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

transmission of vector quantized data over a noisy channel in the transmission of vector quantized data the vector quantizer and the communication system are usually designed separately with such an approach the channel noise results in significant degradations in the performance of the vector quantizer to solve this problem we should properly create the mapping from the codebook of the quantizer to the channel signal set of the communication system this paper proposes a new approach to construct such a mapping based on the ordering property of the self organizing feature map sofm we use the neighborhood structure of the sofm and the neighborhood structure of the channel signal set to construct the mapping simulation results confirm that the proposed approach is robust with respect to channel noise

dynamic estimation of linear systems constrained by bounds this correspondence deals with the minimum variance estimation of a gaussian process constrained by bounds a special truncated gaussian probability is shown to be fairly well adapted to this filtering scheme as its set is linearly closed with respect to convolution and multiplication operations

fuzzy control turns 50 in 2015 we celebrate the 50th anniversary of fuzzy sets ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in fss see 1 ten years is at the same time a long period and short time thinking to the inner dynamics of research this paper presented for these 50 years of fuzzy sets is taking into account both thoughts a first part presents a quick recap of the history of fuzzy control from model free design based on human reasoning to quasi lpv linear parameter varying model based control design via some milestones and key applications the second part shows where we arrived and what the improvements are since the milestone of the first 40 years a last part is devoted to discussion and possible future research topics

piecewise linear skeletonization using principal curves proposes an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves the development of the method was inspired by the apparent similarity between the definition of principal curves smooth curves which pass through the middle of a cloud of points and medial axes smooth curves that run equidistantly from the contours of a character image the central fitting and smoothing step of the algorithm is an extension of the polygonal line algorithm which approximates principal curves of data sets by piecewise linear curves the polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization an initialization method to capture the approximate topology of the character and a collection of restructuring operations to improve the structural quality of the skeleton produced by the initialization method an advantage of our approach over existing methods is that we optimize the skeleton graph by minimizing an intuitive and explicit objective function that captures the two competing criteria of smoothing the skeleton and fitting it closely to the pixels of the character image we tested the algorithm on isolated handwritten digits and images of continuous handwriting the results indicated that the proposed algorithm can find a smooth medial axis in the great majority of a wide variety of character templates and that it substantially improves the pixel wise skeleton obtained by traditional thinning methods

evaluating kohonen s learning rule an approach through genetic algorithms this paper examines the technical foundations of the self organising map som it compares kohonen s heuristic based training algorithm with direct optimisation of a locally weighted distortion index also used by kohonen direct optimisation is achieved through a genetic algorithm ga although gas have been used before with the som this has not been done in conjunction with the distortion index comparing heuristic based training and direct optimisation for the som is analogous to comparing the backpropagation algorithm for feedforward networks with direct optimisation of rms error our experiments reveal lower values of the distortion index with direct optimisation as to whether the heuristic based algorithm is able to provide an approximation to gradient descent our results suggest the answer should be in the negative theorems for one dimensional and for square maps indicate that different point densities will emerge for the two training approaches our findings are in accordance with these results

gtm the generative topographic mapping latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent or hidden variables a familiar example is factor analysis which is based on a linear transformations between the latent space and the data space in this paper we introduce a form of non linear latent variable model called the generative topographic mapping for which the parameters of the model can be determined using the em algorithm gtm provides a principled alternative to the widely used self organizing map som of kohonen 1982 and overcomes most of the significant limitations of the som we demonstrate the performance of the gtm algorithm on a toy problem and on simulated data from flow diagnostics for a multi phase oil pipeline

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

spline smoothing the equivalent variable kernel method on considere une approche spline pour la regression non parametrique et l estimation de courbe on montre que dans un certain sens le lissage spline correspond approximativement au lissage par une methode du noyau avec une largeur de bande dependant de la densite locale des points du plan de regression

a smoothly constrained kalman filter this paper presents the smoothly constrained kalman filter sckf for nonlinear constraints a constraint is any relation that exists between the state variables constraints can be treated as perfect observations but linearization errors can prevent the estimate from converging to the true value therefore the sckf iteratively applies nonlinear constraints as nearly perfect observations or equivalently weakened constraints integration of new measurements is interlaced with these iterations which reduces linearization errors and hence improves convergence compared to other iterative methods the weakening is achieved by artificially increasing the variance of the nonlinear constraint the paper explains how to choose the weakening values and when to start and stop the iterative application of the constraint

target tracking problems subject to kinematic constraints filtering problems with kinematic constraints which may arise in target tracking problems are considered a novel approach which treats kinematic constraints as additional fictitious or pseudomeasurements is proposed a numerical example is provided to show the technical feasibility of the proposed idea for target tracking problems this example shows that the proposed method can improve estimation accuracy significantly for velocity and acceleration states in the tracking problem however it is noted that the tracking performance may be deteriorated if the constraints do not properly represent the target characteristics and a small r sub c is chosen

kernel based equiprobabilistic topographic map formation we introduce a new unsupervised competitive learning rule the kernel based maximum entropy learning rule kmer which performs equiprobabilistic topographic map formation in regular fixed topology lattices for use with nonparametric density estimation as well as nonparametric regression analysis the receptive fields of the formal neurons are overlapping radially symmetric kernels compatible with radial basis functions rbfs but unlike other learning schemes the radii of these kernels do not have to be chosen in an ad hoc manner the radii are adapted to the local input density together with the weight vectors that define the kernel centers so as to produce maps of which the neurons have an equal probability to be active equiprobabilistic maps both an online and a batch version of the learning rule are introduced which are applied to nonparametric density estimation and regression respectively the application envisaged is blind source separation bss from nonlinear noisy mixtures

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

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

incorporate intelligence into an ecological system an adaptive fuzzy control approach in this paper we incorporate intelligence into kolmogorov s ecological system that is we propose a fuzzy system to combine heuristic rules into the design of nonlinear adaptive controller where the heuristic rules are in the form of fuzzy if then rules by using lyapunov synthesis approach we attain an adaptive law adjusting the free parameters in the controller such that the closed loop system follows a desired trajectory although there exist uncertainty and chaos in komogorov s model application shows that an adaptive fuzzy control is a powerful tool to pursuit sustainable development of ecology

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

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

convergence properties of a class of learning vector quantization algorithms a mathematical analysis of a class of learning vector quantization lvq algorithms is presented using an appropriate time coordinate transformation we show that the lvq algorithms under consideration can be transformed into linear time varying stochastic difference equations using this fact we apply stochastic lyapunov stability arguments and we prove that the lvq algorithms under consideration do indeed converge provided that some appropriate conditions hold

learning and design of principal curves principal curves have been defined as self consistent smooth curves which pass through the middle of a d dimensional probability distribution or data cloud they give a summary of the data and also serve as an efficient feature extraction tool we take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution the new definition makes it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction our theoretical learning scheme chooses a curve from a class of polygonal lines with k segments and with a given total length to minimize the average squared distance over n training points drawn independently convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented in each iteration of the algorithm a new vertex is added to the polygonal line and the positions of the vertices are updated so that they minimize a penalized squared distance criterion simulation results demonstrate that the new algorithm compares favorably with previous methods both in terms of performance and computational complexity and is more robust to varying data models

fuzzy tracking adaptive control of discrete time switched nonlinear systems this paper is concerned with the problem of fuzzy tracking adaptive control for a class of discrete time switched uncertain nonlinear systems with arbitrary switching based on the common lyapunov function method and by utilizing the fuzzy logic systems to approximate the unknown nonlinear functions an adaptive fuzzy controller is firstly constructed for a class of uncertain nonlinear discrete time switched systems meanwhile the proposed adaptive control algorithm reduces the amount of online adjustable parameters based on the above techniques the constructed fuzzy controllers and the adaptive law can guarantee that all the signals are bounded and the system output can converge to a small neighborhood of the reference signal in the closed loop system an illustrative example is provided to demonstrate the effectiveness of the proposed approaches

adaptive control of markov jump distributed parameter systems via model reference abstract this paper studies adaptive control of markov jump distributed parameter systems via model reference where a finite dimensional adaptive control approach is used for the distributed parameter systems in order to obtain the stability criteria the galerkin s technique is initially applied to the distributed parameter systems to get a slow system of finite dimensional markov jump system governed by nonlinear ordinary differential functions subsequently a t s fuzzy model is employed to represent exactly the nonlinear markov jump slow system then an adaptive controller subject to reference model is proposed to control the markov jump distributed parameter systems by employing the gronwall inequality and strong law of large numbers technics criterion on most surely exponential stability of the closed loop system is established finally two examples and numerical simulations are given to illustrate the effectiveness of the obtained results

self organization as an iterative kernel smoothing process kohonen s self organizing map when described in a batch processing mode can be interpreted as a statistical kernel smoothing problem the batch som algorithm consists of two steps first the training data are partitioned according to the voronoi regions of the map unit locations second the units are updated by taking weighted centroids of the data falling into the voronoi regions with the weighing function given by the neighborhood then the neighborhood width is decreased and steps 1 2 are repeated the second step can be interpreted as a statistical kernel smoothing problem where the neighborhood function corresponds to the kernel and neighborhood width corresponds to kernel span to determine the new unit locations kernel smoothing is applied to the centroids of the voronoi regions in the topological space this interpretation leads to some new insights concerning the role of the neighborhood and dimensionality reduction it also strengthens the algorithm s connection with the principal curve algorithm a generalized self organizing algorithm is proposed where the kernel smoothing step is replaced with an arbitrary nonparametric regression method

stable adaptive fuzzy control for mimo nonlinear systems in this paper an indirect adaptive fuzzy control scheme is presented for a class of multi input and multi output mimo nonlinear systems whose dynamics are poorly understood within this scheme fuzzy systems are employed to approximate the plant s unknown dynamics in order to overcome the controller singularity problem the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices a robustifying control term is used to compensate for the lumped errors and all parameter adaptive laws and robustifying control term are derived based on lyapunov stability analysis the proposed scheme guarantees that all the signals in the resulting closed loop system are uniformly ultimately bounded uub moreover the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large a simulation example is used to demonstrate the effectiveness of the proposed control scheme

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

stable indirect fuzzy adaptive control this paper investigates new fuzzy model based observer adaptive control for multi input multi output continuous time nonlinear systems the proposed adaptive scheme uses takagi seguno ts fuzzy models to estimate the plant states and dynamics using stability arguments it is shown that the proposed scheme is globally asymptotically stable the observation and tracking errors are shown to converge asymptotically to zero despite the presence of external disturbances and approximation errors the performance of the developed approach is illustrated by simulation on two link robot model

quasiconformal kernel common locality discriminant analysis with application to breast cancer diagnosis dimensionality reduction dr is a popular method in recognition and classification in many areas such as facial and medical imaging in this paper we propose a novel supervised dr method namely quasiconformal kernel common locality discriminant analysis qkclda qkclda preserves the local and discriminative relationships of the data moreover it adjusts the kernel structure according to the distribution of the input data and thus possesses a classification advantage over traditional kernel based methods in qkclda the parameter of the quasiconformal kernel is automatically calculated through optimizing an objective function of maximizing the class discriminative ability qkclda is employed in breast cancer diagnoses and some experiments using wisconsin diagnostic breast cancer wdbc and mini mias databases have tested its feasibility and performance in assigning these diagnoses

robust impedance control of robot manipulators using differential equations as universal approximator abstractthis paper presents a robust impedance controller for robot manipulators using function approximation techniques fat recently some fat based robust impedance control approaches have been presented using fourier series expansion or legendre polynomials for uncertainty estimation however the dimensions of regressor matrices in these approaches are relatively large this problem becomes hypersensitive especially for higher degree of freedom robot manipulators in this paper a simpler and less computational fat based robust controller is presented without considering discontinuous nonlinearities it is assumed that the lumped uncertainty can be modeled by a linear differential equation with unknown coefficients then using stone weierstrass theorem it is verified that these differential equations are universal approximators the advantage of proposed controller in comparison with previous related works is reducing the dimensions of regressor matrices simulation results on a puma560 robot man

adaptive fuzzy decentralized control for a class of nonlinear systems with different performance constraints abstract this paper investigates an adaptive fuzzy decentralized control approach for a class of nonlinear systems with unknown control direction and different performance constraints in the control design the different performance constraints that are the prescribed performance error constraints for some subsystems and the asymmetric time varying output constraints for the others can be unified as one form by selecting proper performance functions the fuzzy systems are employed to approximate the unknown nonlinear functions and an adaptive fuzzy decentralized controller loaded with the nussbaum type function is developed to resolve the unknown control direction issues it is proved that all the signals in the resulting closed loop systems are bounded and that the different performance constraints for the subsystems can be achieved simultaneously the performance of the proposed scheme is highlighted through the simulation example

fuzzy adaptive control for a class of nonlinear systems an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamic is either unknown or impossible the architecture employs fuzzy systems to approximate nonlinear functions uses fuzzy sliding controller to compensate for the plant uncertainties global asymptotic stability is established in the lyapunov sense with the tracking errors converging to a neighborhood of zero

a bayesian analysis of self organizing maps in this paper bayesian methods are used to analyze some of the properties of a special type of markov chain the forward transitions through the chain are followed by inverse transitions using bayes theorem backward through a copy of the same chain this will be called a folded markov chain if an appropriately defined euclidean error between the original input and its reconstruction via bayes theorem is minimized with respect to the choice of markov chain transition probabilities then the familiar theories of both vector quantizers and self organizing maps emerge this approach is also used to derive the theory of self supervision in which the higher layers of a multilayer network supervise the lower layers even though overall there is no external teacher

nonparametric identification of quasi stationary systems abstract recursive estimates of a regression function based on the parzen rosenblatt kernels are applied for identification of quasi stationary systems it is shown that these estimates do not lose their asymptotic properties even if the data are not stationary conditions for weak and strong pointwise consistency are given

noninteracting adaptive control of pmsm using interval type 2 fuzzy logic systems based on the type 2 fuzzy logic systems and adaptive control theory this paper develops a decentralized adaptive fuzzy controller for a permanent magnet synchronous motor pmsm the adaptive law is designed to compensate for the interconnection effects and the reconstruction errors using a sliding mode term the type 2 fuzzy logic systems are used to model the unknown functions based on lyapunov s stability theorem the stability of closed loop systems can be verified moreover the proposed overall control schemes guarantee that all the signals that are involved are bounded to demonstrate the effectiveness of the proposed methods simulation results are illustrated in this paper

on line identification of time varying systems by nonparametric techniques a nonparametric algorithm based on orthogonal series is proposed for real time identification of nonstationary systems it is proved that the algorithm converges in the mean square sense the convergence conditions are closely related to those in dupac 2

stable fuzzy adaptive control for a class of nonlinear systems abstract in this paper two adaptive fuzzy control schemes for a class of nonlinear systems are proposed each scheme employs a fuzzy control with an adaptive law and a compensation control it is proved that the closed loop system is asymptotically stable based on lyapunov synthesis approach while the identification of the controlled plant is unnecessary finally these schemes are applied to control a chaotic system the simulation results show that our schemes are superior to the scheme of 12

constrained signal restoration via iterated extended kalman filtering the problem of estimating the input signal restoration to a known linear system point spread function given the noisy observations of the output is considered the input signal is assumed to satisfy certain known physical constraints such as positivity it is proposed to incorporate the constraints by introducing a memoryless non linearity in the system a statistical approach is taken leading to a closed form type of recursive solution in the form of iterated extended kalman filtering with two local iterations at every new data point a simulation example is presented which demonstrates the superiority of the proposed approach over the conventional kalman wiener filtering

hyperparameter selection for self organizing maps the self organizing map som algorithm for finite data is derived as an approximate maximum a posteriori estimation algorithm for a gaussian mixture model with a gaussian smoothing prior which is equivalent to a generalized deformable model gdm for this model objective criteria for selecting hyperparameters are obtained on the basis of empirical bayesian estimation and cross validation which are representative model selection methods the properties of these criteria are compared by simulation experiments these experiments show that the cross validation methods favor more complex structures than the expected log likelihood supports which is a measure of compatibility between a model and data distribution on the other hand the empirical bayesian methods have the opposite bias

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

self organizing maps for the skeletonization of sparse shapes this paper presents a method for computing the skeleton of planar shapes and objects which exhibit sparseness lack of connectivity within their image regions such sparseness in images may occur due to poor lighting conditions incorrect thresholding or image sub sampling furthermore in document image analysis sparse shapes are characteristic of texts faded due to aging and or poor ink quality given the pixel distribution for a shape the proposed method involves an iterative evolution of a piecewise linear approximation of the shape skeleton by using a minimum spanning tree based self organizing map som by constraining the som to lie on the edges of the delaunay triangulation of the shape distribution the adjacency relationships between regions in the shape are detected and used in the evolution of the skeleton the som on convergence gives the final skeletal shape the skeletonization is invariant to euclidean transformations the potential of the method is demonstrated on a variety of sparse shapes from different application domains

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

adaptive fuzzy control of a class of siso nonaffine nonlinear systems this paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous time single input single output siso nonaffine nonlinear dynamic systems based on the implicit function theory the existence of an ideal controller that can achieve control objectives is firstly shown since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it a fuzzy system is employed to approximate this unknown ideal control law the adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm this algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law the stability analysis of the closed loop system is performed using a lyapunov approach in particular it is shown that the tracking error converges to a neighborhood of zero the effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system

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

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

theory of ocular dominance pattern formation we investigate a general and analytically tractable model for the activity dependent formation of neuronal connectivity patterns previous models are contained as limiting cases as an important example we analyze the formation of ocular dominance patterns in the visual cortex a linear stability analysis reveals that the model undergoes a turing type instability as a function of interaction range and receptive field size the phase transitions is of second order after the linear instability the patterns may reorganize which we analyze in terms of a potential for the dynamics our analysis demonstrates that the experimentally observed dependency of ocular dominance patterns on interocular correlations of visual experience during development can emerge according to two generic scenarios either the system is driven through the phase transition during development thereby selecting and stabilizing the first unstable mode or a primary pattern reorganizes towards larger wavelength according their lower energy experimentally observing the time course of ocular dominance pattern formation will decide which scenario is realized in the brain s1063 651x 99 12705 3

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

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

adaptive fuzzy finite time stability of uncertain nonlinear systems based on prescribed performance abstract the semi globally practical finite time stability sgpfs problem for a class of uncertain strict feedback nonlinear systems is discussed in this paper a novel performance function called finite time performance function ftpf is first defined moreover this paper is the first to solve an adaptive semi globally practical finite time control issue by combining with backstepping prescribed performance control ppc and fuzzy logic systems furthermore it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite time but also all the signals of the closed loop systems are sgpf stable simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method

convergence and ordering of kohonen s batch map the convergence and ordering of kohonen s batch mode self organizing map with heskes and kappen s 1993 winner selection are proved selim and ismail s 1984 objective function for k means clustering is generalized in the convergence proof of the self organizing map it is shown that when the neighborhood relation is doubly decreasing order in the map is preserved an unordered map becomes ordered when a degenerate state of ordering is entered where the number of distinct winners is one or two one strategy to enter this state is to run the algorithm with a broad neighborhood relation

an analysis of the elastic net approach to the traveling salesman problem this paper analyzes the elastic net approach durbin and willshaw 1987 to the traveling salesman problem of finding the shortest path through a set of cities the elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities the tradeoff between these two requirements is controlled by a scale parameter k a global minimum is found for large k and is then tracked to a small value in this paper we show that 1 in the small k limit the elastic path passes arbitrarily close to all the cities but that only one path point is attracted to each city 2 in the large k limit the net lies at the center of the set of cities and 3 at a critical value of k the energy function bifurcates we also show that this method can be interpreted in terms of extremizing a probability distribution controlled by k the minimum at a given k corresponds to the maximum a posteriori map bayesian estimate of the tour under a natural statistical interpretation the analysis presented in this paper gives us a better understanding of the behavior of the elastic net allows us to better choose the parameters for the optimization and suggests how to extend the underlying ideas to other domains

adaptive control for systems with bounded disturbances the authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum and nonminimum phase systems subject to bounded disturbances the parameter estimation scheme is a least squares algorithm with dead zone the dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates in the minimum phase case the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value the projection procedure can also be used to avoid pole zero cancellations in an adaptive pole placement algorithm

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

an error control scheme for transmission of vector quantization data over noisy channels this paper presents an error control scheme for transmitting vector quantized data over noisy channels first we review a self organizing feature map sofm based approach to construct the mapping from the codebook of the quantizer to the channel signal set of the communication system this approach is robust with respect to channel noise even if we do not use any error control scheme in the communication system afterwards a new trellis type quantizer namely the trellis coded kohonen 1984 map tckm is presented the design process of the tckm which is based on the neighborhood structure of sofms is simpler than that of conventional trellis coded vector quantizers tcvqs simulation results show that the performance of tckms is comparable with that of tcvqs last we introduce the error control scheme based on the concepts of the above two applications of sofms simulation results show that the proposed error control scheme is more robust with respect to channel noise the advantage of our approaches mentioned above is that the design processes of transmission systems are predefined before the construction of the codebook thus different codebooks with the same neighborhood structure can share the same design

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

kernel based topographic map formation by local density modeling we introduce a new learning algorithm for kernel based topographic map formation the algorithm generates a gaussian mixture density model by individually adapting the gaussian kernels centers and radii to the assumed gaussian local input densities

batch map extensions of the kernel based maximum entropy learning rule in this letter two batch map extensions are described for the kernel based maximum entropy learning rule kmer in the first the weights are iteratively set to weighted component wise medians while in the second the generalized median is used enabling kmer to process symbolic data simulations are performed to illustrate the extensions

a unified model for probabilistic principal surfaces principal curves and surfaces are nonlinear generalizations of principal components and subspaces respectively they can provide insightful summary of high dimensional data not typically attainable by classical linear methods solutions to several problems such as proof of existence and convergence faced by the original principal curve formulation have been proposed in the past few years nevertheless these solutions are not generally extensible to principal surfaces the mere computation of which presents a formidable obstacle consequently relatively few studies of principal surfaces are available we previously 2000 proposed the probabilistic principal surface pps to address a number of issues associated with current principal surface algorithms pps uses a manifold oriented covariance noise model based on the generative topographical mapping gtm which can be viewed as a parametric formulation of kohonen s self organizing map building on the pps we introduce a unified covariance model that implements pps 0 1 by varying the clamping parameter spl alpha then we comprehensively evaluate the empirical performance of pps gtm and the manifold aligned gtm on three popular benchmark data sets it is shown in two different comparisons that the pps outperforms the gtm under identical parameter settings convergence of the pps is found to be identical to that of the gtm and the computational overhead incurred by the pps decreases to 40 percent or less for more complex manifolds these results show that the generalized pps provides a flexible and effective way of obtaining principal surfaces

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

neural gas network for vector quantization and its application to time series prediction a neural network algorithm based on a soft max adaptation rule is presented this algorithm exhibits good performance in reaching the optimum minimization of a cost function for vector quantization data compression the soft max rule employed is an extension of the standard k means clustering procedure and takes into account a neighborhood ranking of the reference weight vectors it is shown that the dynamics of the reference weight vectors during the input driven adaptation procedure are determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter and resemble the dynamics of brownian particles moving in a potential determined by the data point density the network is used to represent the attractor of the mackey glass equation and to predict the mackey glass time series with additional local linear mappings for generating output values the results obtained for the time series prediction compare favorably with the results achieved by backpropagation and radial basis function networks

derivation of a class of training algorithms a novel derivation is presented of t kohonen s topographic mapping training algorithm self organization and associative memory 1984 based upon an extension of the linde buzo gray lbg algorithm for vector quantizer design thus a vector quantizer is designed by minimizing an l sub 2 reconstruction distortion measure including an additional contribution from the effect of code noise which corrupts the output of the vector quantizer the neighborhood updating scheme of kohonen s topographic mapping training algorithm emerges as a special case of this code noise model this formulation of kohonen s algorithm is a specific instance of the robust hidden layer principle which stabilizes the internal representations chosen by a network against anticipated noise or distortion processes

adaptive nonlinear manifolds and their applications to pattern recognition dimensionality reduction has long been associated with retinotopic mapping for understanding cortical maps multisensory information is processed fused and mapped to an essentially 2 d cortex in an information preserving manner data processing and projection techniques inspired by this biological mechanism are playing an increasingly important role in pattern recognition computational intelligence data mining information retrieval and image recognition dimensionality reduction involves reduction of features or volume of data and has become an essential step of information processing in many fields the topic of manifold learning has recently attracted a great deal of attention and a number of advanced techniques for extracting nonlinear manifolds and reducing data dimensions have been proposed from statistics geometry theory and adaptive neural networks this paper provides an overview of this challenging and emerging topic and discusses various recent methods such as self organizing map som kernel pca principal manifold isomap local linear embedding and laplacian eigenmap many of them can be considered in a learning manifold framework the paper further elaborates on the biologically inspired som model and its metric preserving variant visom under the framework of adaptive manifold and their applications in dimensionality reduction with face recognition are investigated the experiments demonstrate that adaptive visom based methods produce markedly improved performance over the others due to their metric scaling and preserving properties along the nonlinear manifold

minimum variance estimation of parameters constrained by bounds this correspondence deals with an extension of minimum variance estimation when the parameter to be estimated is constrained by bounds it is shown that a particular initial distribution allows finite dimensional calculation and leads to a nonlinear filter more precisely it is shown that a truncated gaussian distribution is preserved a long time leading to a finite number of parameters to be computed proof of the main theorem is straightforward with significant application such as positive real amplitude estimation performance gains are shown on the loran c signal reception example

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

a type of duality between self organizing maps and minimal wiring i show here that two interpretations of neural maps are closely related the first due to kohonen sees these maps as forming by an adaptive process in response to stimuli the second the minimal wiring or dimension reduction perspective interprets the maps as the solution of a minimization problem where the goal is to keep the wiring between neurons with similar receptive fields as short as possible recent work by luttrell provides a bridging concept by showing that kohonen s algorithm can be regarded as an approximation to gradient descent on a certain functional i show how this functional can be generalized in a way that allows it to be interpreted as a measure of wirelength

adaptive fuzzy control for mimo nonlinear systems with nonsymmetric control gain matrix and unknown control direction in this paper an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi input multi output nonlinear systems with nonsymmetric control gain matrix and unknown control direction the nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix and the symmetric matrix as well as the skew symmetric matrix is approximated by fuzzy systems by using the symmetric matrix decomposition technique the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes based on the decomposition results the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem a robust control term is employed to compensate for the lumped errors and a nussbaum type function is incorporated in the robust control term to deal with the unknown control direction the proposed scheme guarantees that all the signals in the resulting closed loop system are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

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

kernel class wise locality preserving projection in the recent years the pattern recognition community paid more attention to a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among them locality preserving projection lpp is one of the most promising feature extraction techniques however when lpp is applied to the classification tasks it shows some limitations such as the ignorance of the label information in this paper we propose a novel local structure based feature extraction method called class wise locality preserving projection clpp clpp utilizes class information to guide the procedure of feature extraction in clpp the local structure of the original data is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper moreover a kernel version of clpp namely kernel clpp kclpp is developed through applying the kernel trick to clpp to increase its performance on nonlinear feature extraction experiments on orl face database and yale face database are performed to test and evaluate the proposed algorithm

adaptive fuzzy control for feedback linearizable mimo nonlinear systems with prescribed performance abstract in this paper a new adaptive fuzzy control scheme with prescribed performance is developed for a class of feedback linearizable uncertain mimo nonlinear systems with unknown control direction and external disturbances the fuzzy systems are employed to approximate the unknown nonlinear functions and a nussbaum type function is applied to resolve the unknown control direction problems by using the prescribed performance bounds an adaptive fuzzy controller equipped with the nussbaum type gain function is developed the proposed design scheme guarantees that all the signals in the closed loop systems are bounded and that the tracking errors converge to a prescribed performance bounds by guaranteeing the convergence of the filtered tracking error to a predefine performance bounds two simulation examples are used to demonstrate the effectiveness of the proposed scheme