output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

adaptive fuzzy output feedback control for output constrained nonlinear systems in the presence of input saturation abstract in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states to address output constraint and input constraint a barrier lyapunov function and an auxiliary design system are employed respectively fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are bounded and the input and output constraints are circumvented simultaneously a numerical example is provided to illustrate the effectiveness of the proposed approach

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

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

adaptive fuzzy backstepping output feedback tracking control of mimo stochastic pure feedback nonlinear systems with input saturation abstract in this paper the adaptive fuzzy backstepping output feedback tracking control problem is considered for a class of uncertain stochastic multi input and multi output mimo nonlinear systems in pure feedback form the stochastic mimo nonlinear systems under study have unknown nonlinear functions input saturation and immeasurable states by using fuzzy logic systems to identify the uncertain nonlinear system and a smooth function to approximate the input saturation a fuzzy state observer is designed and the estimations of the immeasurable states are obtained based on the backstepping recursive design technique an adaptive fuzzy output feedback tracking control approach is developed it is shown that the proposed control approach guarantees that all the signals of the resulting closed loop system are semi globally uniformly ultimately bounded sguub in mean square in the sense of probability and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately a simulation example is provided to show the effectiveness of the proposed approach

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

adaptive fuzzy backstepping approach for temperature control of continuous stirred tank reactors in this paper an adaptive fuzzy controller based on backstepping technique has been proposed for temperature control of a general class of continuous stirred tank reactors cstrs using the observability concept an adaptive fuzzy controller using temperature measurement has been designed a fuzzy logic system is used to estimate the concentration dependent terms and other unknown system parameters appearing in the control law it is shown that the closed loop system is asymptotically stable and influences of minimum approximation error and external disturbance on the l 2 norm of the output tracking error can be attenuated arbitrarily the performance of the proposed controller has been examined for temperature control of an unstable reactor and its effectiveness has been demonstrated through computer simulation

lower bounds on the mean squared error of low rank matrix reconstruction we investigate the behavior of the mean square error mse of low rank matrix reconstruction and its special case matrix completion we first derive the constrained cramer rao bound crb on the mse matrix of any locally unbiased estimator and then analyze the behavior of the constrained crb when a subset of entries of the underlying matrix is randomly observed we design an alternating minimization procedure to compute the maximum likelihood estimator mle for the low rank matrix and demonstrate through numerical simulations that the performance of the mle approaches the constrained crb when the signal to noise ratio is high applying a chapman robbins type barankin bound allows us to derive lower bounds on the worst case scalar mse we demonstrate that the worst case scalar mse is infinite even if the model is identifiable however the infinite scalar mse is achieved only on a set of low rank matrices with measure zero we discuss the implications of these bounds and compare them with the empirical performance of the matrix lasso estimator and the existing bounds in the literature

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

fuzzy h_ infty filter design for a class of nonlinear discrete time systems with multiple time delays this paper studies the fuzzy hinfin filter design problem for signal estimation of nonlinear discrete time systems with multiple time delays and unknown bounded disturbances first the takagi sugeno t s fuzzy model is used to represent the state space model of nonlinear discrete time systems with time delays next we design a stable fuzzy hinfin filter based on the t s fuzzy model which guarantees asymptotic stability and a prescribed hinfin index for the filtering error system irrespective of the time delays and uncertain disturbances a sufficient condition for the existence of such a filter is established by using the linear matrix inequality lmi approach the proposed lmi problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm simulation examples are provided to illustrate the design procedure of the present method

adaptive fuzzy controller for multivariable nonlinear state time varying delay systems subject to input nonlinearities in this paper an adaptive fuzzy variable structure controller is investigated for a class of uncertain multi input multi output mimo nonlinear time delay systems with both sector nonlinearities and dead zones a decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis the unknown time varying delay uncertainties are compensated for using an appropriate lyapunov krasovskii functional the boundedness of all signals of the closed loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established the effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results

adaptive fuzzy output tracking control of mimo nonlinear uncertain systems in this paper the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple input multiple output mimo nonlinear systems with the block triangular structure the fuzzy logic systems are used to approximate the unknown nonlinear functions by using the backstepping technique the adaptive fuzzy tracking control design scheme is developed which has minimal learning parameterizations the adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed loop system are semiglobally uniformly ultimately bounded two examples are used to show the effectiveness of the approach

adaptive fuzzy output feedback control for mimo switched nonlinear systems with prescribed performances abstract this paper proposes an adaptive fuzzy output feedback control approach for a class of uncertain multiple input and multiple output mimo switched nonlinear systems with prescribed performance and immeasurable states in this research fuzzy logic systems are used to identify the unknown nonlinear functions a fuzzy switched state observer is established to observe the unmeasured states based on backstepping technique and the prescribed performance theory a new adaptive fuzzy control method with prescribed performance is developed it is proved that the proposed control approach can ensure that all the signals of the resulting closed loop system are bounded and the tracking errors are within the prescribed performance bounds for all times simulation studies illustrate the effectiveness of the proposed approach

adaptive feedback control of nonlinear time delay systems the lasalle razumikhin based approach this note presents a new method to design adaptive feedback controller for nonlinear time delay systems first by using the lasalle razumikhin theorem a sufficient condition is derived that ensures the convergence of a part of the solution with stability for a class of functional differential equations then using this condition the adaptive stabilization problem is solved for nonlinear time delay systems moreover it is shown that for a class of nonlinear time delay systems with triangular structure the adaptive stabilizing controller can be obtained by recursively constructing the lyapunov razumikhin function it will be shown that the provided recursive design approach which is obviously motivated by the typical backstepping method is not a trivial extension of the existing design method

adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems an adaptive fuzzy control approach is proposed for a class of multiple input multiple output mimo nonlinear systems with completely unknown nonaffine functions the mimo systems are composed of n subsystems and each of subsystems is in the nested lower triangular form it is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems this difficulty is overcome by introducing some special type lyapunov functions and taking advantage of the mean value theorem the backstepping design method and the approximation property of the fuzzy systems the proposed control approach can guarantee that all the signals in the closed loop system are bounded a simulation experiment is utilized to verify the feasibility of the proposed approach

adaptive fuzzy fault tolerant control with guaranteed tracking performance for nonlinear strict feedback systems in this study we propose two backstepping based adaptive fuzzy fault tolerant control ftc methods for a class of nonlinear strict feedback systems with actuator failures first a traditional ftc tftc method is considered our analysis shows that tftc has poor tracking performance due to the existence of approximation errors and external disturbances inspired by the idea that the magnitudes of control inputs decrease as the error of the last step decreases in the backstepping procedure we propose a new prescribed performance ftc npp ftc method based on the improved error transformation technique compared with previous methods where only the output tracking error is guaranteed within the prescribed performance bound ppb we show that the state tracking error for each step between the intermediate control and virtual control remains within the ppb regardless of actuator faults the main advantage of the npp ftc method is that the tracking errors and magnitudes of the control inputs can be reduced by adjusting the ppb parameters of the errors in the first and last steps our simulation results demonstrate the effectiveness of the proposed npp ftc method

stable adaptive control for nonlinear multivariable systems with a triangular control structure a stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators by utilizing the system triangular property integral type lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the decoupling matrix of the multivariable nonlinear system it is shown that stability of the adaptive closed loop system is guaranteed and transient performance is analytically quantized by mean square and l sub spl infin tracking error bound criteria

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

adaptive fuzzy terminal sliding mode control for a class of mimo uncertain nonlinear systems this paper presents a new adaptive terminal sliding mode tracking control design for a class of nonlinear systems using fuzzy logic system the terminal sliding mode control tsm was developed to provide faster convergence and higher precision control than the linear hyperplane based sliding control however the original tsm encountered singularity problem with discontinuous control action moreover a prior knowledge about the plant to be controlled is required the proposed controller combines a continuous non singular tsm with an adaptive learning algorithm and fuzzy logic system to estimate the dynamics of the controlled plant so that closed loop stability and finite time convergence of tracking errors can be guaranteed the performance of the proposed control strategy is evaluated through the control of a two link rigid robotic manipulator finally the effectiveness of the proposed scheme is demonstrated through the control of the ankle and knee movements in paraplegic subjects using functional electrical stimulation simulation and experimental results verify that the proposed control strategy can achieve favorable control performance with regard to system parameter variations and external disturbances 2011 elsevier b v all rights reserved

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

adaptive fuzzy tracking control of nonlinear mimo systems with time varying delays this paper focuses on the problem of adaptive fuzzy tracking control for a class of nonlinear multi input and multi output mimo time delay systems in strict feedback form the time delays in the systems may be time varying based on razumikhin functional method the state feedback adaptive fuzzy tracking controllers are constructed via backstepping technique the proposed adaptive fuzzy controllers guarantee that all the signals in the closed loop system are bounded and the system s outputs converge to a small neighborhood of the reference signals three examples are used to illustrate the effectiveness of the proposed approach

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

observer based adaptive fuzzy output constrained control for mimo nonlinear systems with unknown control directions in this paper an adaptive fuzzy output feedback control approach is proposed for a class of multi input and multi output mimo uncertain nonlinear systems with unmeasured states and unknown control directions in the control design by using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive state observer is designed for state estimation as well as system identification and a nussbaum gain function is introduced into the control design to solve the unknown control direction problem by applying the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively to address the problems of output constraint and explosion of complexity the barrier lyapunov function method and dynamic surface control technique are employed respectively it is proved that the proposed control approach can guarantee the semi globally uniform ultimate boundedness for all the signals and the tracking errors to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

fuzzy approximate disturbance decoupling of mimo nonlinear systems by backstepping and application to chemical processes fuzzy approximate disturbance decoupling concept is introduced for a class of multiple input multiple output mimo nonlinear systems with completely unknown nonlinearities based on backstepping technique a fuzzy almost disturbance decoupling control scheme is proposed the fuzzy controllers guarantee internal uniform ultimate boundedness of the closed loop adaptive systems and render a bounded approximate l sub 2 gain from the disturbance input to the output the developed design scheme is applied to control a two continuous stirred tank reactor process the simulation results illustrate the effectiveness of the method proposed in this paper

adaptive fuzzy tracking control of nonlinear time delay systems with unknown virtual control coefficients in this paper a novel adaptive fuzzy control scheme is proposed for a class of uncertain single input and single output siso nonlinear time delay systems with the lower triangular form fuzzy logic systems are used to approximate unknown nonlinear functions then the adaptive fuzzy tracking controller is constructed by combining lyapunov krasovskii functionals and the backstepping approach the proposed controller guarantees uniform ultimate boundedness of all the signals in the closed loop system while the tracking error converges to a small neighborhood of the origin an advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration finally simulation studies are given to demonstrate the effectiveness of the proposed design scheme

fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization in this paper the problem of adaptive fuzzy quantized output feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form the considered switched systems contain unknown nonlinearities hysteretic quantized input and without requiring the system states being available for measurement fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a switched fuzzy state observer is designed to estimate the unmeasured states the hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions based on the estimated states and using the backstepping design principle an adaptive fuzzy quantized output feedback control scheme is developed it is proved that whole adaptive fuzzy quantized control scheme can guarantee that all the variables in the closed loop system are bounded under a class of switching signals with average dwell time and also that the system output can track a given reference signal as closely as possible the simulation results are given to check the effectiveness of the proposed approach

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

eigenvalue finite difference approximations for regular and singular sturm liouville problems this paper includes two parts in the first part general error estimates for stable eigenvalue approximations are obtained these are practical in the sense that they are based on the discretization error of the difference formula over the eigenspace associated with the isolated eigenvalue under consideration verification of these general estimates are carried out on two difference schemes that of numerov to solve the schrodinger singular equation and that of the central difference formula for regular sturm liouville problems in the second part a sufficient condition for obtaining a stable difference scheme is derived such a condition condition n of theorem 2 1 leads to a simple by hand verification when one selects a difference scheme to compute eigenvalues of a differential operator this condition is checked for one and two dimensional problems introduction in this work we are concerned with eigenvalue eigenvector ap proximation by finite difference methods for differential operators defined on functions with bounded or unbounded domains our results will be illustrated in particular for the schrodinger radial operator whose energy levels are obtained numerically using difference schemes let

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear time delay systems this paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict feedback nonlinear systems with time delays and unknown virtual control coefficients fuzzy logic systems in mamdani type are used to approximate the unknown nonlinear functions then the adaptive fuzzy tracking controller is designed by using the backstepping technique and lyapunov krasovskii functionals the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal an advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system finally two examples are used to demonstrate the effectiveness of our results proposed in this paper

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme

a hierarchical structure of observer based adaptive fuzzy neural controller for mimo systems an observer based adaptive controller developed from a hierarchical fuzzy neural network hfnn is employed to solve the controller time delay problem for a class of multi input multi output mimo non affine nonlinear systems under the constraint that only system outputs are available for measurement by using the implicit function theorem and taylor series expansion the observer based control law and the weight update law of the hfnn adaptive controller are derived according to the design of the hfnn hierarchical fuzzy neural network the observer based adaptive controller can alleviate the online computation burden moreover the common adaptive controller is utilized to control all the mimo subsystems hence the number of adjusted parameters of the hfnn can be further reduced in this paper we prove that the proposed observer based adaptive controller can guarantee that all signals involved are bounded and that the outputs of the closed loop system track asymptotically the desired output trajectories