characteristic value problems the results indicate that the present algorithm based on dtm could be used as a promising method for solving characteristic value problems

adaptive fuzzy neural network control for a dsp based permanent magnet linear synchronous motor servo drive an adaptive fuzzy neural network afnn control system is proposed to control the position of the mover of a field oriented control permanent magnet linear synchronous motor pmlsm servo drive system to track periodic reference trajectories in this paper in the proposed afnn control system an fnn with accurate approximation capability is employed to approximate the unknown dynamics of the pmlsm and a robust compensator is proposed to confront the inevitable approximation errors due to finite number of membership functions and disturbances including the friction force the adaptive learning algorithm that can learn the parameters of the fnn on line is derived using lyapunov stability theorem moreover to relax the requirement for the value of lumped uncertainty in the robust compensator which comprises a minimum approximation error optimal parameter vectors higher order terms in taylor series and friction force an adaptive lumped uncertainty estimation law is investigated furthermore all the control algorithms are implemented in a tms320c32 dsp based control computer the simulated and experimental results due to periodic reference trajectories show that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

numerical method for non linear wave and diffusion equations by the variational iteration method this paper applies he s variational iteration to the wave equations in an infinite one dimensional medium and some non linear diffusion equations a suitable choice of an initial solution can lead to the needed exact solution by a few iterations copyright 2007 john wiley sons ltd

application of he s variational iteration method and adomian s decomposition method to the fractional kdv burgers kuramoto equation in this work the fractional kdv burgers kuramoto equation is studied he s variational iteration method vim and adomian s decomposition method adm are applied to obtain its solution comparison with ham is made to highlight the significant features of the employed methods and their capability of handling completely integrable equations

output feedback control of nonlinear systems using direct adaptive fuzzy neural controller in this paper a direct adaptive fuzzy neural output feedback controller dafoc for a class of uncertain nonlinear systems is developed under the constraint that only the system output is available for measurement an output feedback control law and an update law are derived for on line tuning the weighting factors of the dafoc by using strictly positive real lyapunov theory the stability of the closed loop system compensated by the dafoc can be verified moreover the proposed overall control scheme guarantees that all signals involved are bounded and the output of the closed loop system asymptotically tracks the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

on the two dimensional differential transform method in this paper two dimensional differential transform method of solution of the initial value problem for partial differential equations pdes have been studied new theorems have been added and some linear and nonlinear pdes solved by using this method the method can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational work in this work additionally analytical form solutions of two diffusion problems have been obtained and the solutions are compared very well with those obtained by decomposition method

on the solution of partial differential equations with specified boundary conditions abstract the decomposition method is applied to solution of partial differential equations in two and three dimensions with specified boundary conditions

technical communique further result on a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems in kim et al 1997 a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems automatica 33 8 1539 1543 authors present an excellent neural network nn observer for a class of nonlinear systems however the output error equation in their paper is strictly positive real spr which is restrictive assumption for nonlinear systems in this note by introducing a vector b 0 and lyapunov equation the observer design is obtained without requiring the spr condition thus our observer can be applied to a wider class of systems

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

the variational iteration method a powerful scheme for handling linear and nonlinear diffusion equations in this work we introduce a framework for obtaining exact solutions to linear and nonlinear diffusion equations exact solutions are developed for some diffusion processes of power law diffusitivies he s variational iteration method vim is used for analytic treatment of these equations the powerful vim method is capable of handling both linear and nonlinear equations in a direct manner

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

exact solutions of nonlinear diffusion equations by variational iteration method in this paper he s variational iteration method is applied to obtain exact solutions of some nonlinear diffusion equations the variational iteration method is used to construct correction functionals using general lagrange multipliers identified optimally via the variational theory and the initial approximations can be freely chosen with unknown constants the solutions obtained are compared with those obtained by the adomian decomposition method and homotopy perturbation method showing excellent agreement but the variational iteration method is more effective he s variational iteration method can be introduced to overcome the difficulties arising in calculating adomian polynomials

extended luenberger observer for non linear multivariable systems for non linear multiple input multiple output systems xdot f x u y h x u nonlinear observers are designed using a transformation into the non linear observer canonical form and an extended linearization the differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory and dimensioned by eigenvalue assignment with reference to the extended kalman filter algorithm this non linear observer design is called the extended luenberger observer this observer design is possible for all sufficiently smooth and locally observable systems in comparison with single output systems the non linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs

the non classical solution of the inhomogeneous non linear diffusion equation a complete classification of the symmetry reductions of the inhomogeneous nonlinear diffusion inld equation using the non classical method leads to one family of symmetry generators the resulting ordinary differential equation is of second order and non linear new solutions are obtained for some physical processes corresponding to particular values of n and p m

