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

an improved stable adaptive fuzzy control method stable adaptive fuzzy control is a self tuning concept for fuzzy controllers that uses a lyapunov based learning algorithm thus guaranteeing stability of the system plant controller learning algorithm and convergence of the plant output to a given reference signal in the paper two new methods for stable adaptive fuzzy control are presented the first method is an extension of an existing concept it is shown that a major drawback of that concept the necessity for new adaptation at every change of the reference signal can be avoided by a simple modification the main focus of the paper is on the presentation of a second method which extends the applicability of stable adaptive fuzzy control to a broader class of nonlinear plants this is achieved by an improved controller structure adopted from the neural network domain performance and limitations of the proposed methods as well as some practical design aspects are discussed and illustrated with simulation results

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

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 control of robot manipulators using fuzzy logic systems under actuator constraints in this paper a stable fuzzy adaptive controller for trajectory tracking is developed for robot manipulators without velocity measurements taking into account the actuator constraints the controller is based on structural knowledge of the dynamics of the robot and measurements of link positions only the gravity torque including system uncertainty like payload variation etc is estimated by a fuzzy logic system fls the adaptive controller represents an amalgamation of a filtering technique to eliminate velocity measurements and the theory of function approximation using fls to estimate the gravity torque the proposed controller ensures the local asymptotic stability and the convergence of the position error to zero the proposed controller is robust not only to structured uncertainty such as payload parameter variation but also to unstructured one such as disturbances the validity of the control scheme is shown by simulations on a two link robot manipulator

fuzzy adaptive control of a certain class of siso discrete time processes in this manuscript we address the problem of the stability of a certain class of siso discrete time processes controlled by an adaptive fuzzy controller by using lyapunov stability theory these results were recently obtained for adaptive neural controllers and are extended here to adaptive fuzzy controllers of sugeno s type in order to achieve tracking of a reference signal with this kind of fuzzy system we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law we first present the gradient based steepest descent adaptation law and we argue that this gradient based adaptation law can be simplified dramatically thereafter we show the asymptotic stability of the overall system the convergence of the tracking error to zero when using this simplified parameters adjustment law unfortunately this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking that is when the parameters are initialized not too far from their optimal values local stability however when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules i e the membership functions of the premises are not modified and when the reference signal is the delayed desired output the stability result is strictly valid the parameters do not have to be initialized around the perfectly tuned values in this case the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input

fuzzy adaptive filters with application to nonlinear channel equalization two fuzzy adaptive filters are developed one uses a recursive least squares rls adaptation algorithm and the other uses a least mean square lms adaptation algorithm the rls fuzzy adaptive filter is constructed through the following four steps 1 define fuzzy sets in the filter input space rn whose membership functions cover u 2 construct a set of fuzzy if then rules which either come from human experts or are determined during the adaptation procedure by matching input output data pairs 3 construct a filter based on the set of rules and 4 update the free parameters of the filter using the rls algorithm the design procedure for the lms fuzzy adaptive filter is similar the most important advantage of the fuzzy adaptive filters is that linguistic information in the form of fuzzy if then rules and numerical information in the form of input output pairs can be combined in the filters in a uniform fashion the filters are applied to nonlinear communication channel equalization problems

optimal integral sliding mode control scheme based on pseudospectral method for robotic manipulators for a multi input multi output nonlinear system an optimal integral sliding mode control scheme based on pseudospectral method is proposed in this paper and the controller is applied on rigid robotic manipulators with constraints first a general form of integral sliding mode is designed with the aim of restraining disturbance then pseudospectral method is adopted to deal with constrained optimal control problem in consideration of the benefits of both methods an optimal integral sliding mode controller is given which is based on the combination of integral sliding mode and pseudospectral method the stability analysis shows that the controller can guarantee stability of robotic manipulator system simulations show the effectiveness of proposed method

computation of second order accurate unsteady aerodynamic generalized forces a classical variational statement is used to derive special properties of a weighted residual method it is shown that some weighted integral of the sought solution can be obtained to second order accuracy in the solution to the original and adjoint problems for aerodynamic problems it is assumed that the reverse flow problem is adjoint to the original problem examples on airfoils and wings demonstrate the fast convergence of generalized aerodynamic forces the singular behavior of aerodynamic problems is shown to be the factor that makes the application of these techniques so attractive in aerodynamics

robust design of rule based fuzzy controllers this paper deals with the design of stable and robust rule based fuzzy control systems new expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented the relation between the modification of the rules and the stability is studied through the so called sensitivity indices the paper presents procedures that make use of these indices to improve the design of fuzzy control systems including the modification of the rules to obtain the global stability of an unstable system with multiple attractors and to improve the dynamic behavior or the robustness of a non linear plant an example with a fuzzy controller for a system with non linear damping and saturation in the actuation is presented to illustrate the design procedure

