direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

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

design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

l kernel classification nonparametric kernel methods are widely used and proven to be successful in many statistical learning problems well known examples include the kernel density estimate kde for density estimation and the support vector machine svm for classification we propose a kernel classifier that optimizes the l2 or integrated squared error ise of a difference of densities we focus on the gaussian kernel although the method applies to other kernels suitable for density estimation like a support vector machine svm the classifier is sparse and results from solving a quadratic program we provide statistical performance guarantees for the proposed l2 kernel classifier in the form of a finite sample oracle inequality and strong consistency in the sense of both ise and probability of error a special case of our analysis applies to a previously introduced ise based method for kernel density estimation for dimensionality greater than 15 the basic l2 kernel classifier performs poorly in practice thus we extend the method through the introduction of a natural regularization parameter which allows it to remain competitive with the svm in high dimensions simulation results for both synthetic and real world data are presented

direct learning of sparse changes in markov networks by density ratio estimation we propose a new method for detecting changes in markov network structure between two sets of samples instead of naively fitting two markov network models separately to the two data sets and figuring out their difference we directly learn the network structure change by estimating the ratio of markov network models this density ratio formulation naturally allows us to introduce sparsity in the network structure change which highly contributes to enhancing interpretability furthermore computation of the normalization term a critical bottleneck of the naive approach can be remarkably mitigated we also give the dual formulation of the optimization problem which further reduces the computation cost for large scale markov networks through experiments we demonstrate the usefulness of our method

data imputation through the identification of local anomalies we introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources e g an occluder in the case of a visual recording within this framework we propose 1 a novel algorithm to efficiently separate i e detect and localize possible corruptions from a given suspicious data instance and 2 a maximum a posteriori estimator to impute the corrupted data as a generalization to euclidean distance we also propose a novel distance measure which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted clean reference data set once each part is labeled as anomalous versus normal the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed under a certain conditional independency structure assumed for the binary patterns we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning the proposed framework is tested over several well known machine learning data sets with synthetically generated corruptions and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions

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

probabilistic optimization for conceptual rainfall runoff models a comparison of the shuffled complex evolution and simulated annealing algorithms automatic optimization algorithms are used routinely to calibrate conceptual rainfall runoff crr models the goal of calibration is to estimate a feasible and unique global set of parameter estimates that best fit the observed runoff data most if not all optimization algorithms have difficulty in locating the global optimum because of response surfaces that contain multiple local optima with regions of attraction of differing size discontinuities and long ridges and valleys extensive research has been undertaken to develop efficient and robust global optimization algorithms over the last 10 years this study compares the performance of two probabilistic global optimization methods the shuffled complex evolution algorithm sce ua and the three phase simulated annealing algorithm sa sx both algorithms are used to calibrate two parameter sets of a modified version of boughton s 1984 sfb model using data from two australian catchments that have low and high runoff yields for the reduced well identified parameter set the algorithms have a similar efficiency for the low yielding catchment but sce ua is almost twice as robust although the robustness of the algorithms is similar for the high yielding catchment sce ua is six times more efficient than sa sx when fitting the full parameter set the performance of sa sx deteriorated markedly for both catchments these results indicated that sce ua s use of multiple complexes and shuffling provided a more effective search of the parameter space than sa sx s single simplex with stochastic step acceptance criterion especially when the level of parameterization is increased examination of the response surface for the low yielding catchment revealed some reasons why sce ua outperformed sa sx and why probabilistic optimization algorithms can experience difficulty in locating the global optimum

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

multivariate calibration of a water and energy balance model in the spectral domain 1 the objective of this paper is to explore the possibility of using multiple variables in the calibration of hydrologic models in the spectral domain a simple water and energy balance model was used combined with observations of the energy balance and the soil moisture profile the correlation functions of the model outputs and the observations for the different variables have been calculated after the removal of the diurnal cycle of the energy balance variables these were transformed to the frequency domain to obtain spectral density functions which were combined in the calibration algorithm it has been found that it is best to use the square root of the spectral densities in the parameter estimation under these conditions spectral calibration performs almost equally as well as time domain calibration using least squares differences between observed and simulated time series incorporation of the spectral coefficients of the cross correlation functions did not improve the results of the calibration calibration on the correlation functions in the time domain led to worse model performance when the meteorological forcing and model calibration data are not overlapping in time spectral calibration has been shown to lead to an acceptable model performance overall the results in this paper suggest that in case of data scarcity multivariate spectral calibration can be an attractive tool to estimate model parameters

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

a new bayesian recursive technique for parameter estimation 1 the performance of any model depends on how well its associated parameters are estimated in the current application a localized bayesian recursive estimation lobare approach is devised for parameter estimation the lobare methodology is an extension of the bayesian recursive estimation bare method it is applied in this paper on two different types of models an artificial intelligence ai model in the form of a support vector machine svm application for forecasting soil moisture and a conceptual rainfall runoff crr model represented by the sacramento soil moisture accounting sac sma model support vector machines based on statistical learning theory slt represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology they require estimation of three parameters sac sma is a very well known model that estimates runoff it has a 13 dimensional parameter space in the lobare approach presented here bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set this is done by narrowing the sampling space through updating the parent bounds based on their fitness these bounds are actually the parameter sets that were selected by bare runs on subspaces of the initial parameter space the new approach results in faster convergence toward the optimal parameter set using minimum training calibration data and fewer sets of parameter values the efficacy of the localized methodology is also compared with the previously used bare algorithm

adaptive tracking control of uncertain mimo nonlinear systems with input constraints in this paper adaptive tracking control is proposed for a class of uncertain multi input and multi output nonlinear systems with non symmetric input constraints the auxiliary design system is introduced to analyze the effect of input constraints and its states are used to adaptive tracking control design the spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix subsequently the constrained adaptive control is presented where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure under the proposed control techniques the closed loop semi global uniformly ultimate bounded stability is achieved via lyapunov synthesis finally simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control

kernel methods for measuring independence we introduce two new functionals the constrained covariance and the kernel mutual information to measure the degree of independence of random variables these quantities are both based on the covariance between functions of the random variables in reproducing kernel hilbert spaces rkhss we prove that when the rkhss are universal both functionals are zero if and only if the random variables are pairwise independent we also show that the kernel mutual information is an upper bound near independence on the parzen window estimate of the mutual information analogous results apply for two correlation based dependence functionals introduced earlier we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels and prove the latter to be an upper bound on the mutual information near independence the performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

calibration of a water and energy balance model recursive parameter estimation versus particle swarm optimization 1 it is well known that one of the major problems in the application of land surface models is the determination of the various model parameters in most cases only one or a limited number of variables are used to estimate these parameters this study evaluates the use of two fundamentally different global optimization methods multistart weight adaptive recursive parameter estimation mwarpe and particle swarm optimization pso for the estimation of hydrologic model parameters on the basis of data for multiple variables mwarpe iteratively uses the linear recursive filter equations in a monte carlo setting and therefore does not rely on the explicit minimization of an objective function however a major drawback of the mwarpe method is the high dimensionality determined by the number of observations of the matrix to be inverted on the other hand pso is a stochastic optimization method based on the collective strength of a population of individuals with flocking or herding behavior as observed in a wide number of biological systems in situ observations of net radiation latent sensible and ground heat fluxes and the soil moisture profile are used to determine the parameters of a simplified water and energy balance model both optimization methods are analyzed in terms of model performance and computational efficiency comparable results expressed in terms of the root mean square error values were obtained for both methods however it was found that mwarpe tends to slightly overfit the data

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

geometric convergence and central limit theorems for multidimensional hastings and metropolis algorithms we develop results on geometric ergodicity of markov chains and apply these and other recent results in markov chain theory to multidimensional hastings and metropolis algorithms for those based on random walk candidate distributions we find sufficient conditions for moments and moment generating functions to converge at a geometric rate to a prescribed distribution by phrasing the conditions in terms of the curvature of the densities we show that the results apply to all distributions with positive densities in a large class which encompasses many commonly used statistical forms from these results we develop central limit theorems for the metropolis algorithm converse results showing non geometric convergence rates for chains where the rejection rate is not bounded away from unity are also given these show that the negative definiteness property is not redundant

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

dynamic averaging of rainfall runoff model simulations from complementary model parameterizations 1 in this paper we analyze how our evaluation of the capacity of a rainfall runoff model to represent low or high flows depends on the objective function used during the calibration process we present a method to combine models to produce a more satisfactory streamflow simulation on the basis of two different parameterizations of the same model where we previously had to choose between a more efficient simulation for either high flows or low flows but inevitably less efficient in the other range we show that a balanced simulation can be obtained by using a seasonal index to weigh the two simulations providing good efficiency in both low and high flows

a shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters author s vrugt ja gupta hv bouten w sorooshian s abstract markov chain monte carlo mcmc methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models however mcmc methods require the a priori definition of a proposal or sampling distribution which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the markov chain and its rate of convergence in this paper we present an mcmc sampler entitled the shuffled complex evolution metropolis algorithm scem ua which is well suited to infer the posterior distribution of hydrologic model parameters the scem ua algorithm is a modified version of the original sce ua global optimization algorithm developed by duan et al 1992 the scem ua algorithm operates by merging the strengths of the metropolis algorithm controlled random search competitive evolution and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution three case studies demonstrate that the adaptive capability of the scem ua algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional metropolis hastings samplers

parametric statistical modeling by minimum integrated square error the likelihood function plays a central role in parametric and bayesian estimation as well as in nonparametric function estimation via local polynomial modeling however integrated square error has enjoyed a long tradition as the goodness of fit criterion of choice in nonparametric density estimation in this article i investigate the use of integrated square error or l2 distance as a theoretical and practical estimation tool for a variety of parametric statistical models i show that the asymptotic inefficiency of the parameters estimated by minimizing the integrated square error or l2estimation l2e criterion versus the maximum likelihood estimator is roughly that of the median versus the mean i demonstrate by example the well known result that minimum distance estimators including l2e are inherently robust however l2e does not require specification of any tuning factors found in robust likelihood algorithms l2e is particularly appropriate for analyzing massive datasets in which data cleanin

calibration of rainfall runoff models application of global optimization to the sacramento soil moisture accounting model conceptual rainfall runoff models are difficult to calibrate by means of automatic methods one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters this paper investigates the consistency with which two global optimization methods the shuffled complex evolution sce ua method developed by the authors and the multistart simplex msx method are able to find the optimal parameter set during calibration of the sacramento soil moisture accounting model sac sma of the national weather service river forecast system nwsrfs in the first phase of this study error free synthetic data are used to conduct a comparative evaluation of the algorithms under ideal conditions in 10 independent trials of each algorithm in which 13 parameters of the sac sma model were optimized simultaneously the sce ua method achieved a 100 success rate in locating the precise global optimum i e the true parameter values while the msx method failed in all trials even with more than twice the number of function evaluations in the second phase historical data from the leaf river watershed are used to conduct a comparative evaluation of the algorithms under real conditions using two different estimation criteria drms and hmle the sce ua algorithm obtained consistently lower function values and more closely grouped parameter estimates while using one third fewer function evaluations than the msx algorithm

adaptive markov chain monte carlo through regeneration abstract markov chain monte carlo mcmc is used for evaluating expectations of functions of interest under a target distribution this is done by calculating averages over the sample path of a markov chain having as its stationary distribution for computational efficiency the markov chain should be rapidly mixing this sometimes can be achieved only by careful design of the transition kernel of the chain on the basis of a detailed preliminary exploratory analysis of an alternative approach might be to allow the transition kernel to adapt whenever new features of are encountered during the mcmc run however if such adaptation occurs infinitely often then the stationary distribution of the chain may be disturbed we describe a framework based on the concept of markov chain regeneration which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages

on nonparametric discrimination using density differences summary we propose a technique for nonparametric discrimination in which smoothing parameters are chosen jointly according to a criterion based on the difference between two densities the approach is suitable for categorical continuous and mixed data and uses information from both populations to determine the smoothing parameter for any one population in the case of categorical data optimal performance is sometimes achieved using negative smoothing parameters a property which does not emerge if the smoothing parameters are chosen individually

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

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

h tracking based adaptive fuzzy neural control for mimo uncertain robotic systems with time delays in this paper a novel adaptive fuzzy neural control afnc scheme for multi input multi output uncertain robotic systems is proposed for h tracking performance and to suppress the effects caused by multiple time delayed state uncertainties unmodeled dynamics and disturbances each delayed uncertainty is assumed to be bounded by an unknown gain a reference model with the desired amplitude and phase properties is given to construct an error model a fuzzy neural fn system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors the proposed afnc scheme uses two on line estimations which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the fn system simultaneously stability and robustness of the afnc scheme is analyzed in lyapunov sense it is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed loop system with h tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties the performance of the proposed scheme is evaluated through the simulation results simulations are given to show the validity and confirm the performance of the proposed scheme

parameter identification for a runoff model for forest roads rainfall simulation is a commonly used approach for studying runoff and erosion from forest roads and a method is needed to estimate infiltration parameters from these experiments we used two algorithms the simplex and shuffled complex evolution to estimate parameters for a physically based infiltration and overland flow model each algorithm was tested by estimating parameters for 92 field measured hydrographs from forest roads nine of the field measured hydrographs allowed us to further test whether estimated parameters could be extended to other antecedent conditions and plot sizes the results demonstrate 1 the physically based model is able to estimate hydrographs from forest roads 2 the two algorithms find unique parameter sets in spite of an error surface that suggests identifiability problems between the hydraulic conductivity and pressure parameters 3 the two algorithms converged to the same parameter values and 4 that parameters estimated for one antecedent condition and plot size can be extended to others with reasonably small error

zadeh s extension principle for continuous functions of non interactive variables a parallel optimization approach there is a growing interest in the use of fuzzy intervals in many engineering applications however a direct implementation of zadeh s extension principle which forms the basis for computing with fuzzy intervals is still computationally too demanding for practical use in the case of a continuous function and fuzzy intervals that describe non interactive variables as inputs the output is a fuzzy interval as well and can be determined for each cut separately the problem thus reduces to finding the endpoints of these cuts which amounts to a number of interwoven optimization problems in the case of a non monotone continuous function however these optimization problems are non trivial in this paper different optimization algorithms are applied for that purpose gradient descent based on sequential quadratic programming simplex simulated annealing particle swarm optimization and particle swarm optimization combined with gradient descent in addition two approaches are followed to determine a suitable number of cuts either a fixed predetermined number is used or an initially very small number is chosen that is subsequently increased according to a linearity criterion both a non parallel and a parallel implementation are designed the parallel version is restricted to work with particle swarm optimization and employs communication to optimize its internal performance by exploiting the dependence between the various optimization problems different configurations are evaluated on a set of benchmark functions in terms of the mean area under the output fuzzy interval and the number of function evaluations particle swarm optimization combined with gradient descent starting from a small number of cuts leads to the most accurate fuzzy intervals at the cost of a relatively large number of function evaluations

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

probability density estimation from optimally condensed data samples the requirement to reduce the computational cost of evaluating a point probability density estimate when employing a parzen window estimator is a well known problem this paper presents the reduced set density estimator that provides a kernel based density estimator which employs a small percentage of the available data sample and is optimal in the l sub 2 sense while only requiring spl oscr n sup 2 optimization routines to estimate the required kernel weighting coefficients the proposed method provides similar levels of performance accuracy and sparseness of representation as support vector machine density estimation which requires spl oscr n sup 3 optimization routines and which has previously been shown to consistently outperform gaussian mixture models it is also demonstrated that the proposed density estimator consistently provides superior density estimates for similar levels of data reduction to that provided by the recently proposed density based multiscale data condensation algorithm and in addition has comparable computational scaling the additional advantage of the proposed method is that no extra free parameters are introduced such as regularization bin width or condensation ratios making this method a very simple and straightforward approach to providing a reduced set density estimator with comparable accuracy to that of the full sample parzen density estimator

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

direct density derivative estimation estimating the derivatives of probability density functions is an essential step in statistical data analysis a naive approach to estimate the derivatives is to first perform density estimation and then compute its derivatives however this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator to cope with this problem in this letter we propose a novel method that directly estimates density derivatives without going through density estimation the proposed method provides computationally efficient estimation for the derivatives of any order on multidimensional data with a hyperparameter tuning method and achieves the optimal parametric convergence rate we further discuss an extension of the proposed method by applying regularized multitask learning and a general framework for density derivative estimation based on bregman divergences applications of the proposed method to nonparametric kullback leibler divergence approximation and bandwidth matrix selection in kernel density estimation are also explored

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

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

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

robust kernel density estimation we propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample this method achieves robustness by combining a traditional kernel density estimator kde with ideas from classical m estimation we interpret the kde based on a positive semi definite kernel as a sample mean in the associated reproducing kernel hilbert space since the sample mean is sensitive to outliers we estimate it robustly via m estimation yielding a robust kernel density estimator rkde an rkde can be computed efficiently via a kernelized iteratively re weighted least squares irwls algorithm necessary and sufficient conditions are given for kernelized irwls to converge to the global minimizer of the m estimator objective function the robustness of the rkde is demonstrated with a representer theorem the influence function and experimental results for density estimation and anomaly detection

effective and efficient algorithm for multiobjective optimization of hydrologic models 1 practical experience with the calibration of hydrologic models suggests that any single objective function no matter how carefully chosen is often inadequate to properly measure all of the characteristics of the observed data deemed to be important one strategy to circumvent this problem is to define several optimization criteria objective functions that measure different complementary aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated efficient or pareto optimal solutions in this paper we present an efficient and effective markov chain monte carlo sampler entitled the multiobjective shuffled complex evolution metropolis moscem algorithm which is capable of solving the multiobjective optimization problem for hydrologic models moscem is an improvement over the shuffled complex evolution metropolis scem ua global optimization algorithm using the concept of pareto dominance rather than direct single objective function evaluation to evolve the initial population of points toward a set of solutions stemming from a stable distribution pareto set the efficacy of the moscem ua algorithm is compared with the original mocom ua algorithm for three hydrologic modeling case studies of increasing complexity

automatic calibration of conceptual rainfall runoff models optimization algorithms catchment conditions and model structure from 32 crr catchment cases combinations from four conceptual rainfall runoff models crr and eight catchments calibrated with either two or three optimization methods 1 the shuffle complex evolution method sce ua 2 the multiple start simplex msx and 3 the local simplex it seems that all three methods produced parameter sets of comparable local optimum quality even with comparable performance among the models some parameter values derived by the three optimization methods for the same crr catchment cases are surprisingly different from each other in addition parameter sets of sce ua or msx which often produce marginally better results than the local simplex at the calibration stage could end up with worse results at the validation stage apparently given the inherent limitations of calibration data model inadequacies and identifiability problems it is impossible to achieve global convergence in the parameter search however other than those for dry catchments such as ihimbu or bird creek the parameter sets obtained are generally feasible both sce ua and the local simplex are viable optimization tools while msx is inefficient computationally sce ua can complete the parameter search in one run while the local simplex often requires multirun operations to get good results

ensemble based assimilation of discharge into rainfall runoff models a comparison of approaches to mapping observational information to state space 1 the optimization of hydrologic models using the ensemble kalman filter has received increasing attention during the last decade the application of this algorithm is straightforward when the relationship between the state variables and the observations is linear in other words when the observations can be directly mapped onto the state space however when this relationship is nonlinear a number of methods can be derived in order to perform this transfer up till now it has not been demonstrated which of these methods is recommended for discharge assimilation with the ensemble kalman filter the objective of this paper is to analyze these methods for conceptual rainfall runoff models in a small scale catchment the study has been performed in the bellebeek catchment 86 36 km2 in belgium using two time series models and one conceptual rainfall runoff model a first analysis of the algorithms has been performed using the one time step ahead discharge predictions the results indicate that linearization of the storage discharge relationship the observation system should be avoided if discharge data are assimilated using the ensemble kalman filter further assimilating discharge data into conceptual rainfall runoff models for small catchments does not work well when a unit hydrograph is used for runoff routing this can be explained by the stronger impact of the model error caused by errors in the forcings model structure and parameters accumulated over the duration of the unit hydrograph as compared to the impact of erroneous initial conditions a second analysis using longer lead times has led to the conclusion that for the type of catchment and model used in this study the accuracy of the meteorological forcings is more important than an accurate estimation of the model initial conditions through data assimilation

design of a multilevel fuzzy controller for nonlinear systems and stability analysis in this paper a multilevel fuzzy control mlfc system is developed and implemented to deal with the real world nonlinear plants with intrinsic uncertainties and time varying parameters the proposed fuzzy control strategy has a hierarchical structure with an adaptation mechanism embedded in the lower level to tune the output membership functions mfs of the first layer fuzzy controller and can be used to control a system with an input output monotonic relationship or a piecewise monotonic relationship the stability of the closed loop system under the proposed mlfc is theoretically proven simulations are carried out by applying the proposed multilevel fuzzy control mlfc to a uncertain nonlinear plants and it is shown that much better system performances are achieved compared with conventional fuzzy logic controllers flc even in presence of disturbance and noise

a multistart weight adaptive recursive parameter estimation method 1 the determination of the parameters for hydrologic models has been the subject of a large number of studies during the last 3 decades a multitude of methods have been developed for this purpose generally the mismatch between the model simulations and the observations is lumped into an objective function which is then is optimized by these methods this can lead to parameter values that result in a good model performance under certain e g low flow conditions but not under other e g high flow conditions the objective of this paper is to demonstrate a calibration algorithm which leads to a good model performance under all boundary conditions this algorithm is referred to as multistart weight adaptive recursive parameter estimation mwarpe for this purpose the equations of the extended kalman filter ekf have been used recursively in a monte carlo approach strongly increasing the chance that a globally optimal parameter set is obtained instead of a local optimum the method has been applied to a rainfall runoff model for the zwalm catchment in belgium using a 1 year a 2 year and a 3 year calibration period the results have been compared to the shuffled complex evolution sce ua method a synthetic study revealed that for narrow parameter limits the sce ua algorithm outperformed mwarpe while for broad parameter limits the opposite occurred for the test case using in situ observed data the sce ua method resulted in slightly lower rmse values than mwarpe but mwarpe performed better outside the calibration period it has been found that mwarpe can bypass local optima in the determination of the final parameter set also the best initial parameter sets with the lowest rmse do not lead to the best final parameter values to apply the method only four parameters need to be specified more specifically the number of starting points the number of iterations per starting point one parameter used to initialize the model error covariance matrix and the observation error for this reason the method could be a simple alternative to more complex methods if model parameters have to be determined when time and or computational power are limited

a search grid for parameter optimization as a byproduct of model sensitivity analysis inverse problem solving i e the retrieval of optimal values of model parameters from experimental data remains a bottleneck for modelers therefore a large variety of heuristic optimization algorithms has been developed to deal with the inverse problem however in some cases the use of a grid search may be more appropriate or simply more practical in this paper an approach is presented to improve the selection of the grid points to be evaluated and which does not depend on the knowledge or availability of the underlying model equations it is suggested that using the information acquired through a sensitivity analysis can lead to better grid search results using the sensitivity analysis information a gauss newton like matrix is constructed and the eigenvalues and eigenvectors of this matrix are employed to transform naive search grids into better thought out ones after a theoretical analysis of the approach some computational experiments are performed using a simple linear model as well as more complex nonlinear models