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

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

multiscale tikhonov total variation image restoration using spatially varying edge coherence exponent edge preserving regularization using partial differential equation pde based methods although extensively studied and widely used for image restoration still have limitations in adapting to local structures we propose a spatially adaptive multiscale variable exponent based anisotropic variational pde method that overcomes current shortcomings such as over smoothing and staircasing artifacts while still retaining and enhancing edge structures across scale our innovative model automatically balances between tikhonov and total variation tv regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor the multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties the discretization method we use satisfies the maximum minimum principle which guarantees that artificial edge regions are not created extensive experimental results using synthetic and natural images indicate that the proposed multiscale tikhonov tv mttv and dynamical mttv methods perform better than many contemporary denoising algorithms in terms of several metrics including signal to noise ratio improvement and structure preservation promising extensions to handle multiplicative noise models and multichannel imagery are also discussed

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

semi implicit finite volume scheme for image processing in 3d cylindrical geometry nowadays 3d echocardiography is a well known technique in medical diagnosis inexpensive echocardiographic acquisition devices are applied to scan 2d slices rotated along a prescribed direction then the discrete 3d image information is given on a cylindrical grid usually this original discrete image intensity function is interpolated to a uniform rectangular grid and then numerical schemes for 3d image processing operations e g nonlinear smoothing in the uniform rectangular geometry are used however due to the generally large amount of noise present in echocardiographic images the interpolation step can yield undesirable results in this paper we avoid this step and suggest a 3d finite volume method for image selective smoothing directly in the cylindrical image geometry specifically we study a semi implicit 3d cylindrical finite volume scheme for solving a perona malik type nonlinear diffusion equation and apply the scheme to 3d cylindrical echocardiographic images the l stability and convergence of the scheme to the weak solution of the regularized perona malik equation is proved

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

generalized spatio chromatic diffusion a framework for diffusion of color images is presented the method is based on the theory of thermodynamics of irreversible transformations which provides a suitable basis for designing correlations between the different color channels more precisely we derive an equation for color evolution which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space we apply the proposed equation to images represented in several color spaces such as rgb cielab opponent colors and ihs

direct adaptive fuzzy control with a self structuring algorithm this paper presents a direct self structuring adaptive fuzzy control dsafc scheme for affine nonlinear single input single output systems we show that the only restriction on the control gain is that it be positive no upper bound on this gain nor its derivative needs to be known from an initial fuzzy system with a small number of rules the self structuring algorithm adds membership functions and rules when needed to limit the size of the fuzzy system from growing indefinitely the self structuring algorithm replaces old membership functions by new ones instead of adding more membership functions so that the number of rules never exceeds a predefined upper bound the stability of the closed loop system is guaranteed using the lyapunov synthesis approach the proposed control scheme is demonstrated by application to an inverted pendulum and a magnetic levitation system

a new image flux conduction model and its application to selective image smoothing a discrete image flux conduction equation which is completely new in this field is proposed the new approach starts with formulating a discrete image flux conduction equation based on the concept of heat conduction theory based on this discrete equation the status change at a time point can be directly computed from its spatial neighborhood to more accurately estimate an image flux we have used an orthogonal wavelet basis to approximate the gradient of the intensity at each point since the proposed approach is discrete by nature it is not necessary to formulate a continuous pde to fit the discrete image data set furthermore introduction of different numerical methods to solve the pde can also be avoided since the proposed approach does not require that a pde be solved it is therefore more efficient and accurate than the conventional methods experimental results obtained using both synthetic signals and real images have demonstrated that the proposed model could effectively handle the selective image smoothing problem

on the persistency of excitation in radial basis function network identification of nonlinear systems considers radial basis function rbf network approximation of a multivariate nonlinear mapping as a linear parametric regression problem linear recursive identification algorithms applied to this problem are known to converge provided the regressor vector sequence has the persistency of excitation pe property the main contribution of this paper is formulation and proof of pe conditions on the input variables in the rbf network identification the regressor vector is a nonlinear function of these input variables according to the formulated condition the inputs provide pe if they belong to domains around the network node centers for a two input network with gaussian rbf that have typical width and are centered on a regular mesh these domains cover about 25 of the input domain volume the authors further generalize the proposed solution of the standard rbf network identification problem and study affine rbf network identification that is important for affine nonlinear system control for the affine rbf network the author formulates and proves a pe condition on both the system state parameters and control inputs

an advanced and adaptive mathematical function for an efficient anisotropic image filtering image de noising and enhancement are becoming increasingly widespread anisotropic diffusion is one of the greatest techniques that are used to remove noise of the image while keeping the important information unvaried nevertheless it suffers from many drawbacks such as the image blurring this work is concerned with a new anisotropic diffusion approach founded on an innovative mathematical function for noise reducing and edge preserving the entire contribution can be observed from the experimental results which have shown that the new proposed anisotropic scheme is not only able to remove the noise efficiently but also to preserve the content in the denoised image

pde based image restoration a hybrid model and color image denoising the paper is concerned with pde based image restoration a new model is introduced by hybridizing a nonconvex variant of the total variation minimization tvm and the motion by mean curvature mmc in order to deal with the mixture of the impulse and gaussian noises reliably we suggest the essentially nondissipative enod difference schemes for the mmc component to eliminate the impulse noise with a minimum ideally no introduction of dissipation the mmc tvm hybrid model and the enod schemes are applied for both gray scale and color images for color image denoising we consider the chromaticity brightness decomposition with the chromaticity formulated in the angle domain an incomplete crank nicolson alternating direction implicit time stepping procedure is adopted to solve those differential equations efficiently numerical experiments have shown that the new hybrid model and the numerical schemes can remove the mixture of the impulse and gaussian noises efficiently and reliably preserving edges quite satisfactorily

online adaptive fuzzy neural identification and control of a class of mimo nonlinear systems this paper presents a robust adaptive fuzzy neural controller afnc suitable for identification and control of a class of uncertain multiple input multiple output mimo nonlinear systems the proposed controller has the following salient features 1 self organizing fuzzy neural structure i e fuzzy control rules can be generated or deleted automatically 2 online learning ability of uncertain mimo nonlinear systems 3 fast learning speed 4 fast convergence of tracking errors 5 adaptive control where structure and parameters of the afnc can be self adaptive in the presence of disturbances to maintain high control performance 6 robust control where global stability of the system is established using the lyapunov approach simulation studies on an inverted pendulum and a two link robot manipulator show that the performance of the proposed controller is superior

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

flocking with connectivity preservation for disturbed nonlinear multi agent systems by output feedback abstractthis paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi agent systems in order to deal with the nonlinearities in the dynamic of all agents some auxiliary variables are introduced into the state observer for stability analysis by proposing a bounded potential function and using adaptive theory a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

partial differential equation based approach for empirical mode decomposition application on image analysis the major problem with the empirical mode decomposition emd algorithm is its lack of a theoretical framework so it is difficult to characterize and evaluate this approach in this paper we propose in the 2 d case the use of an alternative implementation to the algorithmic definition of the so called sifting process used in the original huang s emd method this approach especially based on partial differential equations pdes was presented by niang in previous works in 2005 and 2007 and relies on a nonlinear diffusion based filtering process to solve the mean envelope estimation problem in the 1 d case the efficiency of the pde based method compared to the original emd algorithmic version was also illustrated in a recent paper recently several 2 d extensions of the emd method have been proposed despite some effort 2 d versions for emd appear poorly performing and are very time consuming so in this paper an extension to the 2 d space of the pde based approach is extensively described this approach has been applied in cases of both signal and image decomposition the obtained results confirm the usefulness of the new pde based sifting process for the decomposition of various kinds of data some results have been provided in the case of image decomposition the effectiveness of the approach encourages its use in a number of signal and image applications such as denoising detrending or texture analysis

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

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

the perona malik paradox the perona malik equation is a formally ill posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable after discussing the background of this parad