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

adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators recently through the use of parameterized fuzzy approximators various adaptive fuzzy control schemes have been developed to deal with nonlinear systems whose dynamics are poorly understood an important class of parameterized fuzzy approximators is constructed using radial basis function rbf as a membership function however some tuneable parameters in rbf appear nonlinearly and the determination of the adaptive law for such parameters is a nontrivial task in this paper we propose a new adaptive control method in an effort to tune all the rbf parameters thereby reducing the approximation error and improving control performance global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller simulations performed on a simple nonlinear system illustrate the approach

design of a fuzzy controller with fuzzy sliding surface abstract fuzzy logic controllers have succeeded in many control problems that the conventional control theories have difficulties to deal with however the design of the fuzzy logic controllers depends to a large extent on the expert s knowledge or on trial and error moreover due to the linguistic expression of the fuzzy controller it has not been easy to guarantee the stability and robustness of the fuzzy control systems to overcome these drawbacks we propose to design a fuzzy controller with the fuzzy sliding surface the fuzzy rules are defined based on this fuzzy sliding surface and the output of the fuzzy controller is inferred by the proper compositional rule of inference then we show the stability of this fuzzy control system and the boundedness of the tracking error by using the lyapunov theory finally we apply this fuzzy controller to control a nonlinear time varying system and confirm the validity of the controller

adaptive statistic tracking control based on two step neural networks with time delays this paper presents a new type of control framework for dynamical stochastic systems called statistic tracking control stc the system considered is general and non gaussian and the tracking objective is the statistical information of a given target probability density function pdf rather than a deterministic signal the control aims at making the statistical information of the output pdfs to follow those of a target pdf for such a control framework a variable structure adaptive tracking control strategy is first established using two step neural network models following the b spline neural network approximation to the integrated performance function the concerned problem is transferred into the tracking of given weights the dynamic neural network dnn is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function to achieve the required control objective an adaptive controller based on the proposed dnn is developed so as to track a reference trajectory stability analysis for both the identification and tracking errors is developed via the use of lyapunov stability criterion simulations are given to demonstrate the efficiency of the proposed approach

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

approximation accuracy analysis of fuzzy systems as function approximators this paper establishes the approximation error bounds for various classes of fuzzy systems i e fuzzy systems generated by different inferential and defuzzification methods based on these bounds the approximation accuracy of various classes of fuzzy systems is analyzed and compared it is seen that the class of fuzzy systems generated by the product inference and the center average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center average defuzzifier and the class of fuzzy systems defuzzified by the mom defuzzifier in addition it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the mom defuzzified method are given

design and analysis of fuzzy identifiers of nonlinear dynamic systems uses fuzzy systems as identifiers for nonlinear dynamic systems the author provides a theoretical justification for the fuzzy identifiers by proving that they are capable of following the output of a general nonlinear dynamic system to arbitrary accuracy in any finite time interval the fuzzy identifiers are constructed from a set of adaptable fuzzy if then rules and can combine both numerical information in the form of input output pairs obtained by exciting the system with an input signal and measuring the corresponding outputs and linguistic information in the form of if then rules about the behavior of the system in terms of vague and fuzzy words into their designs in a uniform fashion the author develops two fuzzy identifiers the first one is designed through the following four steps 1 define some fuzzy sets in the state space u spl sub r sup n of the system these fuzzy sets do not change 2 construct fuzzy rule bases of the fuzzy identifier which comprise rules whose if parts constitute all the possible combinations of the fuzzy sets defined in 1 3 design the fuzzy systems in the fuzzy identifier based on the fuzzy rule bases of 2 and 4 develop an adaptive law for the free parameters in the fuzzy identifier the second fuzzy identifier is designed in a similar way as the first one except that a the parameters characterizing the fuzzy sets in the state space change during the adaptation procedure and b the fuzzy systems and the adaptive law are different the author proves that 1 both fuzzy identifiers are globally stable in the sense that all variables in the fuzzy identifiers are uniformly bounded and 2 under some conditions the identification errors of both fuzzy identifiers converge to zero asymptotically finally the author simulates the fuzzy identifiers for identifying the chaotic glycolytic oscillator and the results show that 1 the fuzzy identifiers can approximate the chaotic system at a reasonable speed and accuracy without using any linguistic information and 2 by incorporating some fuzzy linguistic if then rules about the behavior of the system into the fuzzy identifiers the speed and accuracy of the fuzzy identifiers are greatly improved

