radial basis function based adaptive fuzzy systems and their applications to system identification and prediction abstract in this paper we describe a neuro fuzzy system with adaptive capability to extract fuzzy if then rules from input and output sample data through learning the proposed system called radial basis function rbf based adaptive fuzzy system afs employs the gaussian functions to represent the membership functions of the premise part of fuzzy rules three architectural deviations of the rbf based afs are also presented according to different consequence types such as constant first order linear function and fuzzy variable these provide versatility of the network to handle arbitrary fuzzy inference schemes we present examples of system identification and time series prediction to illustrate how to solve these problems and to demonstrate its validity and effectiveness using the rbf based afs

categorified central extensions etale lie 2 groups and lieʼs third theorem for locally exponential lie algebras abstract lie s third theorem asserting that each finite dimensional lie algebra is the lie algebra of a lie group fails in infinite dimensions the modern account on this phenomenon is the integration problem for central extensions of infinite dimensional lie algebras which in turn is phrased in terms of an integration procedure for lie algebra cocycles this paper remedies the obstructions for integrating cocycles and central extensions from lie algebras to lie groups by generalising the integrating objects those objects obey the maximal coherence that one can expect moreover we show that they are the universal ones for the integration problem the main application of this result is that a mackey complete locally exponential lie algebra e g a banach lie algebra integrates to a lie 2 group in the sense that there is a natural lie functor from certain lie 2 groups to lie algebras sending the integrating lie 2 group to an isomorphic lie algebra

observer based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems this paper proposes an observer based indirect adaptive fuzzy sliding mode controller with state variable filters for a certain class of unknown nonlinear dynamic systems in which not all the states are available for measurement to design the proposed controller we first construct the fuzzy models to describe the input output behavior of the nonlinear dynamic system then an observer is employed to estimate the tracking error vector based on the observer a fuzzy sliding model controller is developed to achieve the tracking performance then a filtered observation error vector is obtained by passing the observation error vector to a set of state variable filters finally on the basis of the filtered observation error vector the adaptive laws are proposed to adjust the free parameters of the fuzzy models the stability of the overall control system is analyzed based on the lyapunov method simulation results illustrate the design procedures and demonstrate the tracking performance of the proposed controller

a convergent numerical scheme for integrodifferential kinetic models of angiogenesis abstract we study a robust finite difference scheme for integrodifferential kinetic systems of fokker planck type modeling tumor driven blood vessel growth the scheme is of order one and enjoys positivity features we analyze stability and convergence properties and show that soliton like asymptotic solutions are correctly captured we also find good agreement with the solution of the original stochastic model from which the deterministic kinetic equations are derived working with ensemble averages a numerical study clarifies the influence of velocity cut offs on the solutions for exponentially decaying data

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

adaptive hybrid type 2 intelligent sliding mode control for uncertain nonlinear multivariable dynamical systems a new adaptive hybrid interval type 2 fuzzy neural network fnn controller incorporating sliding mode and lyapunov synthesis approaches is proposed in this paper to handle the training data corrupted by noise or rule uncertainties for a class of uncertain nonlinear multivariable dynamic systems the hybrid adaptive fnn controller the free parameters of which can be tuned on line by an output feedback control law and adaptive laws is a combination of interval type 2 indirect and direct adaptive fnn controllers to meet the requirement of sufficient reach for the sliding mode control a weighting factor which can be adjusted based on the trade off between plant knowledge and control knowledge is included when combining the control efforts of the indirect adaptive fnn controller and the direct adaptive fnn controller the overall adaptive control scheme guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded the mass spring damper nonlinear system is fully illustrated to track sinusoidal signals the resulting adaptive hybrid interval type 2 fnn control system shows better performance than the adaptive hybrid type 1 fnn control system it reduces both the tracking error and the control effort and it is more flexible in the design process

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

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

on the homotopy type of higher orbifolds and haefliger classifying spaces abstract we describe various equivalent ways of associating to an orbifold or more generally a higher etale differentiable stack a weak homotopy type some of these ways extend to arbitrary higher stacks on the site of smooth manifolds and we show that for a differentiable stack x arising from a lie groupoid g the weak homotopy type of x agrees with that of b g using this machinery we are able to find new presentations for the weak homotopy type of certain classifying spaces in particular we give a new presentation for the borel construction m g e g of an almost free action of a lie group g on a smooth manifold m as the classifying space of a category whose objects consist of smooth maps r n m which are transverse to all the g orbits where n dim m dim g we also prove a generalization of segal s theorem which presents the weak homotopy type of haefliger s groupoid q as the classifying space of the monoid of self embeddings of r q b emb r q and our generalization gives analogous presentations for the weak homotopy type of the lie groupoids 2 q s p and r q which are related to the classification of foliations with transverse symplectic forms and transverse metrics respectively we also give a short and simple proof of segal s original theorem using our machinery

fuzzy adaptive learning control network with on line neural learning abstract this paper addresses the structure and the associated on line learning algorithms of a feedforward multilayered connectionist network for realizing the basic elements and functions of a traditional fuzzy logic controller the proposed fuzzy adaptive learning control network falcon can be contrasted with the traditional fuzzy logic control systems in their network structure and learning ability the connectionist structure of the proposed falcon can be constructed from training examples by neural learning techniques to find proper fuzzy partitions membership functions and fuzzy logic rules two complementary on line structure parameter learning algorithms falcon fsm and falcon art are proposed for constructing the falcon dynamically the falcon fsm combines the backpropagation learning scheme for parameter learning and a fuzzy similarity measure for structure learning the falcon fsn can find proper fuzzy logic rules membership functions and the size of output partitions simultaneously in the falcon fsm algorithm the input and output spaces are partitioned into grids the grid typed space partitioning certainly makes both the fuzzy logic controller software emulation and fuzzy chip implementation convenient however as the number of input output variables increases the number of partitioned grids will grow combinatorially to avoid the problem of combinatorial growth of partitioned grids in some complex systems the falcon art algorithm is developed which can partition the input and output spaces in a more flexible way based on the distribution of the training data the falcon art combines the backpropagation learning scheme for parameter learning and a fuzzy art algorithm for structure learning the falcon art can on line partition the input and output spaces tune membership functions and find proper fuzzy logic rules dynamically computer simulations were conducted to illustrate the performance and applicability of both falcon fsm and falcon art learning algorithms

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

a novel optimization procedure for training of fuzzy inference systems by combining variable structure systems technique and levenberg marquardt algorithm abstract this paper presents a novel training algorithm for fuzzy inference systems the algorithm combines the levenberg marquardt algorithm with variable structure systems approach the combination is performed by expressing the parameter update rule in continuous time and application of sliding mode control method to the gradient based training procedure the proposed combination therefore exhibits a degree of robustness to the unmodeled multivariable internal dynamics of levenberg marquardt technique with conventional training procedures the excitation of this dynamics during a training cycle can lead to instability which may be difficult to alleviate due to the multidimensionality of the solution space and the ambiguities concerning the environmental conditions this paper proves that a fuzzy inference mechanism can be trained such that the adjustable parameter values are forced to settle down parameter stabilization while minimizing an appropriate cost function cost optimization in the application example control of a two degrees of freedom direct drive scara robotic manipulator is considered as the controller a standard fuzzy system architecture is used and the parameter tuning is performed by the proposed algorithm

analyses for l p μ norm approximation capability of generalized mamdani fuzzy systems abstract the connected piecewise linear functions are introduced to study the l p norm approximation capability of the generalized mamdani fuzzy system it is shown that such general fuzzy systems are the universal approximators to the p integrable functions with l p norm for the given degree of accuracy an upper bound of the fuzzy rule numbers needed in the fuzzy rule base of the system is estimated finally a simulation example is analyzed to demonstrate our conclusions

comments on adaptive manipulator control a case study by j slotine and w li the commenter establishes the stability in the sense of lyapunov of the adaptive motion controller for robot manipulators reported by j slotine and w li ibid vol 33 p 995 1003 nov 1988

adaptive fuzzy hierarchical sliding mode control for a class of mimo nonlinear time delay systems with input saturation in this paper an adaptive fuzzy hierarchical sliding mode control method for a class of multiinput multioutput unknown nonlinear time delay systems with input saturation is proposed the studied system is first transformed into an equivalent system subsequently based on sliding mode control technology and the concept of hierarchical design a set of adaptive fuzzy hierarchical sliding mode controllers are designed for the new defined system by using fuzzy systems to approximate uncertain functions and compensate input saturation choosing an appropriate lyapunov krasovskii function it is theoretically proved that all the signals in the closed loop system together with the proposed sliding surfaces are uniformly ultimately bounded under our designed adaptive fuzzy controllers simulation results demonstrate the effectiveness of the proposed design techniques for the systems under consideration

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

parameter conditions for monotonic takagi sugeno kang fuzzy system this paper presents sufficient conditions on the parameters of the takagi sugeno kang tsk fuzzy system under which the output of the tsk fuzzy system becomes monotonic with respect to its input the output of the tsk fuzzy system is first differentiated with respect to its input and the parameter conditions are derived so as to make the derivative nonnegative the parameter conditions are developed for both single input and multi input tsk fuzzy systems where the involved fuzzy membership functions are differentiable everywhere or bar some finite points the derived monotonicity conditions consist of two parts the conditions on the consequent parts and the conditions on the fuzzy membership functions they are further characterized for the most important types of fuzzy membership functions

chattering free fuzzy sliding mode control in mimo uncertain systems abstract control of nonlinear multivariable systems is very challenging in the area of systems and control this paper is concerned with a framework that unifies sliding mode control smc and fuzzy logic control flc based on the combination of the smc with fuzzy control this paper presents a new and feasible design algorithm to synthesize a robust fuzzy sliding mode controller which can easily tackle the stabilizing and tracking problem of a class of mimo nonlinear systems in the presence of uncertainties and external disturbance a practical design that combines a fuzzy technique with smc to enhance robustness and sliding performance in a class of uncertain mimo nonlinear systems is proposed using a fuzzy scheme a fuzzy sliding mode controller fsmc is used to approximate the hitting control in the neighborhood of the sliding manifold the main contribution of the proposed method is that the structure of the controlled system is partially unknown and does not require the bounds of uncertainty and disturbance of the system to be known meanwhile the chattering phenomenon that frequently appears in the conventional variable structure systems is also eliminated without deteriorating the system robustness a series of computer simulations are included to verify the effectiveness of the proposed design algorithm

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

stability and the fuzzy controller abstract this paper corrects a part of the main result theorem 1 in buckley fuzzy sets and systems 77 1996 167 173

etale stacks as prolongations abstract we give a complete and categorical characterization of etale stacks generalized orbifolds in various geometric contexts including differentiable stacks and topological stacks this characterization states that etale stacks are precisely those stacks that arise as prolongations of stacks on a site of spaces and local homeomorphisms and makes no mention of an atlas or groupoid presentation moreover we show that the bicategory of etale differentiable stacks and local diffeomorphisms is equivalent to the bicategory of stacks on the site of smooth manifolds and local diffeomorphisms an analogous statement holds for other flavors of manifolds topological c k complex super and topological spaces locally homeomorphic to a given space x a slight modification of this result also holds in an even more general context including all etale topological stacks and zariski etale stacks which are analogues of deligne mumford stacks for the zariski topology and we also sketch a proof of an analogous characterization of classical deligne mumford algebraic stacks which we prove in full in 7 by different methods we go on to characterize effective etale stacks e g reduced orbifolds as precisely those stacks arising as the prolongations of sheaves of sets rather than stacks of groupoids it follows that etale stacks and in particular orbifolds induce a small gerbe over their effective part and all gerbes over effective etale stacks arise in this way we show that well known lie groupoids from foliation theory literature can be reproduced from this framework as natural presentations for moduli stacks of certain geometric structures for example there exists a classifying stack for riemannian metrics presented by haefliger s groupoid r 13 and submersions into this stack classify riemannian foliations and similarly for symplectic structures with the role of r replaced with s p we also prove some unexpected results for example the category of smooth n manifolds and local diffeomorphisms has binary products

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

fuzzy hierarchical swing up and sliding position controller for the inverted pendulum cart system in this paper a fuzzy hierarchical swing up and sliding position controller is proposed for the swing up and position controls of an inverted pendulum cart system the proposed fuzzy hierarchical swing up and sliding position controller includes a fuzzy switching controller a fuzzy swing up controller and a twin fuzzy sliding position controller the fuzzy switching controller is designed to smoothly switch between the swing up and position controls with the inverted pendulum cart system decomposed into a pendulum subsystem and a cart subsystem fuzzy sliding position controllers are presented to robustly balance the pendulum and cart at the desired positions the sliding mode and stability of the fuzzy sliding position control systems are guaranteed moreover an adaptive mechanism is provided to on line adjust the parameters in the fuzzy sliding position controllers simulation results are included to illustrate the effectiveness of the proposed fuzzy hierarchical swing up and sliding position controller

adaptive control for nonlinear mimo time delay systems based on fuzzy approximation this paper focuses on the problem of adaptive control for a class of nonlinear multi input and multi output mimo systems with time delays a state feedback adaptive controller is constructed by backstepping technique fuzzy logic systems are used to approximate unknown nonlinear functions in the process of the controller design the main advantages of the proposed approach are twofold 1 the controller design is independent of the knowledge of the basis functions of fuzzy logic systems and 2 the suggested approach requires only m adaptive laws to control a nonlinear time delay system with m inputs simulation results illustrate the effectiveness of the proposed approach

a clustering algorithm for fuzzy model identification the fuzzy model proposed by takagi and sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules in this paper the model is firstly modified to make its identification easier based on the fuzzy c partition space four criteria are proposed for optimization of the model parameters following that a clustering algorithm composed of fuzzy c linear functions clustering and like fuzzy c means clustering is developed for minimizing the four criteria an identification scheme for rule s premise and consequence parameters is deduced from the clustering algorithm in succession finally four examples are demonstrated to verify the effectiveness of the proposed algorithm

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

stability issues on takagi sugeno fuzzy model parametric approach the main objective of this research is to provide a systematic stability analysis technique for fuzzy systems using well established results from robust stability of a family of polynomials the model based takagi sugeno 1985 fuzzy control system is considered and shown to have a dependent coefficient structure involving firing strengths two kharitonov regions via overbounding are established to facilitate the extreme results for stability test in the space of polynomials as well as the complex plane the criterion obtained is a sufficient condition for a fuzzy logic controller three nonlinear examples are demonstrated to show that the systematic approach proposed here can be used to solve fuzzy stability problems fuzzy users concerned over stability issues may find these analytic tools useful

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

support vector learning for fuzzy rule based classification systems to design a fuzzy rule based classification system fuzzy classifier with good generalization ability in a high dimensional feature space has been an active research topic for a long time as a powerful machine learning approach for pattern recognition problems the support vector machine svm is known to have good generalization ability more importantly an svm can work very well on a high or even infinite dimensional feature space this paper investigates the connection between fuzzy classifiers and kernel machines establishes a link between fuzzy rules and kernels and proposes a learning algorithm for fuzzy classifiers we first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function fuzzy inference on the if part of a fuzzy rule can be viewed as evaluating the kernel function the kernel function is then proven to be a mercer kernel if the reference functions meet a certain spectral requirement the corresponding fuzzy classifier is named positive definite fuzzy classifier pdfc a pdfc can be built from the given training samples based on a support vector learning approach with the if part fuzzy rules given by the support vectors since the learning process minimizes an upper bound on the expected risk expected prediction error instead of the empirical risk training error the resulting pdfc usually has good generalization moreover because of the sparsity properties of the svms the number of fuzzy rules is irrelevant to the dimension of input space in this sense we avoid the curse of dimensionality finally pdfcs with different reference functions are constructed using the support vector learning approach the performance of the pdfcs is illustrated by extensive experimental results comparisons with other methods are also provided

robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities in this paper robust adaptive neural network nn control is investigated for a general class of uncertain multiple input multiple output mimo nonlinear systems with unknown control coefficient matrices and input nonlinearities for nonsymmetric input nonlinearities of saturation and deadzone variable structure control vsc in combination with backstepping and lyapunov synthesis is proposed for adaptive nn control design with guaranteed stability in the proposed adaptive nn control the usual assumption on nonsingularity of nn approximation for unknown control coefficient matrices and boundary assumption between nn approximation error and control input have been eliminated command filters are presented to implement physical constraints on the virtual control laws then the tedious analytic computations of time derivatives of virtual control laws are canceled it is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed loop system finally simulation results are presented to illustrate the effectiveness of the proposed adaptive nn control

on adaptive inverse dynamics control of rigid robots the authors derive an adaptive inverse dynamics control law for rigid robots that overcomes the most restrictive difficulty of such schemes to date namely the requirement that the inverse of the estimated inertia matrix remain bounded the control scheme still requires the joint accelerations for its implementation in practice one would implement this scheme by estimating the acceleration from the measured velocity good performance could still be expected without direct acceleration measurement assuming sufficient encoder resolution and sufficiently fast sampling another practical advantage of the authors scheme is that since the nominal inverse dynamics or inner loop portion of their control law is fixed it is more amenable to the development of a dedicated interface and can be burned onto a chip to reduce online computation requirements

fuzzy basis functions comparisons with other basis functions fuzzy basis functions fbf s which have the capability of combining both numerical data and linguistic information are compared with other basis functions because a fbf network is different from other networks in that it is the only one that can combine numerical and linguistic information comparisons are made when only numerical data is available in particular a fbf network is compared with a radial basis function rbf network from the viewpoint of function approximation their architectural interrelationships are discussed additionally a rbf network which is implemented using a regularization technique is compared with a fbf network from the viewpoint of overcoming ill posed problems a fbf network is also compared with specht s probabilistic neural network and his general regression neural network grnn from an architectural point of view a fbf network is also compared with a gaussian sum approximation in which gaussian functions play a central role finally we summarize the architectural relationships between all the networks discussed in this paper

term and variable selection for non linear system identification the purpose of variable selection is to pre select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection it is required that the selected significant variables alone should sufficiently represent the system generally not all the model terms which are produced by combining different variables make an equal contribution to the system output and terms which make little contribution can be omitted a parsimonious representation which contains only the significant terms can often be obtained without the loss of representational accuracy by eliminating the redundant terms based on these observations a new variable and term selection algorithm is proposed in this paper the term detection algorithm can be applied to the general class of non linear modelling problems which can be expressed as a linear in the parameters form the variable selection procedure is based on locally linea

adomian decomposition method for solving fractional nonlinear differential equations in this article we have discussed a new application of adomian decomposition method on time fractional nonlinear fractional differential equations three models with fractional time derivative of order a 0 a 1 are considered and solved by means of adomian decomposition method the behaviour of adomian solutions and the effects of different values of a are investigated numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

non linear fokker planck equation solved with generalized finite differences in 2d and 3d abstract the generalized finite difference method gfdm has been proved to be a good meshless method to solve several both linear and nonlinear partial differential equations pdes wave propagation advection diffusion plates beams etc in this paper it is shown the application of the gfdm for solving the linear and nonlinear fokker planck equation in 2d and 3d criteria for convergence of fully explicit method using gfdm for fokker planck equation in 2d and 3d are given

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

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

homotopy types of topological stacks abstract we introduce the notion of classifying space of a topological stack x it is a topological space x with a morphism x x that is a universal weak equivalence we show that every topological stack x has a classifying space x that is well defined up to weak homotopy equivalence under a certain paracompactness condition on x we show that x is indeed well defined up to homotopy equivalence these results are formulated in terms of functors from the category of topological stacks to the weak homotopy category of topological spaces we prove similar results for small diagrams of topological stacks

numerical solution of two dimensional fokker planck equations we present a robust finite difference scheme for the integration of the fokker planck fp equation with two variables plus time the scheme is checked with problems where analytical solutions exist and it is compared with finite element codes as well as with simulations of the associated stochastic differential equation sde the precision and stability of the scheme are verified

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

indirect adaptive fuzzy sliding mode control part i fuzzy switching in this paper by using the concept of sliding mode control design and lyapunov synthesis approach we propose an indirect adaptive fuzzy sliding mode control iafsmc scheme for a class of nonlinear systems in contrast to the existing sliding mode fuzzy control system designs where the sliding mode control law is directly substituted by a fuzzy controller in our approach both the equivalent control term and switching type control term in the sliding mode control law are approximated by fuzzy systems respectively an on line adaptive tuning algorithm for the consequent parameters in the fuzzy rules is also designed the sliding mode based design procedure ensures the stability and robustness of the proposed iafsmc we prove that the proposed adaptive scheme can achieve asymptotically stable tracking of a reference input with a guarantee of the bounded system signals the chattering phenomena in the sliding mode control is attenuated and the steady error is also alleviated simulation studies have shown that the presented adaptive design of fuzzy sliding mode controller performs very well in the presence of an unknown disturbance

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

presentations of noneffective orbifolds it is well known that an effective orbifold m one for which the local stabilizer groups act effectively can be presented as a quotient of a smooth manifold p by a locally free action of a compact lie group k we use the language of groupoids to provide a partial answer to the question of whether a noneffective orbifold can be so presented we also note some connections to stacks and gerbes

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

stable indirect adaptive control based on discrete time t s fuzzy model this paper presents an indirect adaptive fuzzy control scheme for uncertain nonlinear asymptotically stable plants a discrete time t s fuzzy input output model is employed to approximate the unknown plant dynamics the t s fuzzy model is fed with its own states which are indeed its past outputs rather than the measurements from the plants entirely based on this model a feedback linearization control law is designed by using the model structure model parameters and model states and then applied to control the model and the plant premise and consequent parameters of the model are updated on line by gradient descent algorithm and recursive least square estimation method using plant output measurements stability analysis shows that if there the model structure is accurate the adaptive controller achieves the bounded tracking error and boundedness of all the closed loop signals in the ideal case where the signals are persistently exciting during the model parameter adaptation a perfect asymptotic tracking is ensured the effectiveness of the method is verified by simulation application to siso and mimo example plants

numerical solution of non linear fokker planck equation using finite differences method and the cubic spline functions in this paper we proposed a finite difference scheme for solving the nonlinear fokker planck equation we apply a finite difference approximation for discretizing spatial derivatives then we use the cubic c1 spline collocation method which is an a stable method for the time integration of the resulting nonlinear system of ordinary differential equations the proposed method has second order accuracy in space and fourth order accuracy in time variables the numerical results confirm the validity of the method

improved structure optimization for fuzzy neural networks fuzzy neural network based inference systems are well known universal approximators which can produce linguistically interpretable results unfortunately their dimensionality can be extremely high due to an excessive number of inputs and rules which raises the need for overall structure optimization in the literature various input selection methods are available but they are applied separately from rule selection often without considering the fuzzy structure this paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously first a method is developed to select the most significant rules along with a refinement stage to remove unnecessary correlations an improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model leading to a balanced tradeoff between interpretability and accuracy simulation results confirm the efficacy of the proposed method

a novel takagi sugeno based robust adaptive fuzzy sliding mode controller in this paper a nonlinear dynamic system is first approximated by n fuzzy based linear state space subsystems to track a trajectory dominant by a specific frequency the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule similarly the same fuzzy sets of the system rule are employed to design robust fuzzy sliding mode control rfsmc and adaptive fuzzy sliding mode control afsmc the difference between rfsmc and afsmc is that afsmc contains an updating law to learn system uncertainties and then an extra compensation is designed it is different from the most previous papers to learn the whole nonlinear functions as the norm of the sliding surface is inside of a defined set the updating law starts simultaneously as it is outside of the other set the updating law stops for the purpose of smoothing the possibility of discontinuous control input a transition between rfsmc and afsmc is also assigned under the circumstances the proposed control robust adaptive fuzzy sliding mode control rafsmc can automatically tune as a rfsmc or an afsmc then the advantages coming from the rfsmc and afsmc are obtained finally the stabilities of the overall system of rfsmc afsmc and rafsmc are verified by lyapunov stability theory the compared simulations among rfsmc afsmc and rafsmc are also carried out to confirm the usefulness of the proposed control scheme

