global attractor for the kirchhoff type equation with a strong dissipation abstract the paper studies the longtime behavior of the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the related continuous semigroup s t possesses in the phase space with low regularity a global attractor which is connected and an example is shown

long time dynamics of kirchhoff wave models with strong nonlinear damping we study well posedness and long time dynamics of a class of quasilinear wave equations with a strong damping we accept the kirchhoff hypotheses and assume that the stiffness and damping coefficients are functions of the l2 norm of the gradient of the displacement we prove the existence and uniqueness of weak solutions and study their properties for a wide class of nonlinearities which covers the case of possible degeneration or even negativity of the stiffness coefficient and the case of a supercritical source term our main results deal with global attractors for strictly positive stiffness factors we prove that in the natural energy space endowed with a partially strong topology there exists a global finite dimensional attractor in the non supercritical case this attractor is strong in this case we also establish the existence of a fractal exponential attractor and give conditions that guarantee the existence of a finite number of determining functionals

parameterization and adaptive control of multivariable noncanonical t s fuzzy systems this paper conducts a new study for adaptive takagi sugeno t s fuzzy approximation based control of multi input and multi output mimo noncanonical form nonlinear systems canonical form nonlinear systems have explicit relative degree structures whose approximation models can be directly used to derive desired parameterized controllers noncanonical form nonlinear systems usually do not have such a feature nor do their approximation models which are also in noncanonical forms this paper shows that it is desirable to reparameterize noncanonical form t s fuzzy system models with smooth membership functions for adaptive control and such system reparameterization can be realized using relative degrees a concept yet to be studied for mimo noncanonical form t s fuzzy systems this paper develops an adaptive feedback linearization scheme for control of such general system models with uncertain parameters by first deriving various relative degree structures and normal forms for such systems then a reparameterization procedure is developed for such system models based on which adaptive control designs are derived with desired stability and tracking properties analyzed a detailed example is presented with simulation results to show the new control design procedure and desired control system performance

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

global fuzzy adaptive hierarchical path tracking control of a mobile robot with experimental validation due to the nature of the complete model with motor dynamics virtual control input i e desired motor current is designed by the first sliding surface so that the indirect output i e 3 d pose of mobile robot is controlled by the direct output i e motor current subsequently the linear dynamic tracking error of the virtual control input is employed to establish the second sliding surface then the hierarchical path tracking control hptc is constructed so that the direct output asymptotically and robustly tracks the virtual control input in the meanwhile the asymptotic tracking of the indirect output is achieved to improve only asymptotical tracking to convex set due to the existence of huge uncertainties e g different ground conditions time varying system parameters external disturbances two online fuzzy models of uncertainties are plunged into the hptc with a switching mechanism to design the so called global fuzzy adaptive hptc for a mobile robot moreover the global adaptive path tracking control for different initial system states outside of approximated set is achieved the simulations confirm the effectiveness efficiency and practicality of the proposed technique two compared experiments also validate the consistence with the simulation result

some notes on equivalent fuzzy sets and fuzzy subgroups this paper discusses the problems of equivalent fuzzy sets and fuzzy subgroups first a critical discussion of previous results by murali and makamba is provided second this paper discusses the conditions under which the equivalence relation of fuzzy sets can be equivalently described by their level sets it also suggests that the equivalence approach to the classification of fuzzy subgroups is suitable only for finite groups and proposes a new definition for the classification of fuzzy subgroups s equivalence showing that any two fuzzy subgroups of an infinite cyclic group with infinite membership values are s equivalent

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

set membership approximation theory for fast implementation of model predictive control laws in this paper the use of set membership sm methodologies is investigated in the approximation of model predictive control mpc laws for linear systems such approximated mpc laws are derived from a finite number n of exact control moves computed off line properties in terms of guaranteed approximation error closed loop stability and performance are derived assuming only the continuity of the exact predictive control law these results are achieved by means of two main contributions at first it will be shown that if the approximating function enjoys two key properties i e fulfillment of input constraints and explicit evaluation of a bound on the approximation error which converges to zero as n increases then it is possible to guarantee the boundedness of the controlled state trajectories inside a compact set their convergency to an arbitrary small neighborhood of the origin and satisfaction of state constraints moreover the guaranteed performance degradation in terms of maximum state trajectory distance can be explicitly computed and reduced to an arbitrary small value by increasing n then two sm approximations are investigated both enjoying the above key properties the first one minimizes the guaranteed approximation error but its on line computational time increases with n the second one has higher approximation error but lower on line computational time which is constant with n when the off line computed moves are suitably chosen the presented approximation techniques can be systematically employed to obtain an efficient mpc implementation for fast processes the effectiveness of the proposed techniques is tested on two numerical examples