adaptive control of robot manipulator using fuzzy compensator this paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncertainties in order to compensate these uncertainties we use the fls fuzzy logic system that has the capability to approximate any nonlinear function over the compact input space in the proposed control schemes we need not derive the linear formulation of robot dynamic equation and tune the parameters we also suggest the robust adaptive control laws in all proposed schemes for decreasing the effect of approximation error to reduce the number of fuzzy rules of the fls we consider the properties of robot dynamics and the decomposition of the uncertainty function the proposed controllers are robust not only to the structured uncertainty such as payload parameter but also to the unstructured one such as friction model and disturbance the validity of the control scheme is shown by computer simulations of a two link planar robot manipulator

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

multiplication free radial basis function network for the purpose of adaptive function approximation a new radial basis function network is proposed which is nonlinear in its parameters the goal is to reduce significantly the computational effort for a serial processor by avoiding multiplication in both the evaluation of the function model and the computation of the parameter adaptation the approximation scheme makes use of a grid based gaussian basis function network due to the local support of digitally implemented gaussian functions the function representation is parametric local and therefore well suited for an online implementation on a microcomputer a gradient descent based nonlinear learning algorithm is presented and the convergence of the algorithm is proved

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

adaptive compensation for infinite number of time varying actuator failures in fuzzy tracking control of uncertain nonlinear systems the problem of direct adaptive compensation for infinite number of time varying actuator failures faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems however due to the technical difficulties so far very limited result is available in addressing such an issue which thus motivates us to propose a new fuzzy control methodology in this paper the proposed scheme is established from the techniques of projection adaptation design a new piecewise lyapunov function analysis and an optimized fuzzy adaptation it is shown that all the closed loop signals are bounded and the steady state tracking error converges to a residual around zero irrespective of a possibility that there are infinite number of time varying actuator failures simulations are provided to illustrate the effectiveness and applicability of the proposed scheme

three dimensional structured networks for matrix equation solving two three dimensional structured networks are developed for solving linear equations and the lyapunov equation the basic idea of the structured network approaches is to first represent a given equation solving problem by a 3 d structured network so that if the network matches a desired pattern array the weights of the linear neurons give the solution to the problem then train the 3 d structured network to match the desired pattern array using some training algorithms and finally obtain the solution to the specific problem from the converged weights of the network the training algorithms for the two 3 d structured networks are proved to converge exponentially fast to the correct solutions simulations were performed to show the detailed convergence behaviors of the 3 d structured networks

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

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

variable universe stable adaptive fuzzy control of a nonlinear system abstract a kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first in 1 first of all the basic structure of variable universe adaptive fuzzy controllers is briefly introduced then the contraction expansion factor which is a key tool of the variable universe method is defined by means of the integral regulation idea and then a kind of adaptive fuzzy controller is designed by using such a contraction expansion factor the simulation on the first order nonlinear system is done and as a result its simulation effect is quite good in comparison with the corresponding result in 2 3 second it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of liapunov theory the simulation on a second order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result in 2 besides a useful tool called symbolic factor is proposed which may be of universal significance it can greatly reduce the setting time and enhance the robustness of the system

adaptive control based on explicit model of robot manipulator adaptive and nonadaptive control algorithms which make use of a fundamental mathematical property concerning positive definite matrices and lyapunov stability theory are proposed for the control of robot manipulators using the fact that the matrix dd q dt 2c q dq dt is skew symmetric nonadaptive controllers which have a simplified structure with less computational burden are proposed using the dynamic equations for robot manipulators parameter adaptation rules are developed for updating the controller s partially or totally unknown parameters generalizing them to model reference adaptive controllers to further take advantage of the simplified structure of the proposed adaptive controllers a method for deriving the dynamic model of a robot manipulator which is linear in terms of its parameters is given this dynamic model is also suitable for the pure identification of the parameters of links and payload of the manipulator

adaptive fuzzy sliding mode control of nonlinear system in this paper the fuzzy approximator and sliding mode control smc scheme are considered we propose two methods of adaptive smc schemes that the fuzzy logic systems approximators are used to approximate the unknown system functions in designing the smc of nonlinear system in the first method a fuzzy logic system is utilized to approximate the unknown function f of the nonlinear system x sup n f x t b x t u and the robust adaptive law is proposed to reduce the approximation errors between the true nonlinear functions and fuzzy approximators in the second method two fuzzy logic systems are utilized to approximate the f and b respectively and the control law which is robust to approximation error is also designed the stabilities of proposed control schemes are proved and these schemes are applied to an inverted pendulum system the comparisons between the proposed control schemes are shown in simulations

fuzzy direct adaptive control for a class of nonlinear systems a direct adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems to approximate the optimal controller which is designed on the assumption that all the dynamics in the system are known develops fuzzy sliding controller to compensate for the plant uncertainties smooth the control signals and increase robustness global asymptotic stability is established in the lyapunov sense with the tracking errors converging to a neighborhood of zero the simulation results verify the effectiveness of the proposed control algorithm

second order sliding fuzzy interval type 2 control for an uncertain system with real application a new second order sliding mode type 2 fuzzy controller for nonlinear uncertain perturbed systems is developed in this paper to overcome the constraint on the knowledge of the system model we have used local models that are related to some operating points to synthesize a type 2 nominal fuzzy global model the control is based on the super twisting algorithm which is among second order sliding mode controls smcs moreover two adaptive fuzzy type 2 systems have been introduced to generate the two super twisting signals to avoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upper bounds these adaptive fuzzy type 2 systems are adjusted online by two adaptation laws that are deduced from the stability analysis in the lyapunov sense it has only one input i e the sliding surface and one output i e the optimal values of the gains control which are hard to compute with the original algorithm many results of the one link manipulator are obtained first by the simulation in order to compare the performances of the proposed method with that given by levant and then in a real time application in order to confirm the efficiency of the proposed approach the experimentation and simulation are done for the tracking control problem

observer based adaptive fuzzy control for siso nonlinear systems abstract the observer based indirect and direct adaptive fuzzy controllers are developed for a class of siso uncertain nonlinear systems the proposed approaches do not need the availability of the state variables by designing the state observer the adaptive fuzzy systems which are used to model the unknown functions can be constructed using the state estimations thus a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the h control technique based on lyapunov stability theorem the proposed adaptive fuzzy control system can guarantee the stability of the whole closed loop systems and obtain good tracking performance as well the proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

design of fuzzy wavelet neural networks using the ga approach for function approximation and system identification in this paper an efficient method is proposed to design fuzzy wavelet neural network fwnn for function learning and identification by tuning fuzzy membership functions and wavelet neural networks the structure of fwnn is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules in order to improve the function approximation accuracy and general capability of the fwnn system an efficient genetic algorithm ga approach is used to adjust the parameters of dilation translation weights and membership functions by minimizing a quadratic measure of the error derived from the output of the system the design problem can be characterized by the proposed ga formulation moreover the solution is directly obtained without any need for complicated computations the performance of our approximation is superior to that of existing methods several numerical design examples are likewise presented to demonstrate the design flexibility and usefulness of this presented approach

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

adaptive control of a class of nonlinear pure feedback systems using fuzzy backstepping approach a controller is proposed for the robust backstepping control of a class of nonlinear pure feedback systems using fuzzy logic the proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the usual controllers and the approximation errors can be efficiently counteracted by employing smooth robust compensators most importantly the uniform ultimate boundedness of all signals in the closed loop system can be guaranteed and a priori knowledge of the plant dynamics is no longer required furthermore the proposed method can be used for adaptive control of a large class of single input single output nonlinear systems in both strict feedback and pure feedback forms and has great potential in many diverse applications the performance of the proposed approach is demonstrated through three simulation examples including one nonlinear pure feedback and two nonlinear strict feedback systems

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

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

adaptive fuzzy wavelet network control design for nonlinear systems this paper presents a new adaptive fuzzy wavelet network controller a fwnc for control of nonlinear affine systems inspired by the theory of multiresolution analysis mra of wavelet transforms and fuzzy concepts the proposed adaptive gain controller which results from the direct adaptive approach has the ability to tune the adaptation parameter in the then part of each fuzzy rule during real time operation each fuzzy rule corresponds to a sub wavelet neural network sub wnn and one adaptation parameter each sub wnn consists of wavelets with a specified dilation value the degree of contribution of each sub wnn can be controlled flexibly orthogonal least square ols method is used to determine the number of fuzzy rules and to purify the wavelets for each sub wnn since the efficient procedure of selecting wavelets used in the ols method is not very sensitive to the input dimension the dimension of the approximated function does not cause the bottleneck for constructing fwn fwn is constructed based on the training data set of the nominal system and the constructed fuzzy rules can be adjusted by learning the translation parameters of the selected wavelets and also determining the shape of membership functions then the constructed adaptive fwn controller is employed such that the feedback linearization control input can be best approximated and the closed loop stability is guaranteed the performance of the proposed a fwnc is illustrated by applying a second order nonlinear inverted pendulum system and compared with previously published methods simulation results indicate the remarkable capabilities of the proposed control algorithm it is worth noting that the proposed controller significantly improves the transient response characteristics and the number of fuzzy rules and on line adjustable parameters are reduced

direct robust adaptive fuzzy control drafc for uncertain nonlinear systems using small gain theorem abstract a novel direct robust adaptive fuzzy control drafc is proposed for a class of nonlinear systems with uncertain system and gain functions which both are unstructured or non repeatable state dependent unknown nonlinear functions takagi sugeno type fuzzy logic systems are used to approximate the uncertain system function and the drafc algorithm is designed by use of input to state stability iss approach and small gain theorem the resulting closed loop system is proven to be semi globally uniformly ultimately bounded in addition the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed and the adaptive mechanism with only one learning parameterization can be achieved the control performance of the closed loop system is guaranteed by appropriately choosing the design parameters an example illustrating the proposed method is included for a ship autopilot system to maintain the ship on a pre determined heading simulation results show the effectiveness of the control scheme

a fuzzy decentralized variable structure tracking control with optimal and improved robustness designs theory and applications to begin with each subsystem of a nonlinear interconnected system was approximated by a weighted combination of l linear pulse transfer function systems lptfss for every nominal lptfs of the mth subsystem a dead beat to its switching surface was first designed the output disturbance of the mth lptfs included the interconnections coming from the other subsystems the approximation error of the mth subsystem and the interactions resulting from the other lptfss in general this output disturbance was not small and contains various frequencies under this circumstances the h sup spl infin norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized in addition an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance although the effect of the output disturbance is attenuated and partially rejected a better performance could be enhanced by a switching control based on the lyapunov redesign in addition the stability of the overall system was verified by lyapunov stability theory the simulations for the lptfss with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control finally the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control

parabolic equations for curves on surfaces part i curves with p integrable curvature this is the first of a two part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so called curve shortening of flow by mean curvature problem as well as to a number of models for phase transitions in two dimensions we introduce a class of equations for which the initial value problem is solvable for initial data with p integrable curvature and we also give estimates for the rate at which the p norms of the curvature must blow up if the curve becomes singular in finite time a detailed discussion of the way in which solutions can become singular and a method for continuing the solution through a singularity will be the subject of the second part

robust adaptive fuzzy control in the presence of external disturbance and approximation error robust direct and indirect adaptive fuzzy controllers are proposed for tracking control of a class of nonlinear siso systems the behavior of the adaptive law is investigated in the error state space when the perturbations are introduced in the adaptive fuzzy control system a new adaptation scheme that can eliminate the effect of perturbations on the parameter adaptation is proposed it is proved that all the signals in the closed loop system are bounded in the presence of external disturbances and approximation error of the fuzzy logic system the concept of persistent excitation is utilized to guarantee the convergence and the boundedness of adaptation parameters it has also been observed that the convergence of parameters and tracking error could be smoother and faster with the proposed methods compared with the conventional adaptive fuzzy controllers two simulations have been conducted to demonstrate the effectiveness of the proposed controllers

a computed torque controller for uncertain robotic manipulator systems fuzzy approach computed torque control ctc is an effective motion control strategy for robotic manipulator systems which can ensure globally asymptotic stability however ctc scheme requires precise dynamical models of robotic manipulators to handle this impossibility in this paper a new approach combing ctc and fuzzy control fc is developed for trajectory tracking problems of robotic manipulators with structured uncertainty and or unstructured uncertainty fuzzy part with a set of tunable parameters is employed to approximate lumped uncertainty due to parameters variations unmodeled dynamics and so on in robotic manipulators based on lyapunov stability theorem it is shown that the proposed controller can guarantee stability of closed loop systems and satisfactory tracking performances the proposed approach indicates that ctc method is also valid for controlling uncertain robotic manipulators as long as compensative controller is appropriately designed finally computer simulation results on a two link elbow planar robotic manipulator are presented to show tracking capability and effectiveness of the proposed scheme

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

designing fuzzy controllers from a variable structures standpoint a procedure is presented for designing fuzzy controllers based upon variable structures techniques three such controllers are presented the fuzzy equivalents of sliding mode controllers saturating controllers and tanh controllers by using an approach based upon variables structures vss techniques the stability of each of these controllers is assured by using a sliding surface the order of the rule base is reduced to size r spl times m where r is the number of inputs and m is the number of fuzzification levels this combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties to illustrate the proposed design procedure fuzzy controllers are designed for a ball and beam system it is demonstrated that in spite of this system being a fourth order unstable system the proposed design procedure results in simple stable fuzzy controllers

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented