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

a lagrangian sphere which is not a vanishing cycle we give examples of calabi yau threefolds containing lagrangian spheres which are not vanishing cycles of nodal degenerations answering a question of donaldson in the negative

uniformly ultimately bounded fuzzy adaptive tracking controllers for uncertain systems fuzzy adaptive tracking controllers for a class of uncertain nonlinear dynamical systems are proposed and analyzed the controllers consist of adaptive and robustifying components whose role is to nullify the effects of uncertainties and to achieve a desired tracking performance the interactions between the two components have been investigated the closed loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded in particular the proposed controllers guarantee uniform ultimate boundedness of the tracking error and the time bound of the uniform ultimate boundedness is obtained an upper bound on the steady state tracking error is obtained as a function of the gain of the robustifying term and the parameters of the adaptive component the controllers are tested on an inverted pendulum and simulation results are included a comparison of the proposed controllers with the ones in the literature is conducted

fuzzy model based adaptive control for a class of nonlinear systems a fuzzy model based adaptive control algorithm for a class of continuous time nonlinear dynamic systems is presented the fuzzy model consisting of a set of linear fuzzy local models that are combined using a fuzzy inference mechanism is used to model a class of nonlinear systems each fuzzy local model represents a linearized model corresponding to the operating point of the controlled nonlinear system the proposed control algorithm employs the fuzzy controller that is designed by considering the linear state feedback controller corresponding to the fuzzy local model with the maximum weight and the switching spl sigma modification adaptive controller to adaptively compensate for the plant nonlinearities stability robustness of the closed loop system is analyzed in lyapunov sense it is shown that the proposed control algorithm guarantees global stability of the system with the output of the system approaching the origin if there are no disturbances and uncertainties converging to the neighborhood of the origin for all realizations of uncertainties and disturbances the simulation examples for controlling inverted pendulum system are given to illustrate the effectiveness of the proposed method

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

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

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

fuzzy adaptive output feedback control for mimo nonlinear systems in this paper two observer based adaptive fuzzy output feedback control schemes are presented for a class of uncertain continuous time multi input multi output mimo nonlinear dynamics systems whose states are not available within these schemes fuzzy logic systems are employed to approximate the plant s unknown nonlinear functions and then the state observer is designed for estimating the states of the plant upon which a fuzzy adaptive output feedback controller is firstly investigated in order to overcome the controller singularity problem and relax the requirement of bounding parameter values a second modified fuzzy adaptive output feedback controller is proposed by using a regularized inverse and a robustifying control term all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that convergence to zero of tracking errors and boundedness of all signals in the closed loop system can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

a self organizing fuzzy control approach for bank to turn missiles abstract in this paper an adaptive fuzzy autopilot is developed for bank to turn btt missiles we propose a self organizing rotated fuzzy basis function control system that is more flexible than fuzzy basis function expansion in that not only the output weights but also the shapes of fuzzy basis functions can be tuned another characteristic of this autopilot is to incorporate the terminal attractor controller into the autopilot to speed up the convergence rate the global stability analysis established in the lyapunov sense shows that the states and tracking errors of the btt missile are uniformly bounded finally there are two simulation examples to demonstrate the effectiveness of the proposed autopilot the purpose of the first example is to indicate the better performance including faster convergence speed and lower steady state error obtained by autopilots with terminal attractors as compared with that autopilot without terminal attractor another simulation result proves that btt missile can manipulate under various flight conditions in our scenarios and shows the superior tracking performance

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

nonlinear internal model control application of inverse model based fuzzy control this paper investigates the possible applications of dynamical fuzzy systems to control nonlinear plants with asymptotically stable zero dynamics using a fuzzy nonlinear internal model control strategy the developed strategy consists in including a dynamical takagi sugeno fuzzy model of the plant within the control structure in this way the controller design simply results in a fuzzy model inversion in this framework the originality of the presented work lies in the use of a dynamical fuzzy model and its inversion in order to be able to implement the control structure two crucial points have to be addressed in the considered fuzzy context on the one hand the model representation and identification on the other the model inversion as the fuzzy system can be viewed as a collection of elementary subsystems its inversion is approached here in a local way i e on the elementary subsystems capable to provide an inverse solution in this case the inversion of the global fuzzy system is thus tackled by inversion of some of its components by doing so exact inversion is obtained and offset free performances are ensured in order to guarantee a desired regulation behavior and robustness of stability of the control system the fuzzy controller is connected in series with a robustness filter the potential of the proposed method is demonstrated with simulation examples

layered neural networks with gaussian hidden units as universal approximations a neural network with a single layer of hidden units of gaussian type is proved to be a universal approximator for real valued maps defined on convex compact sets of rn

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

adaptive control of a class of nonlinear systems with fuzzy logic an 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 which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

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

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

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

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

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

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

global far field computational boundary conditions for c and 0 grid topologies global far field computational boundary conditions for inviscid external flow problems have been developed for c and o grid topologies this analysis represents a unified approach for two dimensional external flow problems these boundary conditions are derived from analytic solutions of an asymptotic form of the steady state euler equations and have improved accuracy compared to characteristic boundary conditions commonly used in practice the euler equations are asymptotically linearized about a constant pressure rectilinear flow condition which is the true boundary condition at infinity previous work had developed higher order boundary conditions for c grid topologies by assuming small perturbations in both pressure and flow direction at and beyond the computational boundary by decoupling the inflow and outflow analyses and by linearizing the thermodynamic relations this work lifts these restrictions although some higher order compressibility effects are neglected it is based on a global mapping of the boundary and solution of the resulting dirichlet neumann problem because the euler equations are used to develop the boundary conditions the flow crossing the boundary can be rotational the boundary conditions can be used with any numerical euler solution method and allow computational boundaries to be located very close to the nonlinear region of interest this leads to a significant reduction in the number of grid points required for numerical solution numerical results are presented that show that the boundary conditions and far field analytic solutions provide a smooth transition across a computational boundary to the true far field conditions at infinity they also demonstrate the synergism that can be realized from coupling analytic and computational methods

model reference output feedback fuzzy tracking control design for nonlinear discrete time systems with time delay in this study a model reference fuzzy tracking control design for nonlinear discrete time systems with time delay is introduced first the takagi and sugeno ts fuzzy model is employed to approximate a nonlinear discrete time system with time delay next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs the advantage of proposed tracking control design is that only a simple fuzzy observer based controller is used in our approach without feedback linearization technique and complicated adaptive scheme by the proposed method the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem lmip the lmip can be efficiently solved using the convex optimization techniques simulation example is given to illustrate the design procedures and tracking performance of the proposed method

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

robust integral of neural network and error sign control of mimo nonlinear systems this paper presents a novel state feedback control scheme for the tracking control of a class of multi input multioutput continuous time nonlinear systems with unknown dynamics and bounded disturbances first the control law consisting of the robust integral of a neural network nn output plus sign of the tracking error feedback multiplied with an adaptive gain is introduced the nn in the control law learns the system dynamics in an online manner while the nn residual reconstruction errors and the bounded disturbances are overcome by the error sign signal since both of the nn output and the error sign signal are included in the integral the continuity of the control input is ensured the controller structure and the nn weight update law are novel in contrast with the previous effort and the semiglobal asymptotic tracking performance is still guaranteed by using the lyapunov analysis in addition the nn weights and all other signals are proved to be bounded simultaneously the proposed approach also relaxes the need for the upper bounds of certain terms which are usually required in the previous designs finally the theoretical results are substantiated with simulations

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

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

on the design of observer based fuzzy adaptive controller for nonlinear systems with unknown control gain sign in this paper an observer based fuzzy adaptive controller for nonlinear systems with unknown control gain sign is investigated because the system states are not available for measurement a tracking error observer is constructed in this controller the adaptive fuzzy system is used to approximate the unknown nonlinearities and the nussbaum function is incorporated to deal with the unknown control direction i e with the unknown control gain sign the stability of the closed loop system is proven using the strictly positive real spr condition and lyapunov theory finally simulation results are given to verify the feasibility and effectiveness of the proposed controller

fuzzy system identification using an adaptive learning rule with terminal attractors a fuzzy model with an adaptive learning rule is proposed to approximate a class of nonlinear systems the proposed adaptive learning rule uses the concept of terminal attractors and guarantees that the identification is stable and fast convergence in finite time another subject of this paper is to determine the appropriate rule number of the fuzzy model required for a desired modeling error a learning algorithm is also introduced to identify the centers of membership functions of fuzzy outputs

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