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

necessary conditions for some typical fuzzy systems as universal approximators abstract we investigate necessary conditions for general single input single output fuzzy systems and a class of typical multiple input single output fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds considering the case where the only available data about the continuous function to be approximated are a finite set of its extrema we have established some necessary conditions for the fuzzy systems to be universal approximators of the function the conditions can be used practically to determine input fuzzy sets output fuzzy sets and fuzzy rules of the fuzzy systems furthermore these necessary conditions provide a basis for insightful analysis of the strengths as well as the limitations of the fuzzy systems the main strength is that only a small number of fuzzy rules may be needed to uniformly approximate continuous functions that have a complicated formulation but a relatively small number of extrema the limitation is that in order to approximate highly oscillatory continuous functions the number of fuzzy rules must be large 1997 elsevier science ltd

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

adomian decomposition method for solving the diffusion convection reaction equations abstract adomian decomposition method is used to solve the explicit and numerical solutions of three types of the diffusion convection reaction decr equations the calculations are carried out for three different types of the dcre such as the black scholes equation used in financial market option pricing fokker planck fp equation for lazer filed and fokker planck equation from plasma physics the behaviour of the approximate solutions of the distribution functions is shown graphically and compared with that obtained by other theories such as the variational iteration method

advanced fuzzy inference engines in situation aware computing we focus on the very important family of context aware applications context aware computing relies on tasks like capturing sensing environmental parameters e g lightness location classifying context and inferring further knowledge about that context determine the situation the user is currently in however the relevant applications have to deal with the inherent imperfection of context sensing for decision making we propose an extension of context representation and inference for situation aware applications our model relies on fuzzy set theory to accommodate the imperfection of sensed context based on this model we have developed three fuzzy inference engines which rely on advanced semantics specialization mereological and compatibility relations we have evaluated the proposed engines through a series of experiments involving real users our findings indicate the strong points of the proposed context classification and inference processes

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 note on smooth approximation capabilities of fuzzy systems modeling and prediction in some systems requires the simultaneous approximation of mappings and their derivatives to a certain finite order in this paper universal approximation capabilities of fuzzy systems are extended to this situation by showing the denseness of some general classes of fuzzy models in appropriate function spaces where distance between functions is defined in terms of their derivatives requirements are generally very mild and are often limited to imposing sufficient differentiability conditions on the classes of fuzzy systems to be used the cases covered by this paper include additive fuzzy systems with gaussian membership functions and general additive fuzzy models with realistic membership functions some potential application fields are considered including examples from economics and time series prediction

comments on fuzzy systems approximation by frames siso case we show that the approach taken by shmilovici and maimon to construct fuzzy wavelet is wrong and the example given is also incorrect

adaptive wavelet neural network control with hysteresis estimation for piezo positioning mechanism an adaptive wavelet neural network awnn control with hysteresis estimation is proposed in this study to improve the control performance of a piezo positioning mechanism which is always severely deteriorated due to hysteresis effect first the control system configuration of the piezo positioning mechanism is introduced then a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo positioning mechanism according to this developed dynamics an awnn controller with hysteresis estimation is proposed in the proposed awnn controller a wavelet neural network wnn with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo positioning mechanism and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances optimal parameter vectors and higher order terms in taylor series moreover adaptive learning algorithms for the online learning of the parameters of the wnn are derived based on the lyapunov stability theorem finally the command tracking performance and the robustness to external load disturbance of the proposed awnn control system are illustrated by some experimental results

direct adaptive self structuring fuzzy controller for nonaffine nonlinear system a direct adaptive state feedback controller for highly nonlinear systems is proposed this paper considers uncertain or ill defined nonaffine nonlinear systems and employ a static fuzzy logic system fls with an on line structuring algorithm the fls approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed loop system is stable in the sense of lyapunov the tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term no a priori knowledge of an upper bound on an lumped uncertainty is required

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

indirect adaptive fuzzy sliding mode control part ii parameter projection and supervisory control the objective of this paper is to show that the error dynamics of the lyapunov synthesis is similar to the sliding surface of sliding mode control smc we compare and evaluate the role and performance of sliding surface boundary layer and lyapunov synthesis finally the indirect adaptive fuzzy sliding mode control iafsmc is equipped with state boundedness supervisory controller and parameter projection simulation studies illustrate the application of the proposed method

a fuzzy variable structure approach to feedback regulation of uncertain dynamical systems with application to robotics this paper develops a fuzzy logic based control design methodology for a large class of nonlinear uncertain dynamical systems the proposed control design approach combines the powerful tools of fuzzy logic and approximate reasoning with the advanced mathematical synthesis techniques used in variable structure control systems theory the rationale for the proposed control design approach is motivated by the results of a recent study that has rigorously established some connections between fuzzy logic and variable structure control systems the results of this paper represent a step in the right direction for systematic design of a less expert dependent fuzzy logic control to illustrate the merits of the new control approach the latter is applied to a 2 degree of freedom robot manipulator preliminary simulation results suggest that the proposed control design deals effectively with the chattering problem encountered when the classical variable structure control is used alone

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

variable selection algorithm for the construction of mimo operating point dependent neurofuzzy networks an input variable selection procedure is introduced for the identification and construction of multi input multi output mimo neurofuzzy operating point dependent models the algorithm is an extension of a forward modified gram schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting the proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice based modeling algorithms such as radial basis function neurofuzzy networks enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm

the classifying topos of a continuous groupoid i we investigate some properties of the functor b which asso ciates to any continuous groupoid g its classifying topos bg of equivariant g sheaves in particular it will be shown that the category of toposes can be obtained as a localization of a category of continuous groupoids if g is a group the category of g sets sets equipped with a right g action is a topos bg which classifies principal g bundles for instance if a is a topological space there is an equivalence between topos morphisms sheaves a bg and principal g bundles over x the construction of bg also applies to the case where g is a topological group or more generally a topological groupoid it is a rather surprising result that this essentially exhausts the range of toposes joyal and tierney 1984 have shown that any topos is equivalent to one of the form bg for a topological group g provided one works with a slightly generalized notion of topological space by taking the lattice of open sets as the primitive notion rather than the set of points one sometimes speaks of pointless spaces the continuous groupoids of this paper are the groupoid objects in this category of generalized spaces the aim of this paper is threefold first g bg is a functor and we wish to investigate how the properties of the topos bg depend on those of the contin uous groupoid g and more generally how the properties of a geometric morphism bg bh depend on those of the map of continuous groupoids g h the second aim is to extend the joyal tierney result and not only represent toposes in terms of continuous groupoids but also the geometric morphisms from one topos to another there are several possible solutions to this problem in this paper i present one approach and show that the category of toposes can be obtained as a category of fractions from a category of continuous groupoids another approach somewhat similar in spirit to the morita theorems for categories of modules will be presented elsewhere the third aim of this paper is of a more methodological nature in presenting many arguments concerning generalized pointless spaces i have tried to convey the idea that by using change of base techniques and exploit ing the internal logic of a grothendieck topos point set arguments are perfectly suitable for dealing with pointless spaces at least as long as one stays within the stable part of the theory although the general underlying idea is very clear see e g the discussion in 5 3 below it is a challenging open problem to express this

joint block structure sparse representation for multi input multi output mimo t s fuzzy system identification takagi sugeno t s fuzzy system identification provides a reasonable framework for modeling and approximation by decomposition of a nonlinear system into a collection of local linear models in this paper we extend the multidimensional output fuzzy rule from the corresponding single output fuzzy rule with the important difference in the variable definition of output namely the output of each fuzzy rule is represented by a multidimensional vector instead of a scalar value in this case the consequent of the fuzzy rule with the multidimensional output variable share a common antecedent part different from the traditional methods that separate the multi input multi output fuzzy system into a group of multi input single output fuzzy models in this paper we take into account the block structure information in the t s fuzzy system and cast the problem of multidimensional output fuzzy model identification as a joint structure sparse optimization problem where the consequent parameters are estimated with a common block structured sparsity pattern over all dimensions of the output variable furthermore we exploit a joint block sparse orthogonal match pursuit algorithm to reduce the number of fuzzy rules in terms of all dimensions of the output variable and prove the sufficient conditions in consideration of the multidimensional output together with the block structure in the t s fuzzy model this method is efficient and shows good performance in well known benchmark datasets and real world problems