longtime behavior of the kirchhoff type equation with strong damping on rn abstract the paper studies the longtime behavior of the kirchhoff type equation with strong damping on r n u t t m u 2 u u t u u t g x u f x it shows that the related continuous semigroup s t possesses a global attractor which is connected and has finite fractal and hausdorff dimension

a fuzzy lyapunov krasovskii functional approach to sampled data output feedback stabilization of polynomial fuzzy systems this paper presents an output feedback exponential stabilization condition of sampled data polynomial fuzzy control systems under variable sampling rates compared with previous work the proposed method is less conservative because of the newly developed time dependent fuzzy lyapunov krasovskii functional that is based on the conventional fuzzy lyapunov function moreover the controller is allowed to contain polynomial gain matrices thereby improving the control performance and design flexibility this is realized by assuming the difference between the continuous and discrete time state vectors as time varying norm bounded uncertainties which are manipulated using a robust control technique a new sufficient condition is introduced to cast the stability condition containing the integral term as the sum of square conditions finally the effectiveness of the proposed method is validated by simulations

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

fuzzy radicals and prime fuzzy ideals of ordered semigroups let s be an ordered semigroup a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers motivated by studying prime fuzzy ideals in rings semigroups and ordered semigroups and as a continuation of kehayopulu and tsingelis s works in ordered semigroups in terms of fuzzy subsets in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup s and give a characterization of prime fuzzy ideals of an ordered semigroup s we also introduce the concepts of weakly prime fuzzy ideals completely prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup s and establish the relationship between the five classes of ideals furthermore we characterize weakly prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of s by their level ideals finally we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup s can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it as an application of the results of this paper the corresponding results of semigroups without order are also obtained

fuzzy adaptive control with state observer for a class of nonlinear discrete time systems with input constraint in this paper an adaptive fuzzy controller is constructed for a class of nonlinear discrete time systems with unknown functions and bounded disturbances the main characteristics of the systems are that they take into account the effect of discrete time dead zone and the system states are not required to be measurable the stability problem of this class of systems is for the first time to be addressed in this paper due to the unavailability of the states and the presence of the discrete time dead zone the controller design becomes more difficult to stabilize the uncertain nonlinear discrete time systems the fuzzy logic systems are used to approximate the unknown functions a fuzzy state observer is designed to estimate the immeasurable states and the effect caused by discrete time dead zone can be solved via establishing an adaptation auxiliary signal based on the lyapunov approach it is proved that all the signals of the closed loop system are the semiglobal uniformly ultimately bounded and the tracking error is made within a small neighborhood around zero the feasibility of the developed control scheme is verified via two simulation examples

novel neural control for a class of uncertain pure feedback systems this paper is concerned with the problem of adaptive neural tracking control for a class of uncertain pure feedback nonlinear systems using the implicit function theorem and backstepping technique a practical robust adaptive neural control scheme is proposed to guarantee that the tracking error converges to an adjusted neighborhood of the origin by choosing appropriate design parameters in contrast to conventional lyapunov based design techniques an alternative lyapunov function is constructed for the development of control law and learning algorithms differing from the existing results in the literature the control scheme does not need to compute the derivatives of virtual control signals at each step in backstepping design procedures furthermore the scheme requires the desired trajectory and its first derivative rather than its first n derivatives in addition the useful property of the basis function of the radial basis function which will be used in control design is explored simulation results illustrate the effectiveness of the proposed techniques

adaptive neural pd control with semiglobal asymptotic stabilization guarantee this paper proves that adaptive neural plus proportional derivative pd control can lead to semiglobal asymptotic stabilization rather than uniform ultimate boundedness for a class of uncertain affine nonlinear systems an integral lyapunov function based ideal control law is introduced to avoid the control singularity problem a variable gain pd control term without the knowledge of plant bounds is presented to semiglobally stabilize the closed loop system based on a linearly parameterized raised cosine radial basis function neural network a key property of optimal approximation is exploited to facilitate stability analysis it is proved that the closed loop system achieves semiglobal asymptotic stability by the appropriate choice of control parameters compared with previous adaptive approximation based semiglobal or asymptotic stabilization approaches our approach not only significantly simplifies control design but also relaxes constraint conditions on the plant two illustrative examples have been provided to verify the theoretical results

adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics in this paper the problems of stability and tracking control for a class of large scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach because the dynamic surface control technique is introduced the designed controllers can avoid the issue of explosion of complexity which comes from the traditional backstepping design procedure that deals with large scale nonlinear systems with unmodeled dynamics in addition a reduced order observer is designed to estimate those immeasurable states based on the lyapunov stability method it is proven that all the signals in the closed loop system are bounded and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately the simulation examples are given to verify the effectiveness of the proposed techniques

finite dimensional attractors for the kirchhoff equation with a strong dissipation abstract the paper studies the existence of the finite dimensional global attractors and exponential attractors for the dynamical system associated with the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the above mentioned dynamical system possesses a global attractor which has finite fractal dimension and an exponential attractor for application the fact shows that for the concerned viscoelastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

on an equivalence of fuzzy subgroups ii this paper forms a sequel to the paper on an equivalence of fuzzy subgroups i here we determine the number of distinct equivalence classes of fuzzy subgroups of g z p 1 z p n where p 1 p 2 p n are distinct primes we introduce the notion of a keychain of a chain of length n 1 and index of a keychain in order to determine the number of fuzzy subgroups of g we achieve this by using induction on the index of a keychain

stability of exponential attractors for a family of semilinear wave equations with gentle dissipation abstract the paper investigates the stability of exponential attractors for a family of semilinear wave equations with gentle dissipation u t t u u t f u g x with 0 1 2 i we propose a new criterion on the existence and stability of a family of exponential attractors depending on the perturbation parameters ii by applying this criterion to the equations we construct a family of exponential attractors a e x p and show their stability on the dissipative exponent

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

robust fuzzy neural network control for nonlinear motor toggle servomechanism abstract in this study a robust control system using an takagi sugeno kang tsk type fuzzy neural network fnn is proposed to control a nonlinear toggle mechanism that is driven by a permanent magnet pm synchronous servo motor first the dynamic model of a motor toggle servomechanism is introduced then a robust control system is proposed to control the motor mechanism coupling system for periodic motion the design procedure of the proposed robust control system is described in detail in the robust control system the fnn controller is the main tracking controller which is used to mimic a perfect control law and the compensated controller is proposed to compensate the difference between the perfect control law and the fnn controller moreover an on line parameter training methodology which is derived using the lyapunov stability theorem and the backpropagation method is proposed to increase the learning capability of the fnn in addition to relax the requirement for the bound of minimum approximation error a simple bound estimation algorithm is investigated to control the motor mechanism coupling system the effectiveness of the proposed control scheme is verified by both numerical simulation and experimental results

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

two mode adaptive fuzzy control with approximation error estimator in this paper we propose a two mode adaptive fuzzy controller with approximation error estimator in the learning mode the controller employs some modified adaptive laws to tune the fuzzy system parameters and an approximation error estimator to compensate for the inherent approximation error in the operating mode the fuzzy system parameters are fixed only the estimator is updated online mathematically we show that the closed loop system is stable in the sense that all the variables are bounded in both modes we also establish mathematical bounds on the tracking error state vector control signal and the rms error using these bounds we show that controller s design parameters can be chosen to achieve desired control performance after that an algorithm to automatically switch the controller between two modes is presented finally simulation studies of an inverted pendulum system and a chua s chaotic circuit demonstrate the usefulness of the proposed controller

nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks this paper presents an adaptive nonsingular terminal sliding mode ntsm tracking control design for robotic systems using fuzzy wavelet networks compared with linear hyperplane based sliding control terminal sliding mode controller can provide faster convergence and higher precision control therefore a terminal sliding controller combined with the fuzzy wavelet network which can accurately approximate unknown dynamics of robotic systems by using an adaptive learning algorithm is an attractive control approach for robots in addition the proposed learning algorithm can on line tune parameters of dilation and translation of fuzzy wavelet basis functions and hidden to output weights therefore a robust control law is used to eliminate uncertainties including the inevitable approximation errors resulted from the finite number of fuzzy wavelet basis functions the proposed controller requires no prior knowledge about the dynamics of the robot and no off line learning phase moreover both tracking performance and stability of the closed loop robotic system can be guaranteed by lyapunov theory finally the effectiveness of the fuzzy wavelet network based control approach is illustrated through comparative simulations on a six link robot manipulator

stability of attractors for the kirchhoff wave equation with strong damping and critical nonlinearities abstract the paper investigates longtime dynamics of the kirchhoff wave equation with strong damping and critical nonlinearities u t t 1 u 2 u u t h u t g u f x with 0 1 the well posedness and the existence of global and exponential attractors are established and the stability of the attractors on the perturbation parameter is proved for the ibvp of the equation provided that both nonlinearities h s and g s are of critical growth

stable model reference adaptive fuzzy control of a class of nonlinear systems in this paper we propose a new adaptive fuzzy control scheme called model reference adaptive fuzzy control mrafc the mrafc scheme employs a reference model to provide closed loop performance feedback for generating or modifying a fuzzy controller s knowledge base the mrafc scheme grew from ideas in conventional model reference adaptive control mrac the mrafc scheme is developed to perform adaptive feedback linearization to a class of nonlinear systems a class of fuzzy controllers which can be expressed in an explicit form is used as the primary controller based on lyapunov s second method we have developed mrafc schemes and derived fuzzy rule adaptive laws hence not only the stability of the system can be assured but also the performance such as the issues of robustness and parameter convergence of the mrafc system can be analyzed explicitly we showed that in the case of no modeling error the state error converges to zero asymptotically in the case that persistent excitation is satisfied we showed that the mrafc system is asymptotically stable by considering the periodic signal as reference input signal we showed that the square wave can make the mrafc system be persistently excited the feasibility of applying these techniques has been demonstrated by considering the control of an inverted pendulum in following a reference model response

adaptive fuzzy sliding mode control for electrical servo drive in this study an adaptive fuzzy sliding mode control afsmc system with an integral operation switching surface is adopted to control the position of an electrical servo drive the afsmc system is comprised of a fuzzy control design and a hitting control design in the fuzzy control design a fuzzy controller is designed to mimic a feedback linearization fl control law in the hitting control design a hitting controller is designed to compensate the approximation error between the fl control law and the fuzzy controller the tuning algorithms are derived in the sense of the lyapunov stability theorem thus the stability of the system can be guaranteed moreover to relax the requirement for the bound of approximation error an error estimation mechanism is investigated to observe the bound of approximation error real time experimental results verify that the proposed control systems can achieve favorable tracking performance and robust with regard to parameter variations and external load disturbance

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

fuzzy approximation based adaptive control of nonlinear delayed systems with unknown dead zone this paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict feedback form a new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead zone nonlinearity control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems the proposed adaptive fuzzy controller guarantees that all the closed loop signals are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples illustrate the effectiveness of the proposed approach

global solutions for dissipative kirchhoff strings with non lipschitz nonlinear term we investigate the evolution problem u u m a 1 2 u 2 au 0 u 0 u0 u 0 u1 where h is a hilbert space a is a self adjoint nonnegative operator on h with domain d a 0i s a parameter and m r is a nonnegative function such that m 0 0a ndm is nonnecessarily lipschitz continuous in a neighborhood of 0 we prove that this problem has a unique global solution for positive times provided that the initial data u0 u 1 d a d a 1 2 satisfy a suitable smallness assumption and the nondegeneracy condition m a 1 2 u0 2 0 moreover we study the decay of the solution as t these results apply to degenerate hyperbolic pdes with nonlocal nonlinearities

adaptive fuzzy control with guaranteed convergence of optimal approximation error with no a priori knowledge of plant boundary functions a novel direct adaptive fuzzy controller afc for a class of single input single output siso uncertain affine nonlinear systems is developed in this paper based on the theory of fuzzy logic systems flss with variable universes of discourse uds sufficient conditions that guarantee that the optimal fuzzy approximation error fae is locally convergent are given by the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters a variable ud fls with an optimal fae local convergence is constructed and its parameter adaptive law is derived by virtue of the lyapunov stability theorem under the assumption that the optimal fae is bounded it is proved that the closed loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero the proposed approach eliminates the influence of the fae on the tracking errors by means of the inherent mechanism of the variable ud fls thus it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules simulation studies demonstrate the superiority of the proposed afc in terms of the settling time tracking accuracy smoothness of the control input and robustness against external disturbances and parameter variations

a combined backstepping and stochastic small gain approach to robust adaptive fuzzy output feedback control in this paper an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict feedback systems without the requirement of states measurement the stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties unknown nonlinear functions and in the presence of unmodeled dynamics dynamics disturbances fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by combining the backstepping design technique with the stochastic small gain approach a new adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that the closed loop system is input state practically stability isps in probability and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance in addition the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties

adaptive fuzzy control of a class of mimo nonlinear systems this paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous time multi input multi output nonlinear dynamic systems within these schemes fuzzy systems are employed to approximate the plant s unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors by using a regularized matrix inverse a stable well defined adaptive controller is firstly investigated then in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values a second adaptive controller is proposed all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that under appropriate assumptions semi global stability and asymptotic convergence to zero of tracking errors can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

finite dimensional attractors for the quasi linear strongly damped wave equation abstract we present a new method of investigating the so called quasi linear strongly damped wave equations t 2 u t x u x u f u x x u g in bounded 3d domains this method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non linearity is less than 6 and f may have arbitrary polynomial growth rate moreover the existence of a finite dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity are also established in a particular case 0 which corresponds to the so called semi linear strongly damped wave equation our result allows to remove the long standing growth restriction f u c 1 u 5

adaptive fuzzy decentralized output feedback control for nonlinear large scale systems with unknown dead zone inputs in this paper the problem of adaptive fuzzy decentralized backstepping control is considered for a class of nonlinear large scale strict feedback systems with unknown dead zones and immeasurable states fuzzy logic systems are used to approximate the unknown nonlinear functions and a state filter is designed to estimate the immeasurable states applying an adaptive backstepping design technique and combining it with the dead zone inverse method an adaptive fuzzy decentralized output feedback backstepping control is developed it is proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and tracking errors converge to a small neighborhood of the origin by appropriate choice of design parameters simulation results are given to demonstrate that the proposed adaptive decentralized control approach has a satisfactory control performance

robust control of an lusm based x hbox y hbox theta motion control stage using an adaptive interval type 2 fuzzy neural network the robust control of a linear ultrasonic motor based x y thetas motion control stage to track various contours is achieved by using an adaptive interval type 2 fuzzy neural network ait2fnn control system in this study in the proposed ait2fnn control system an it2fnn which combines the merits of an interval type 2 fuzzy logic system and a neural network is developed to approximate an unknown dynamic function moreover adaptive learning algorithms are derived using the lyapunov stability theorem to train the parameters of the it2fnn online furthermore a robust compensator is proposed to confront the uncertainties including the approximation error optimal parameter vectors and higher order terms in taylor series to relax the requirement for the value of lumped uncertainty in the robust compensator an adaptive lumped uncertainty estimation law is also investigated in addition the circle and butterfly contours are planned using a nonuniform rational b spline curve interpolator the experimental results show that the contour tracking performance of the proposed ait2fnn is significantly improved compared with the adaptive type 1 fnn additionally the robustness to parameter variations external disturbances cross coupled interference and frictional force can also be obtained using the proposed ait2fnn

from fuzzy sets to the decompositions of non rigid sets the concept of identifying a fuzzy subset of a set r with its collection of level sets and its collection of membership values plays an important role in many real life applications such identification is possible only if the fuzzy set can be recaptured this implies that uniqueness of the fuzzy set plays an important role it has been recently shown that in order to have uniqueness it is necessary and sufficient that the collection s of membership values of the fuzzy set be a rigid set with this in mind the authors went on to show that if s has the min max property then s is a rigid set and left the converse as an open problem we start this paper by constructing a counterexample that shows that rigid sets do not have to have the min max property we then take a closer look at non rigid sets by decomposing them into isomorphism invariant components and into s connected components in the hope of getting a characterization of non rigid sets which will lead to a characterization of rigid sets and hence of uniqueness of the fuzzy set we also investigate in the case of nonuniqueness the number of fuzzy sets corresponding to a collection of level sets and a collection of membership values

dynamic structure adaptive neural fuzzy control for mimo uncertain nonlinear systems this paper proposes a novel dynamic structure neural fuzzy network dsnfn to address the adaptive tracking problems of multiple input multiple output mimo uncertain nonlinear systems the proposed control scheme uses a four layer neural fuzzy network nfn to estimate system uncertainties online the main feature of this dsnfn is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors projection type adaptation laws for the network parameters are derived from the lyapunov synthesis approach to ensure network convergence and stable control a hybrid control scheme that combines the sliding mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors as the employment of the dsnfn high quality tracking performance could be achieved in the system furthermore the trained network avoids the problems of overfitting and underfitting simulations performed on a two link robot manipulator demonstrate the effectiveness of the proposed control scheme

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

adaptive fuzzy control compensation design for direct adaptive fuzzy control for direct adaptive fuzzy control of perturbed uncertain nonlinear systems proportional integral derivative control compensation usually has to be used to guarantee h infty tracking performance or l 2 gain property of the closed loop system one common problem is that the control compensation often introduces unwanted high gain at the control input this paper proves that classical direct adaptive fuzzy control with adaptive fuzzy control compensation not only is capable of solving the problem of high gain but also can guarantee l 2 gain property of the closed loop system a sliding surface based adaptive fuzzy control is designed for control compensation by using a class of triangular membership functions nearest to the origin and a simple adaptive law the adaptive fuzzy control term is converted to an equivalence control term which is used to facilitate stability analysis moreover the system output can track not only the constant period periodic signals but also the constant signal compared with previous direct adaptive fuzzy control approaches that can guarantee h infty tracking performance or l 2 gain property in addition to the l 2 gain property of common tracking error rather than modified tracking error the major advantages of our approach are that the assumptions on control gain function are relaxed and a less conservative control design on robustness is achieved simulation results are given to demonstrate the effectiveness of the proposed approach

uniqueness in the generalized representation by fuzzy sets the concept of representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets is widely used in the literature for the classification and study of fuzzy algebraic structures on the same underlying set the problem of existence of such fuzzy sets was investigated by various authors as far as we know the problem of uniqueness of such fuzzy sets was not studied before we establish among other things necessary and sufficient conditions under which uniqueness is guaranteed in the cases of complete as well as partial representations of the level sets of the fuzzy set

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

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

enhanced adaptive fuzzy control with optimal approximation error convergence in this paper an enhanced adaptive fuzzy control afc strategy with guaranteed convergence of an optimal fuzzy approximation error fae is presented for a class of uncertain nonlinear systems in the general brunovsky form based on the fuzzy logic system fls with variable universes of discourse relaxed sufficient conditions that guarantee the optimal fae being convergent are given and the upper bound of the optimal fae is obtained the control singularity problem resulting from the unknown affine term is resolved by a novel fuzzy approximation equation and the parameter adaptive law of the fls is derived by the lyapunov synthesis by means of the optimal fae bound result it is proved that the closed loop system achieves partially asymptotic stability under a certain selection of control parameters the proposed approach retains all advantages of a previous similar approach under relaxed constraint conditions thus it provides a more flexible solution to the afc with optimal fae convergence simulation studies have demonstrated high precision tracking performance with smooth control input of the proposed approach

a note on a natural equivalence relation on fuzzy power set the necessary and sufficient conditions under which two fuzzy sets with the same domain have equal families of cut sets are given consequently there is a corresponding equivalence relation on the related fuzzy power set the collection of classes under this relation can be ordered and we give a necessary and sufficient condition under which it is a lattice

adaptive fuzzy hierarchical sliding mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems the trajectory tracking of uncertain underactuated nonlinear dynamic systems is tackled by an adaptive fuzzy hierarchical sliding mode control afhsmc first one of the subsystems is assigned as the first layer sliding surface next a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem is constructed in this paper the nth layer is supposed to be the top layer or hierarchical layer for including the sliding surfaces of all subsystems because two nonlinear system functions and the time varying external disturbance of each subsystem are supposed to be unknown different online fuzzy models are employed to approximate these nonlinear system functions and the upper bounded functions of external disturbances moreover the upper bound of uncertainties caused by these fuzzy modeling errors is estimated online based on these learning fuzzy models and the estimated upper bound of these modeling errors an afhsmc is developed the stability analysis and tracking performance of the closed loop system are verified by lyapunov stability theory finally two simulation examples including different amplitudes of external disturbance and comparison with hierarchical sliding mode control confirm the effectiveness and robustness of the proposed control