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

non linear observer design by observer canonical forms this paper studies the non linear observer design problem by observer canonical forms we present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non linear state coordinate change under which a time variable system is transformed into an observer canonical form these conditions give the multiple versions of li and tao 1986 for the single output case then a comparison is made with the lie algebraic conditions obtained by krener and respondek 1985 and modified by the authors in a recent paper xia and gao 1987

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

output feedback control of uncertain nonlinear systems using a self structuring adaptive fuzzy observer this paper describes the design of an output feedback controller based on an adaptive fuzzy observer for uncertain single input single output nonlinear dynamical systems we have focused on the realization of a minimal dynamic order for the adaptive fuzzy observer for this purpose we adopt an adaptive fuzzy observer in which no strictly positive real spr condition is needed and we combine a self structuring scheme with an on line estimation of fuzzy parameters by using this proposed scheme we can reduce the dynamic order of the adaptive output feedback fuzzy control system the lyapunov synthesis approach is used to guarantee a global uniform ultimate boundedness property of the state estimation error and tracking error as well as all other signals in the closed loop system no a priori knowledge of an upper limits on the uncertainties including optimal parameters and modeling errors is required the theoretical results are illustrated through simulation examples

exact results for the nonlinear diffusion equations delta u delta t delta delta x u 4 3 delta u delta x and delta u delta t delta delta x u 2 3 delta u delta x the author exploits local and non local symmetries of the two equations of the title and of some related equations some new exact solutions are derived and some specific boundary value problems of physical significance are considered

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

global adaptive observers for nonlinear systems via filtered transformations the problem of determining global adaptive observers for a class of single output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation under additional geometric conditions the original state can be observed as well the results obtained are based on a nonlinear change of coordinates driven by auxiliary filters filtered transformations

general solutions with solitary patterns for the defocusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this work the defocusing branch of the genuinely nonlinear dispersive k n n equation that exhibits solutions with solitary patterns is investigated the equation with constant coefficients to the derivatives is examined in one two and three dimensional spaces general formulas for solutions with solitary patterns are developed for all positive integers n n 1 two sets of entirely new formulas one set produces solutions for even integers n whereas the second set produces solutions in opposite directions for odd integers n n 1 are established

state observer based adaptive fuzzy output feedback control for a class of uncertain nonlinear systems this paper aims to develop state observer based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances an adaptive fuzzy observer is proposed to estimate the system state variables it is shown that the observation errors obtained from the observer are uniformly ultimately bounded applying the estimated system state for design of an output feedback controller the uniformly ultimate boundedness of the tracking errors for the resulting closed loop system can be guaranteed a typical robot arm system is employed in our simulation studies and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances

one phase inverse stefan problem solved by adomian decomposition method abstract in this paper the solution of one phase inverse stefan problem is presented the problem consists of the reconstruction of the function which describes the distribution of temperature on the boundary when the position of the moving interface is well known the proposed solution is based on the adomian decomposition method and the least square method

the existence of noise terms for systems of inhomogeneous differential and integral equations in this paper we develop a framework for the necessary condition for the existence of noise terms for systems of inhomogeneous differential and integral equations we show that the noise terms are conditional and are generated for inhomogeneous equations if specific criteria is justified we numerically test our approach for a variety of systems of inhomogeneous problems

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

robust quasi lpv control based on neural state space models we derive a synthesis result for robust linear parameter varying lpv output feedback controllers for nonlinear systems modeled by neural state space models this result is achieved by writing the neural state space model on a linear fractional transformation lft form in a nonconservative way separating the system description into a linear part and a nonlinear part linear parameter varying control synthesis methods are then applied to design a nonlinear control law for this system since the model is assumed to have been identified from input output measurement data only it must be expected that there is some uncertainty on the identified nonlinearities the control law is therefore made robust to noise perturbations after formulating the controller synthesis as a set of linear matrix inequalities lmis with added constraints some implementation issues are addressed and a simulation example is presented

an adaptive fuzzy hybrid state observer for bioprocesses in order to monitor and control bioprocesses online measurements of certain biological variables like biomass concentration are normally required unfortunately there is a lack of highly reliable and low cost instruments for online measuring these important variables these limitations have motivated the use of observers this paper describes a state observer for bioprocesses based on a hybrid fuzzy model the model combines the mass balances and a fuzzy inference system for approximating the uncertain dynamic of the kinetic reactions the convergence stability and robustness of the observer are analyzed the main features of this observer are illustrated by considering a lactic fermentation

adaptive observers for single output nonlinear systems an adaptive version of the nonlinear observer obtained by a j krener et al 1983 is presented this version involves the cancellation of nonlinear terms by output injection as an intermediate step necessary and sufficient conditions are given for transforming a nonlinear system by state space change of coordinates into the special adaptive observer form that was used by y bastin et al 1988 to design adaptive observers

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

exact solutions to nonlinear diffusion equations obtained by the decomposition method in this paper we develop a framework to obtain exact solutions to the nonlinear diffusion equations by employing the adomian decomposition method exact solutions are obtained for some important physical processes of power law diffusivities the method is capable of greatly reducing the size of computational domain and is presented in a general way so that it can be used in more diffusion classes

how to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems this paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer high gain hg observer sliding mode like observer etc for a class of single input single output siso uncertain or ill defined affine nonlinear systems indeed the corrective term of the proposed observer involves a well defined design function which is shown to be satisfied by the commonly used hg based observers namely for the usual hg observers and the sliding mode observers together with their implementable versions the design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error this particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real spr condition

stable neural controller design for unknown nonlinear systems using backstepping we propose from an adaptive control perspective a neural controller for a class of unknown minimum phase feedback linearizable nonlinear system with known relative degree the control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural network structure the resulting controller however moves the complex mechanics involved in a typical backstepping design from off line to online with appropriate choice of the network size and neural basis functions the same controller can be trained online to control different nonlinear plants with the same relative degree with semi global stability as shown by the simple lyapunov analysis meanwhile the controller also preserves some of the performance properties of the standard backstepping controllers simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller

the adomian decomposition method in turning point problems in this paper the decomposition method is applied to boundary value problems of ordinary differential equations with a parameter exhibiting turning points

bounded state reconstruction error for lpv systems with estimated parameters the note deals with the state reconstruction of a class of discrete time systems with time varying parameters while usually the parameters are assumed to be online available and exactly known the special and realistic situation when the parameters are known with a finite accuracy is considered the main objective of the note is to show that despite of the resulting mismatch between the true system and the model the state reconstruction error boundedness can be guaranteed and an explicit bound can be derived the proof is based upon the concept of input to state stability

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

new classes of similarity solutions of the inhomogeneous nonlinear diffusion equations the lie similarity method has been used to extend the similarity solutions of the one dimensional inhomogeneous nonlinear diffusion equations we determine the lie point symmetry vector fields and calculate the similarity ansatz then we discuss the resulting nonlinear ordinary differential equations exact solutions are found and their relations to some real physical situations are discussed

numerical modelling of linear and nonlinear diffusion equations by compact finite difference method in this work accurate solutions to linear and nonlinear diffusion equations were introduced a combination of a sixth order compact finite difference scheme in space and a low storage third order total variation diminishing runge kutta scheme in time have been used for treatment of these equations the computed results with the use of this technique have been compared with the exact solution to show the accuracy of it here the approximate solution to the diffusion equations has been obtained easily and elegantly with neither transforming nor linearizing the equation the present method is seen to be a very good alternative method to some existing techniques for realistic problems

several new exact solutions for a fast diffusion equation by the differential constraints of the linear determining equations in this paper we propose a new approach to develop several new exact solutions to a fast nonlinear diffusion equation this approach rests on the differential constraints obtained by the method of linear determining equations the method is capable of reducing the nonlinear diffusion equation to systems of nonlinear ordinary equations the proposed scheme is presented in a general way so that it can be used in other diffusion processes

the pythagoras number and the u invariant of laurent series fields in several variables abstract we show that every sum of squares in the three variable laurent series field r x y z is a sum of 4 squares as was conjectured in a paper of choi dai lam and reznick in the 1980 s we obtain this result by proving that every sum of squares in a finite extension of r x y is a sum of 3 squares it was already shown in choi dai lam and reznick s paper that every sum of squares in r x y itself is a sum of two squares we give a generalization of this result where r is replaced by an arbitrary real field our methods yield similar results about the u invariant of fields of the same type

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

convenient analytic recurrence algorithms for the adomian polynomials abstract in this article we present four analytic recurrence algorithms for the multivariable adomian polynomials as special cases we deduce the four simplified results for the one variable adomian polynomials these algorithms are comprised of simple orderly and analytic recurrence formulas which do not require time intensive operations such as expanding regrouping parametrization and so on they are straightforward to implement in any symbolic software and are shown to be very efficient by our verification using mathematica 7 0 we emphasize that from the summation expressions a n k 1 n u n k for the multivariable adomian polynomials and an k 1 n f k u 0 c n k for the one variable adomian polynomials we obtain the recurrence formulas for the u n k and the c n k these provide a theoretical basis for developing new algorithmic approaches such as for parallel computing in particular the recurrence process of one particular algorithm for the one variable adomian polynomials does not involve the differentiation operation but significantly only the arithmetic operations of multiplication and addition are involved precisely c n 1 u n n 1 and c n k 1 n j 0 n k j 1 u j 1 c n 1 j k 1 2 k n we also discuss several other algorithms previously reported in the literature including the adomian rach recurrence algorithm 1 and this author s index recurrence algorithm 23 36