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

fuzzy observed based adaptive consensus tracking control for second order multiagent systems with heterogeneous nonlinear dynamics in this paper the consensus tracking control problem of second order multiagent systems with unknown nonlinear dynamics immeasurable states and disturbances is investigated the nonlinear dynamics in multiagent systems do not satisfy the matched condition in this paper fuzzy logic system is introduced to approximate the unknown nonlinear dynamics and adaptive high gain observer is designed to estimate the unmeasured states based on backstepping approach and lyapunov theory a new adaptive fuzzy distributed controller is proposed for each agent only using the information of itself and its neighbors then the consensus tracking is achieved under the designed distributed controller moreover it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible finally the simulation result illustrates the effectiveness of the designed controller

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

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

consensus tracking for second order nonlinear multi agent systems with switching topologies and a time varying reference state abstractin this study the authors consider the consensus tracking problem for second order nonlinear multi agent systems with switching topologies and a time varying reference state the dynamics of each agent consists of nonlinear inherent dynamics in order to reach consensus tracking a class of nonsmooth control protocols is proposed which only depends on the agent s own information and its neighbours information with the aid of algebraic graph theory matrix theory and lyapunov theory some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived finally the numerical simulations are given to illustrate the effectiveness of the developed theoretical results

leader following consensus for a class of second order nonlinear multi agent systems abstract this paper deals with the leader following consensus problem for a class of multi agent systems with nonlinear dynamics and directed communication topology the control input of the leader agent is assumed to be unknown to all follower agents a distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents which achieves leader following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent compared with previous results the nonlinear functions are not required to satisfy the globally lipschitz or lipschitz like condition and the adaptive consensus protocol is in a distributed fashion a numerical example is given to verify our proposed protocol

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

a fuzzy asymmetric garch model applied to stock markets in this paper we derive a new class of flexible threshold asymmetric generalized autoregression conditional heteroskedasticity garch models we use this tool for analysis and modeling of the properties that are apparent in many financial time series in general the transmission of volatility in the stock market is time varying nonlinear and asymmetric with respect to both positive and negative results given this fact we adopt the method of fuzzy logic systems to modify the threshold values for an asymmetric garch model our simulations use stock market data from the taiwan weighted index taiwan the nikkei 225 index japan and the hang seng index hong kong to illustrate the performance of our proposed method from the simulation results we have determined that the forecasting of volatility performance is significantly improved if the leverage effect of clustering is considered along with the use of expert knowledge enabled by the garch model

nonlinear multiscale wavelet diffusion for speckle suppression and edge enhancement in ultrasound images this paper introduces a novel nonlinear multiscale wavelet diffusion method for ultrasound speckle suppression and edge enhancement this method is designed to utilize the favorable denoising properties of two frequently used techniques the sparsity and multiresolution properties of the wavelet and the iterative edge enhancement feature of nonlinear diffusion with fully exploited knowledge of speckle image models the edges of images are detected using normalized wavelet modulus relying on this feature both the envelope detected speckle image and the log compressed ultrasonic image can be directly processed by the algorithm without need for additional preprocessing speckle is suppressed by employing the iterative multiscale diffusion on the wavelet coefficients with a tuning diffusion threshold strategy the proposed method can improve the image quality for both visualization and auto segmentation applications we validate our method using synthetic speckle images and real ultrasonic images performance improvement over other despeckling filters is quantified in terms of noise suppression and edge preservation indices

a backward forward regularization of the perona malik equation abstract it is shown that the perona malik equation pme admits a natural regularization by forward backward diffusions possessing better analytical properties than pme itself well posedness of the regularizing problem along with a complete understanding of its long time behavior can be obtained by resorting to weak young measure valued solutions in the spirit of kinderlehrer and pedregal 1992 1 and demoulini 1996 2 solutions are unique to an extent to be specified but can exhibit micro oscillations in the sense of minimizing sequences and in the spirit of material science between preferred gradient states in the limit of vanishing regularization the preferred gradients have size 0 or thus explaining the well known phenomenon of staircasing the theoretical results do completely confirm and or predict numerical observations concerning the generic behavior of solutions

robust decentralized direct adaptive output feedback fuzzy control for a class of large sale nonaffine nonlinear systems in the previous work of huang et al a decentralized direct adaptive fuzzy h tracking controller of large scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable in this note we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller by combination of a state observer a fuzzy inference system and robust control technique the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required all the signals of the closed loop large scale system are proved to be uniformly ultimately bounded the effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums

adaptive fuzzy robust tracking controller design via small gain approach and its application an adaptive fuzzy robust tracking control afrtc algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function which are all the unstructured or nonrepeatable state dependent unknown nonlinear functions arising from modeling errors and external disturbances the takagi sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the afrtc algorithm is designed by use of the input to state stability approach and small gain theorem the algorithm is highlighted by three advantages 1 the uniform ultimate boundedness of the closed loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed 2 the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed and 3 the adaptive mechanism with minimal learning parameterizations can be obtained the performance and limitations of the proposed method are discussed the uses of the afrtc for the tracking control design of a pole balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples simulation results show the effectiveness of the control scheme

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

consensus for multi agent systems with inherent nonlinear dynamics under directed topologies abstract this paper considers the consensus problem for multi agent systems with inherent nonlinear dynamics under directed topologies a variable transformation method is used to convert the consensus problem to a partial stability problem both first order and second order systems are investigated under fixed and switching topologies respectively it is assumed that the inherent nonlinear terms satisfy the lipshitz condition sufficient conditions on the feedback gains are given based on a lyapunov function method for first order systems under a fixed topology the consensus is achieved if the feedback gain related to the agents positions is large enough for first order systems under switching topologies the effect of the minimum dwell time for the switching signal on the consensus achievement is considered for second order systems under a fixed topology the consensus is achieved if the feedback gains related to the agents positions and velocities respectively are both large enough for second order systems under switching topologies a switching variable transformation is given then the consensus problem is investigated when all the digraphs are strongly connected and weighted balanced with a common weighted vector finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

fractional order anisotropic diffusion for image denoising this paper introduces a new class of fractional order anisotropic diffusion equations for noise removal these equations are euler lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function so the proposed equations can be seen as generalizations of second order and fourth order anisotropic diffusion equations we use the discrete fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain it is one important aspect of the algorithm that it considers the input image as a periodic image to overcome this problem we use a folded algorithm by extending the image symmetrically about its borders finally we list various numerical results on denoising real images experiments show that the proposed fractional order anisotropic diffusion equations yield good visual effects and better signal to noise ratio

adaptive nonlocal filtering a fast alternative to anisotropic diffusion for image enhancement nonlinear anisotropic diffusion algorithms provide significant improvement in image enhancement as compared to linear filters however the excessive computational cost of solving nonlinear pdes precludes their use in real time vision applications we show that two orders of magnitude speed improvement is provided by a new image filtering paradigm in which an adaptively determined vector field specifies nonlocal application points for an image filter

stable adaptive fuzzy pd plus pi controller for nonlinear uncertain systems abstract this paper presents an improved version of the stable fuzzy adaptive control structure which comprises an approximation of the ideal controller and a supervisory controller wang 1993 2 the proposed adaptive controller cancels the nonlinear function using a fuzzy system whose inputs are the feedback error signals instead of the state variables by using the feedback errors as the inputs to the fuzzy system improved control and disturbance rejection performance may be achieved as the controller is made more sensitive to the presence of tracking errors another useful feature of this structure is that the supervisory controller can be designed without the need of prior knowledge about the plant furthermore the computational burden of on line tuning can be reduced by disabling on line adaptation without incurring stability problems the efficiency of the proposed adaptive fuzzy system is demonstrated through simulation studies

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

stable flocking of multiple inertial agents on balanced graphs in this note we consider the flocking of multiple agents which have significant inertias and evolve on a balanced information graph here by flocking we mean that all the agents move with a common velocity while keeping a certain desired internal group shape we first show that flocking algorithms that neglect agents inertial effect can cause unstable group behavior to incorporate this inertial effect we use the passive decomposition which decomposes the closed loop group dynamics into two decoupled systems a shape system representing the internal group shape and a locked system describing the motion of the center of mass then analyzing the locked and shape systems separately with the help of graph theory we propose a provably stable flocking control law which ensures that the internal group shape is exponentially stabilized to a desired one while all the agents velocities converge to the centroid velocity that is also shown to be time invariant this result still holds for slow switching balanced information graphs simulation is performed to validate the theory

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 leader following consensus for a class of higher order nonlinear multi agent systems with directed switching networks abstract in this paper we study the leader following consensus problem for a class of uncertain nonlinear multi agent systems under jointly connected directed switching networks the uncertainty includes constant unbounded parameters and external disturbances we first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence then by integrating the conventional adaptive control technique with the adaptive distributed observer we present our solution by a distributed adaptive state feedback control law our result is illustrated by the leader following consensus problem for a group of van der pol oscillators

encoding visual information using anisotropic transformations the evolution of information in images undergoing fine to coarse anisotropic transformations is analyzed by using an approach based on the theory of irreversible transformations in particular we show that when an anisotropic diffusion model is used local variation of entropy production over space and scale provides the basis for a general method to extract relevant image features

an efficient edge detection algorithm using relaxation labeling technique abstract edge detection plays an important role in computer vision tasks and has received considerable attention in image processing literature to detect edges correctly and precisely contextual information is needed how to use contextual information is a key issue in this paper we introduce an edge detection method that will use edge contextual information of the whole image efficiency this new method tries to employ contextual information within a certain distance from the focus pixel at a time this distance keeps increasing recursively until the edge feature of a pixel is uniquely defined in this manner we can minimize the need for contextual information experimental results are presented to characterize the performance of our new method in terms of better connectedness of edges and less distortion and in terms of computational efficiency a detailed comparison of our method with the context free zero crossing edge operator that uses optimal exponential filter is discussed in this paper

adaptive smoothing via contextual and local discontinuities a novel adaptive smoothing approach is proposed for noise removal and feature preservation where two distinct measures are simultaneously adopted to detect discontinuities in an image inhomogeneity underlying an image is employed as a multiscale measure to detect contextual discontinuities for feature preservation and control of the smoothing speed while local spatial gradient is used for detection of variable local discontinuities during smoothing unlike previous adaptive smoothing approaches two discontinuity measures are combined in our algorithm for synergy in preserving nontrivial features which leads to a constrained anisotropic diffusion process that inhomogeneity offers intrinsic constraints for selective smoothing thanks to the use of intrinsic constraints our smoothing scheme is insensitive to termination times and the resultant images in a wide range of iterations are applicable to achieve nearly identical results for various early vision tasks our algorithm is formally analyzed and related to anisotropic diffusion comparative results indicate that our algorithm yields favorable smoothing results and its application in extraction of hydrographic objects demonstrates its usefulness as a tool for early vision

comparison of pde based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography a comparison between two nonlinear diffusion methods for denoising oct images is performed specifically we compare and contrast the performance of the traditional nonlinear perona malik filter with a complex diffusion filter that has been recently introduced by gilboa the complex diffusion approach based on the generalization of the nonlinear scale space to the complex domain by combining the diffusion and the free schrodinger equation is evaluated on synthetic images and also on representative oct images at various noise levels the performance improvement over the traditional nonlinear perona malik filter is quantified in terms of noise suppression image structural preservation and visual quality an average signal to noise ratio snr improvement of about 2 5 times and an average contrast to noise ratio cnr improvement of 49 was obtained while mean structure similarity mssim was practically not degraded after denoising the nonlinear complex diffusion filtering can be applied with success to many oct imaging applications in summary the numerical values of the image quality metrics along with the qualitative analysis results indicated the good feature preservation performance of the complex diffusion process as desired for better diagnosis in medical imaging processing

on the development of a coupled nonlinear telegraph diffusion model for image restoration abstract in this work we propose a telegraph coupled partial differential equation tcpde based model for image restoration the new framework interpolates between a couple of nonlinear telegraph equation and a parabolic equation this proposed strategy can be applied to significantly preserve the oscillatory and texture pattern in an image even in low signal to noise ratio snr first we prove that the present model has a unique global weak solution using banach s fixed point theorem then we apply our model over a set of gray level images to illustrate the image denoising ability of the proposed model the experimental results of the proposed model are reported which found better in terms of noise elimination and edge preservation with respect to the recently developed hyperbolic parabolic pde based models as well as coupled diffusion based model

edge preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods this paper introduces a novel image dependent filtering approach derived from concepts known in mathematical morphology and aiming at edge preserving smoothing of natural images like other adaptive methods it assumes that the neighbourhood of a pixel contains the essential information required for the estimation of local features in the image the proposed strategy essentially consists in a weighted averaging combining both spatial and tonal information for that purpose a twofold similarity measure is calculated from local geodesic time functions this way no prior operator definition is required since a weighting neighbourhood and a weighting kernel are determined automatically from the unfiltered input data for each pixel location by designing relevant geodesic masks two adaptive filtering algorithms are derived that are particularly efficient at smoothing heterogeneous areas while preserving relevant structures in greyscale and multichannel images

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

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

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

variational approach for edge preserving regularization using coupled pdes this paper deals with edge preserving regularization for inverse problems in image processing we first present a synthesis of the main results we have obtained in edge preserving regularization by using a variational approach we recall the model involving regularizing functions spl phi and we analyze the geometry driven diffusion process of this model in the three dimensional 3 d case then a half quadratic theorem is used to give a very simple reconstruction algorithm after a critical analysis of this model we propose another functional to minimize for edge preserving reconstruction purposes it results in solving two coupled partial differential equations pdes one processes the intensity the other the edges we study the relationship with similar pde systems in particular with the functional proposed by ambrosio tortorelli 1990 1992 in order to approach the mumford shah 1989 functional developed in the segmentation application experimental results on synthetic and real images are presented

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

nonlinear image filtering with edge and corner enhancement the authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion the method is designed to enhance not only edges but corners and t junctions as well the method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges such a process is ill posed making the results depend strongly on how the algorithm differs from the diffusion process two ways of modifying the equations using simulations on a variable grid are studied

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

a new iterated two band diffusion equation theory and its application we propose an iterated two band filtering method to solve the selective image smoothing problem we prove that a discrete computation step in an iterated nonlinear diffusion based filtering algorithm is equivalent to a sequence of operations including decomposition regularization and then reconstruction in the proposed two band filtering scheme to correctly separate the high frequency components from the low frequency ones in the decomposition process we adopt a dyadic wavelet based approximation scheme in the regularization process we use a diffusivity function as a guide to retain useful data and suppress noises finally the signal of the next stage which is a smoother version of the signal at the previous stage can be computed by reconstructing the decomposed low frequency component and the regularized high frequency component based on the proposed scheme the smoothing operation can be applied to the correct targets experimental results show that our new approach is really efficient in noise removing

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

parameter convergence in nonlinearly parameterized systems a large class of problems in parameter estimation concerns nonlinearly parametrized systems over the past few years a stability framework for estimation and control of such systems has been established we address the issue of parameter convergence in such systems in this paper systems with both convex concave and general parameterizations are considered in the former case sufficient conditions are derived under which parameter estimates converge to their true values using a min max algorithm in the latter case to achieve parameter convergence a hierarchical min max algorithm is proposed where the lower level consists of a min max algorithm and the higher level component updates the bounds on the parameter region within which the unknown parameter is known to lie using this hierarchical algorithm a necessary and sufficient condition is established for global parameter convergence in systems with a general nonlinear parameterization in both cases the conditions needed are shown to be stronger than linear persistent excitation conditions that guarantee parameter convergence in linearly parametrized systems explanations and examples of these conditions and simulation results are included to illustrate the nature of these conditions a general definition of nonlinear persistent excitation that leads to parameter convergence is proposed at the end of this paper

two mode indirect adaptive control approach for the synchronization of uncertain chaotic systems by the use of a hierarchical interval type 2 fuzzy neural network two mode adaptive controllers have two phases of operation a learning phase and an operation phase this paper presents a two mode indirect adaptive control approach for the synchronization of chaotic systems using a hierarchical interval type 2 fuzzy neural network ht2fnn its contribution to the existing literature is the adaptation laws derived for the parameters of the membership functions based on lyapunov stability analysis since in hierarchical case each t2fnn has only two inputs the computing of the derivatives is much simpler than the case in classical interval type 2 fnn moreover a novel approach is presented for the compensation of the approximation error the tuning of the parameters of the membership functions mf and the use of an interval type 2 fnn ensures that the estimation error is very small so that it can be negligible furthermore the number of mf required is seen to be less than that needed with type 1 fuzzy sets the simulation results confirm the efficacy of the proposed scheme in the synchronization of a uncertain nonidentical chaotic systems

on the choice of the parameters for anisotropic diffusion in image processing anisotropic diffusion filtering is highly dependent on some crucial parameters such as the conductance function the gradient threshold parameter and the stopping time of the iterative process the various alternative options at each stage of the algorithm are examined and evaluated and the best choice is selected an automatic stopping criterion is proposed that takes into consideration the quality of the preserved edges as opposed to just the level of smoothing achieved the proposed scheme is evaluated with the help of real and simulated images and compared with other state of the art schemes using objective criteria

h tracking based decentralized hybrid adaptive output feedback fuzzy control for a class of large scale nonlinear systems this paper proposes a novel h tracking based decentralized hybrid adaptive fuzzy controller via output feedback for a class of large scale uncertain nonlinear systems to achieve better adaptation properties the proposed controller is a weighted combination of indirect and direct adaptive fuzzy controls iafc and dafc such that both fuzzy descriptions and control rules can be incorporated at the same time after proper filtering of the observation error dynamics the developed observer based feedback and adaptation mechanisms become implementable indeed by using fuzzy inference systems a state observer and h tracking technique the decentralized combined indirect and direct adaptive fuzzy control algorithm is developed based upon a united h tracking controller design for the modification of the previous work of huang et al the resultant closed loop systems are guaranteed to be stable and a good h tracking performance is obtained simulation results of interrelated inverted pendulums substantiate that the proposed cafc system stands out as being better properties than typical iafc and dafc systems in that the tracking performance is much better while the control effort is even smaller

a new nonlocal nonlinear diffusion of image processing abstract a novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing the equation can be viewed as a new paradigm for the regularization of the well known perona malik equation the regularization is implemented via nonlinearity intensity reduction through fractional derivatives well posedness in the weak setting is established global existence and convergence to the average holds in the purely diffusive limit whereas an interesting dynamic behavior is engendered by the presence of nontrivial equilibria as the intensity of the nonlinearity is increased and comes close to the one of perona malik

a robust approach to image enhancement based on fuzzy logic in this paper we propose a robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement i removing impulse noise ii smoothing out nonimpulse noise and iii enhancing or preserving edges and certain other salient structures we derive three different filters for each of the above three tasks using the weighted or fuzzy least squares ls method and define the criteria for selecting each of the three filters the criteria are based on the local context and they constitute the antecedent clauses of the fuzzy rules the overall result of the fuzzy rule based system is the combination of the results of the individual filters where each result contributes to the degree that the corresponding antecedent clause is satisfied this approach gives us a powerful and flexible image enhancement paradigm results of the proposed method on several types of images are compared with those of other standard techniques

iterative solvers for image denoising with diffusion models a comparative study abstract in this paper we propose and compare the use of two iterative solvers using the crank nicolson finite difference method to address the task of image denoising via partial differential equations pdes models such as regularized perona malik equation or c model and bazan model bilateral filter based model the solvers which are considered in this paper are the successive over relaxation sor and an advanced solver known as hybrid bi conjugate gradient stabilized hybrid bicgstab method from numerical experiments it is found that the crank nicolson method with hybrid bicgstab iterative solver produces better results and is more efficient than sor and already existing in terms of mssim and psnr

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed