digital optimal control of continuous time systems with control delay abstract this paper solves the digital stationary optimal control problem in the case of scalar linear stochastic continuous time systems with control delay quadratic integral criteria complete state information and constant sampling periods by transforming the problem to an equivalent discrete time one without control delay expressions are given for the eigenvalues of the control system and the parameters of the feedback matrix the influence of the sampling period on the cost is investigated for different values of the control delay by means of some examples

constructing a fuzzy controller from data abstract fuzzy control at the executive level can be interpreted as an approximation technique for a control function based on typical imprecisely specified input output tuples that are represented by fuzzy sets the imprecision is characterized by similarity relations that are induced by transformations of the canonical distance function between real numbers taking this interpretation of fuzzy controllers into account in order to derive a fuzzy controller from observed data typical input output tuples have to be identified in addition a concept of similarity based on a transformations of the canonical distance is needed in order to characterize the typical input output tuples by suitable fuzzy sets a variety of fuzzy clustering algorithms that are exactly working in this spirit exists they identify prototypes and assign fuzzy sets to the prototypes on the basis of a suitable transformed distance in this paper we discuss how such fuzzy clustering techniques can be applied to construct a fuzzy controller from data and introduce special clustering algorithms that are tailored for this problem

certainty equivalent control of stochastic systems stability property this work presents sufficient conditions for infinite and sliding finite horizon certainty equivalence controllers to stabilize discrete linear systems disturbed by scalar multiplicative white noise sequences these conditions also guarantee stabilizability by the optimal controllers

gaussian limits for multidimensional random sequential packing at saturation consider the random sequential packing model with infinite input and in any dimension when the input consists of non zero volume convex solids we show that the total number of solids accepted over cubes of volume is asymptotically normal as we provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized gaussian field the method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization

random parking sequential adsorption and the jamming limit identical cars are dropped sequentially from above into a large parking lot each car is positioned uniformly at random subject to non overlap with its predecessors until jamming occurs there have been many studies of the limiting mean coverage as the parking lot becomes large but no complete proof that such a limit exists until now

fuzzy sets and vague environments abstract in this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking different tolerance or error bounds into account fuzzy sets are induced by scaling factors that describe the magnitude of the imprecision on the other the scaling factors can be derived from given fuzzy sets so that we have a correspondence between scaling factors and fuzzy sets when these concepts are applied to control problems the max min rule is rediscovered as an interpolation technique viewing fuzzy control as an interpolation technique in vague environments enables us to validate various concepts for the design and tuning of fuzzy controllers and also suggests new methods based on clear semantics

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

a comparative study of fuzzy sets and rough sets this paper reviews and compares theories of fuzzy sets and rough sets two approaches for the formulation of fuzzy sets are reviewed one is based on many valued logic and the other is based on modal logic two views of rough sets are presented set oriented view and operator oriented view rough sets under set oriented view are closely related to fuzzy sets which leads to non truth functional fuzzy set operators both of them may be considered as deviations of classical set algebra in contrast rough sets under operator oriented view are different from fuzzy sets and may be regarded as an extension of classical set algebra

limit theorems for monolayer ballistic deposition in the continuum we consider a deposition model in which balls rain down at random towards a 2 dimensional surface roll downwards over existing adsorbed balls are adsorbed if they reach the surface and discarded if not we prove a spatial law of large numbers and central limit theorem for the ultimate number of balls adsorbed onto a large toroidal surface and also for the number of balls adsorbed on the restriction to a large region of an infinite surface

a contribution to convergence theory of fuzzy c means and derivatives in this paper we revisit the convergence and optimization properties of fuzzy clustering algorithms in general and the fuzzy c means fcm algorithm in particular our investigation includes probabilistic and a slightly modified implementation of possibilistic memberships which will be discussed under a unified view we give a convergence proof for the axis parallel variant of the algorithm by gustafson and kessel that can be generalized to other algorithms more easily than in the usual approach using reformulated fuzzy clustering algorithms we apply banach s classical contraction principle and establish a relationship between saddle points and attractive fixed points for the special case of fcm we derive a sufficient condition for fixed points to be attractive allowing identification of them as local minima of the objective function excluding the possibility of a saddle point

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

about the use of fuzzy clustering techniques for fuzzy model identification abstract in this work we present an alternative approach to generate fuzzy rules with a functional consequent associated to the tsk fuzzy model in our case using fuzzy clustering algorithms that look for linear behaviours in the product space of the input output data we analyse different methods to generate the associated fuzzy rules using in some cases multidimensional reference fuzzy sets in the product space of the input variables and in other cases fuzzy sets in each of the different dimensions in any case the rules being generated correspond to a tsk fuzzy model

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

tasc two attribute set clustering through decision tree construction clustering is the process of grouping a set of objects into classes of similar objects in the past clustering algorithms had a common problem that they use only one set of attributes for both partitioning the data space and measuring the similarity between objects this problem has limited the use of the existing algorithms on some practical situation hence this paper introduces a new clustering algorithm which partitions data space by constructing a decision tree using one attribute set and measures the degree of similarity using another three different partitioning methods are presented the algorithm is explained with illustration the performance and accuracy of the four partitioning methods are evaluated and compared

a hierarchical fuzzy clustering approach to fuzzy modeling abstract this paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy clustering scheme the method consists of a sequence of steps aiming towards developing a takagi sugeno ts fuzzy model of optimal structure where the fuzzy sets in the premise part are of gaussian type starting from an initial ordinary fuzzy partition of the input space the algorithm performs a nearest neighbor search and groups the original input training data into a number of clusters the centers of these clusters are further processed using an optimal fuzzy clustering technique which is based on the weighted fuzzy c means algorithm the resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters which in a next step are fine tuned using the well known gradient descend algorithm the proposed method is successfully applied to three test examples where the produced fuzzy models prove to be very accurate as well as compact in size

robust tsk fuzzy modeling for function approximation with outliers the takagi sugeno kang tsk type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications most approaches for modeling tsk fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions besides training data sets algorithms often contain outliers which seriously affect least square error minimization clustering and learning algorithms a robust tsk fuzzy modeling approach is presented in the approach a clustering algorithm termed as robust fuzzy regression agglomeration rfra is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers to obtain a more precision model a robust fine tuning algorithm is then employed various examples are used to verify the effectiveness of the proposed approach from the simulation results the proposed robust tsk fuzzy modeling indeed showed superior performance over other approaches

on relationship between modified sets topological spaces and rough sets abstract in this paper we define modifiers by relations especially weakening and substantiating modifiers are defined by a so called accessibility relation which is a reflexive relation on a non empty set x after presenting some main results we prove that this type of modifiers will satisfy the kuratowski closure axioms this means that modifiers in fact induce topological spaces also rough sets are considered to be a special case of modified sets

design of a near optimal wide range fuzzy logic controller the paper describes a novel method for the design of a fuzzy logic controller with near optimal performance in the wide range of operating conditions the approach is based on the analysis of the system behaviour in the error state space the final control structure in a form of a dual fuzzy logic controller is arrived at in two stages the first stage encompasses design and tuning of the pi like fuzzy controller the second stage consists of placing an additional fuzzy controller of a structure similar to that of the first one in parallel with the pi like fuzzy controller designed in the first stage the final structure of the dual fuzzy controller is obtained by synthesis and tuning of those segments of the second controller that are different the resulting dual controller is characterised with high performance in the wide range of operating conditions and with small number of parameters that can be adjusted using simple optimisation methods the controller is developed and tested for a plant comprising a variable speed dc motor drive

estimating the concentration of optically active constituents of sea water by takagi sugeno models with quadratic rule consequents determining the concentrations of chlorophyll suspended particulate matter and coloured dissolved organic matter in the sea water is basic to support the monitoring of upwelling phenomena algae blooms and changes in the marine ecosystem since these concentrations affect the spectral distribution of the solar light back scattered by the water body their estimation can be computed by using a set of remotely sensed multispectral measurements of the reflected sunlight in this paper the relation between the concentrations of interest and the average subsurface reflectances is modelled by means of a set of second order takagi sugeno ts fuzzy rules unlike first order ts rules which adopt linear functions as consequent second order ts rules exploit quadratic functions thus improving the modelling capability of the rule in the subspace determined by the antecedent first we show how we can build a second order ts model through a simple transformation which allows estimating the consequent parameters using standard linear least squares algorithms and by adopting one of the most used methods proposed in the literature to generate first order ts models then we compare first order and second order ts models against mean square error and interpretability of rules we highlight how second order ts models allow us to achieve better approximation than first order ts models though maintaining interpretability of the rules finally we show how second order ts models perform considerably better the mean square error is lower by two orders of magnitude than the specific implementations of radial basis function networks and multi layer perceptron networks used in previous papers for the same application domain

a study about dimensional change of industrial parts using fuzzy rules abstract this work presents the development of a fuzzy model aimed to predict the dimensional changes of actual industrial parts made in a new emerging material called austempered ductile iron adi the dimensional change is an important factor that must be taken into account to improve the fabrication process of any actual part of adi this change is produced during a heat treatment cycle and in the factory practice its prediction is difficult due to the high number of variables affecting it in the present case it was considered that the dimensional change is strongly influenced by 11 operative variables of the fabrication process associated to the chemical composition and heat treatment temperatures and holding times the data employed to build the model corresponds to measurements done by experts on different actual industrial parts the knowledge acquisition about the origin of the data was necessary to understand the uncertainty factors and to adjust the parameters for obtaining a proper model the model was developed with a takagi sugeno type structure and its parameters adjusted with the anfis learning algorithm and introduced into an expert system previously developed it allows the accurate prediction of dimensional changes and helps in the efficient design of new industrial adi parts

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

optimal design of radial basis function neural networks for fuzzy rule extraction in high dimensional data abstract the design of an optimal radial basis function neural network rbfnf is not a straightforward procedure in this paper we take advantage of the functional equivalence between rbfn and fuzzy inference systems to propose a novel efficient approach to rbfn design for fuzzy rule extraction the method is based on advanced fuzzy clustering techniques solutions to practical problems are proposed by combining these different solutions a general methodology is derived the efficiency of our method is demonstrated on challenging synthetic and real world data sets

kernel based fuzzy clustering and fuzzy clustering a comparative experimental study in this study we present a comprehensive comparative analysis of kernel based fuzzy clustering and fuzzy clustering kernel based clustering has emerged as an interesting and quite visible alternative in fuzzy clustering however the effectiveness of this extension vis a vis some generic methods of fuzzy clustering has neither been discussed in a complete manner nor the performance of clustering quantified through a convincing comparative analysis our focal objective is to understand the performance gains and the importance of parameter selection for kernelized fuzzy clustering generic fuzzy c means fcm and gustafson kessel gk fcm are compared with two typical generalizations of kernel based fuzzy clustering one with prototypes located in the feature space kfcm f and the other where the prototypes are distributed in the kernel space kfcm k both generalizations are studied when dealing with the gaussian kernel while kfcm k is also studied with the polynomial kernel two criteria are used in evaluating the performance of the clustering method and the resulting clusters namely classification rate and reconstruction error through carefully selected experiments involving synthetic and machine learning repository http archive ics uci edu beta data sets we demonstrate that the kernel based fcm algorithms produce a marginal improvement over standard fcm and gk for most of the analyzed data sets it has been observed that the kernel based fcm algorithms are in a number of cases highly sensitive to the selection of specific values of the kernel parameters

control of randomly varying systems with prescribed degree of stability the control of linear discrete time systems with stochastic parameter matrices is discussed two control techniques are particularly used infinite horizon and finite moving horizon optimal regulators it is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes in this way the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems

brief paper optimal reduced order compensation of time varying discrete time systems with deterministic and white parameters the finite horizon optimal compensation problem is considered in the case of linear time varying discrete time systems with deterministic and white stochastic parameters and quadratic criteria the dimensions of the compensator are a priori fixed and may be time varying also the dimensions of the system may be time varying strengthened discrete time optimal projection equations sdope are developed which within the class of minimal compensators are equivalent to the first order necessary optimality conditions based on the sdope and their associated boundary conditions two numerical algorithms are presented to solve the two point boundary value problem one is a homotopy algorithm while the second iterates the sdope repeatedly forward and backward in time the latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation riccati equations associated with the full order problem for systems with deterministic parameters the algorithms are illustrated with a numerical example the case of systems with deterministic parameters will be treated as a special case of systems with white parameters

new robustness bounds for discrete systems with random perturbations some new stochastic stability robustness bounds for state space models are reported nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness the methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one the results are compared with each other and with the exact stability region in an example

a generalization of the uncertainty threshold principle a generalized version of the uncertainty threshold principle is presented for discrete time systems with both jump markov parameters and independent white multiplicative noises it is shown that this threshold is not to be exceeded for the existence of the quadratically optimal steady state control for this class of systems

parametrization of all linear compensators for discrete time stochastic parameter systems abstract for discrete time stochastic parameter systems this paper presents a characterization of all state covariances assignable by a linear controller and a parametrization of all controllers that achieves a desired covariance these results indirectly provide the parametrization of all linear fixed order compensators which are mean square stabilizing for this class of systems the paper also includes robustification of the derived compensators and an example to illustrate the results

optimal stabilizing control of a stochastic system driven by randomly correlated noise the problem of optimal stabilization of a discrete time linear system subjected to additive correlated noise disturbances with an uncertain model is considered this problem is first converted to one of stabilizing a system with multiplicative and additive noises with time wise uncorrelated characteristics a novel controller different from the infinite horizon optimal controller is then chosen from among the class or constant feedback controllers in order to stabilize the system in the mean square sense it is shown that for a special case of this problem stronger results of both mean square and almost sure asymptotic stability are possible we also present a simpler stabilizability condition to make it easier to use the particular method proposed an example is incorporated to illustrate the new technique

the influence of finite word length on digital optimal control this paper is concerned with the performance of linear discrete time systems controlled by a finite word length computer with floating point arithmetic and of which the state is directly measurable with an a d converter of the same word length the effect of using finite word length is twofold first roundings are made after addition or multiplication of two rounded numbers second the control parameters are represented in the controller s memory by rounded numbers the first effect can be accounted for by considering the control parameters stochastic the second effect is deterministic after a description of the stochastlcs of the roundoff errors has been derived the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered

a central limit theorem with applications to percolation epidemics and boolean models suppose x x x x zd is a white noise process and h b defined for finite subsets b of z d is determined in a stationary way by the restriction of x to b using a martingale approach we prove a central limit theorem clt for h as b becomes large subject to h satisfying a stabilization condition the effect of changing x x at a single site needs to be local this clt is then applied to component counts for percolation and boolean models to the size of the big cluster for percolation on a box and to the final size of a spatial epidemic

gaussian fields and random packing consider sequential packing of unit volume balls in a large cube in any dimension and with poisson input we show after suitable rescaling that the spatial distribution of packed balls tends to that of a gaussian field in the thermodynamic limit the results cover related applied models including ballistic deposition and spatial birth growth models

full and reduced order observer design for discrete stochastic bilinear systems the author considers a general discrete time stochastic bilinear system model and derives the mean square optimal linear unbiased observer equations to be used in reconstructing a prespecified linear combination of state variables based on noisy output measurements

further remarks on the relation between rough and fuzzy sets abstract based on results of pawlak and wygralak some remarks on the relation between rough sets and fuzzy sets are given an improved definition of rough set is also proposed

deterministic and stochastic robustness measures for discrete systems deterministic and stochastic lyapunov theorems are used to demonstrate the robustness of a stable linear time variant discrete time nominal system to both unknown deterministic and stochastic perturbations time domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system it is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed loop system is known to be stable with a certain degree e g as in the case of linear quadratic optimal control with alpha degree of prescribed stability

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

a neuro fuzzy method to learn fuzzy classification rules from data abstract neuro fuzzy systems have recently gained a lot of interest in research and application neuro fuzzy models as we understand them are fuzzy systems that use local learning strategies to learn fuzzy sets and fuzzy rules neuro fuzzy techniques have been developed to support the development of e g fuzzy controllers and fuzzy classifiers in this paper we discuss a learning method for fuzzy classification rules the learning algorithm is a simple heuristics that is able to derive fuzzy rules from a set of training data very quickly and tunes them by modifying parameters of membership functions our approach is based on nefclass a neuro fuzzy model for pattern classification we also discuss some results obtained by our software implementation of nefclass which is freely available on the internet

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method

performance of digital linear regulators which use logarithmic arithmetic this paper analyzes the performance of digital linear regulators which use finite precision logarithmic arithmetic a linear equation is derived which describes the steady state covariance matrix of such a closed loop regulator system the utility of this covariance matrix in designing regulators which use logarithmic arithmetic is illustrated through several numerical examples and the presentation of a regulator design methodology

stabilizing compensator design for discrete time non linear stochastic systems with incomplete state information in this work an approach to stabilizing compensator design is presented that is suitable for a large class of discrete time non linear stochastic systems with incomplete state information the non linearity is contained either in the state or the measurement equation and it involves a white noise vector sequence the proposed compensator is a combination of a constant gain observer and a constant feedback control gain the stabilizability conditions depend upon the system and chosen design parameter characteristics and are given for both mean square and almost sure stochastic boundedness and stability of the controlled system a specific subclass of these systems subject to certain control laws is shown to possess stabilizability conditions that can be tested a priori

on variance neutrality of systems within general random parameters a necessary condition for variance neutrality of discrete time linear systems within general random parameters and with arbitrary observations is established it is proved that this condition is sufficient as well if the observations are linear this result is of importance in connection with separability of optimal control and state estimation