on fujita s spectrum conjecture abstract we prove fujita s spectrum conjecture on the discreteness of pseudo effective thresholds for polarized varieties

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

second chern class of fano manifolds and anti canonical geometry let x be a fano manifold of picard number one we establish a lower bound for the second chern class of x in terms of its index and degree as an application if y is a n dimensional fano manifold with k y n 3 h for some ample divisor h we prove that h 0 y h ge n 2 moreover we show that the rational map defined by vert mh vert is birational for m ge 5 and the linear system vert mh vert is basepoint free for m ge 7 as a by product the pluri anti canonical systems of singular weak fano varieties of dimension at most 4 are also investigated

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

a galerkin neural network based design of guaranteed cost control for nonlinear distributed parameter systems this paper presents a galerkin neural network based guaranteed cost control gcc design for a class of parabolic partial differential equation pde systems with unknown nonlinearities a parabolic pde system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement motivated by this in the proposed control scheme galerkin method is initially applied to the pde system to derive an ordinary differential equation ode system with unknown nonlinearities which accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently parameterized by a multilayer neural network mnn with one hidden layer and zero bias terms then based on the neural model and a lure type lyapunov function a linear modal feedback controller is developed to stabilize the closed loop pde system and provide an upper bound for the quadratic cost function associated with the finite dimensional slow system for all admissible approximation errors of the network the outcome of the gcc problem is formulated as a linear matrix inequality lmi problem moreover by using the existing lmi optimization technique a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained finally the proposed design method is applied to the control of the temperature profile of a catalytic rod

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

the cone of pseudo effective divisors of log varieties after batyrev in these notes we investigate the cone of nef curves of projective varieties which is the dual cone to the cone of pseudo effective divisors we prove a structure theorem for the cone of nef curves of projective mathbb q factorial klt pairs of arbitrary dimension from the point of view of the minimal model program this is a generalization of batyrev s structure theorem for the cone of nef curves of projective terminal threefolds

global generation of pluricanonical and adjoint linear series on smooth projective threefolds the purpose of this paper is to show how the cohomological techniques developed by kawamata reid shokurov and others lead to some effective and practical results of reider type on freeness of linear series on smooth complex projective threefolds in recent years there has been a great deal of interest in the geometric properties of pluricanonical and adjoint linear systems on surfaces and higherdimensional varieties among other things one wants to understand as explicitly as possible when the systems in question are base point free or very ample modem work in this area goes back to kodaira kod and bombieri bmb who studied pluricanonical maps of surfaces of general type more recently many of their results have emerged as special cases of a celebrated theorem of reider rdr reider uses vector bundle techniques to show that if b is a nef line bundle on a surface x such that b2 5 then kx b is globally generated unless there exist certain special curves c c x such that b c 1 he also obtains analogous criteria for kx b to be very ample a cohomological approach to these theorems based on miyaoka s vanishing theorem for zariski decompositions was given by sakai sak2

h output feedback control of fuzzy system models under sampled measurements this paper studies the problem of control for a class of fuzzy system models by using a linear output controller the system under consideration is described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are assumed unmeasurable we develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models a design algorithm for constructing the linear output controller is given a numerical simulation example is given to show the potential of the proposed techniques

finite time boundedness for switched systems with sector bounded nonlinearity and constant time delay finite time boundedness and finite time stability of switched systems with sector bounded nonlinearity and constant time delay are investigated sufficient conditions which guarantee finite time stability or finite time boundedness of the switched nonlinear system are presented respectively average dwell time of switching signals is also given moreover finite time weighted l2 gain of the switched nonlinear system is addressed to measure its disturbance tolerance capability in the fixed time interval detail proofs are accomplished by using multiple lyapunov like functions an example is employed to verify the efficiency of the proposed method

on the number of factors of sturmian words abstract we prove that for m 1 card a m 1 m i 1 m i 1 i where a m is the set of factors of length m of all the sturmian words and is the euler function this result was conjectured by dulucq and gouyou beauchamps 1987 who proved that this result implies that the language m 0 a m c is inherently ambiguous we also give a combinatorial version of the riemann hypothesis

global exponential convergence of cohen grossberg neural networks with time delays in this paper we derive a general sufficient condition ensuring global exponential convergence of cohen grossberg neural networks with time delays by constructing a novel lyapunov functional and smartly estimating its derivative the proposed condition is related to the convex combinations of the column sum and the row sum of the connection matrices and also relaxes the constraints on the network coefficients therefore the proposed condition generalizes some previous results in the literature

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

exponential stability and global stability of cellular neural networks in this paper we present two types of matrix stability complete stability and strong stability and some properties of them by using these properties we discuss stability of cellular neural networks and obtain some conditions ensuring uniqueness exponential stability and global asymptotic stability of the equilibrium point for cellular neural networks in particular in the two cell case the network is globally exponentially stable if and only if the feedback matrix minus the unit matrix is a complete stable matrix

on exponential stability results for fuzzy impulsive neural networks complex nonlinear systems can be represented to a set of linear sub models by using fuzzy sets and fuzzy reasoning via ordinary takagi sugeno ts fuzzy models in this paper the exponential stability of ts fuzzy neural networks with impulsive effect and time varying delays is investigated the model for fuzzy impulsive neural networks with time varying delays is first established as a modified ts fuzzy model in which the consequent parts are composed of a set of impulsive neural networks with time varying delays secondly the exponential stability for fuzzy impulsive neural networks is presented by utilizing the lyapunov krasovskii functional and the linear matrix inequality lmi approach in addition two numerical examples are provided to illustrate the applicability of the result using lmi control toolbox in matlab

a fast ellipse circle detector using geometric symmetry through the use of a global geometric symmetry a fast ellipse circle detector is proposed in this paper based on the geometric symmetry the proposed method first locates candidates of ellipse and circle centers in the meantime according to these candidate centers all feature points in an input image are grouped into several subimages then for each subimage by using geometric symmetry again all ellipses and circles are obtained the method significantly reduces the time required to evaluate all possible parameters without using edge direction information experimental results are given to show the correctness and effectiveness of the proposed method

on covering a digital disc with concentric circles in z2 digital circles and digital discs satisfy many bizarre anisotropic properties understanding of which is essential for solving various problems in image analysis and computer graphics in this paper we study the underlying properties of absentee pixels that appear while covering a digital disc with concentric digital circles we present for the first time a mathematical characterization of these pixels based on number theory and digital geometry interestingly the absentees occur in multitude and we show that their count varies quadratically with the radius the notion of infimum parabola and supremum parabola has been used to derive the count of these absentees using this parabolic characterization we derive a necessary and sufficient condition for a pixel to be a disc absentee and obtain the geometric properties of the absentees an algorithm to locate the absentees is presented we show that the ratio of the absentee pixels to the total number of disc pixels approaches a constant with increasing radius test results have been furnished to substantiate our theoretical findings

a general fuzzy scheme for nonlinear processes with stability analysis abstract in this paper we develop a general fuzzy control scheme for nonlinear processes assuming little knowledge about the dynamics of the controlled process the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation a simple local controller is then designed at each fuzzy locality a fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm by employing a newly developed structure adaptive fuzzy modelling scheme the appropriate fuzzy rule base for the inference mechanism can be extracted stably and efficiently the conditions for the stability of the global controller are rigourously established simulation results are presented to illustrate the effectiveness of the scheme

sampled data synchronization of chaotic lur e systems with time delays this paper studies the problem of sampled data control for master slave synchronization schemes that consist of identical chaotic lur e systems with time delays it is assumed that the sampling periods are arbitrarily varying but bounded in order to take full advantage of the available information about the actual sampling pattern a novel lyapunov functional is proposed which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals based on the lyapunov functional an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems the desired sampled data controller is designed by a linear matrix inequality approach the effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of chua s circuit and neural network

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

an h sub spl infin design approach for neural net based control schemes presents an h sub spl infin design approach for a neural net based control scheme in this scheme a class of nonlinear systems is approximated by two multilayer perceptrons the neural networks are piecewisely interpolated to generate a linear differential inclusion model based on this model a state feedback control law is designed the h sub spl infin control is specified to eliminate the effect of approximation errors and external disturbances to achieve the desired performance it is shown that finding the permissible control gain matrices can be transformed to a standard linear matrix inequality problem and solved using the convex optimization method

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm

lur e systems with multilayer perceptron and recurrent neural networks absolute stability and dissipativity sufficient conditions for absolute stability and dissipativity of continuous time recurrent neural networks with two hidden layers are presented in the autonomous case this is related to a lur e system with multilayer perceptron nonlinearity such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form the conditions are expressed as matrix inequalities and can be employed for nonlinear h sub spl infin control and imposing closed loop stability in dynamic backpropagation

on fujita s freeness conjecture in dimension 5 abstract let x be a smooth projective variety of dimension 5 and a an integral ample divisor on x we show that k x k a is basepoint free for any integer k 6

a geometric approach to problems in birational geometry a classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces each of these vector spaces admits a typical metric structure which is also birationally invariant these vector spaces so metrized will be referred to as the pseudonormed spaces of the original varieties a fundamental question is the following given two mildly singular projective varieties with some of the first variety s pseudonormed spaces being isometric to the corresponding ones of the second variety s can one construct a birational map between them that induces these isometries in this work a positive answer to this question is given for varieties of general type this can be thought of as a theorem of torelli type for birational equivalence

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

a methodology to design stable nonlinear fuzzy control systems the stability of nonlinear systems has to be investigated without making linear approaches in order to do this there are several techniques based on lyapunov s second method for example krasovskii s method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems this method requires the calculation of the jacobian matrix in this paper an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed later this model is used to compute the jacobian matrix of a closed loop fuzzy system next an algorithm to solve the jacobian matrix is proposed the algorithm uses a methodology based on the extension of the state vector the developed algorithm is completely general it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models and it allows the compound of different membership functions in a same model we have developed a matlab s function that implements the improved algorithm together with a series of additional applications for its use the designed software provides complementary functions to facilitate the reading and writing of fuzzy systems as well as an interface that makes possible the use of all the developed functions from the matlab s environment which allows to complement and to extend the possibilities of the matlab s fuzzy logic toolbox an example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented the work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

on complete intersections with trivial canonical class abstract we prove birational boundedness results on complete intersections with trivial canonical class of base point free divisors in some version of fano varieties our results imply in particular that batyrev borisov toric construction produces only a bounded set of hodge numbers in any given dimension even as the codimension is allowed to grow

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

a new approach to robust and non fragile h control for uncertain fuzzy systems this paper investigates the robust h control and non fragile control problems for takagi sugeno t s fuzzy systems with linear fractional parametric uncertainties the robust h control problem is to design a state feedback controller such that the robust stability and a prescribed h performance of the resulting closed loop system is ensured and the non fragile h control problem is to design a state feedback controller with parameter uncertainties based on the linear matrix inequality lmi approach new sufficient conditions for the solvability of the two problems are obtained it is shown that the desired state feedback fuzzy controller can be constructed by solving a set of lmis numerical examples are also provided to demonstrate the effectiveness of the proposed design method

stability analysis of the simplest takagi sugeno fuzzy control system using circle criterion in this paper we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest takagi sugeno t s fuzzy control system based on the circle criterion and its graphical interpretation these conditions are significant in graphically designing the simplest t s fuzzy controller in the frequency domain four numerical examples are provided to demonstrate the efficiency of our two frequency domain based conditions furthermore this t s fuzzy controller and the linear proportional controllers are also compared it is concluded that the simplest t s fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

an approach to stability criteria of neural network control systems this paper discusses stability of neural network nn based control systems using lyapunov approach first it is pointed out that the dynamics of nn systems can be represented by a class of nonlinear systems treated as linear differential inclusions ldi next stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single nn systems and feedback nn control systems furthermore a method of parameter region pr representation which graphically shows the location of parameters of nonlinear systems is proposed by introducing new concepts of vertex point and minimum representation from these concepts an important theorem which is useful for effectively finding a lyapunov function is derived stability criteria of single nn systems are illustrated in terms of pr representation finally stability of feedback nn control systems which consist of a plant represented by an nn and an nn controller is analyzed

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

an approach to the analysis of fuzzy systems this paper deals with a formal description of ill defined processes fuzzy systems by the use of fuzzy relational equations it is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory some equivalence between these two kinds of description is presented basic problems of fuzzy systems e g identification prediction sensitivity and stability are shown and numerical algorithms are given indices of each method are introduced especially the degree of fuzziness the sensitivity index which makes it possible to express the quality of each of them

delayed standard neural network models for control systems in order to conveniently analyze the stability of recurrent neural networks rnns and successfully synthesize the controllers for nonlinear systems similar to the nominal model in linear robust control theory the novel neural network model named delayed standard neural network model dsnnm is presented which is the interconnection of a linear dynamic system and a bounded static delayed or nondelayed nonlinear operator by combining a number of different lyapunov functionals with s procedure some useful criteria of global asymptotic stability and global exponential stability for the continuous time dsnnms cdsnnms and discrete time dsnnms ddsnnms are derived whose conditions are formulated as linear matrix inequalities lmis based on the stability analysis some state feedback control laws for the dsnnm with input and output are designed to stabilize the closed loop systems most rnns and neurocontrol nonlinear systems with or without time delays can be transformed into the dsnnms to be stability analyzed or stabilization synthesized in a unified way in this paper the dsnnms are applied to analyzing the stability of the continuous time and discrete time rnns with or without time delays and synthesizing the state feedback controllers for the chaotic neural network system and discrete time nonlinear system it turns out that the dsnnm makes the stability conditions of the rnns easily verified and provides a new idea for the synthesis of the controllers for the nonlinear systems

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

from prima quadraginta octant to lattice sphere through primitive integer operations we present here the first integer based algorithm for constructing a well defined lattice sphere specified by integer radius and integer center the algorithm evolves from a unique correspondence between the lattice points comprising the sphere and the distribution of sum of three square numbers in integer intervals we characterize these intervals to derive a useful set of recurrences which in turn aids in efficient computation each point of the lattice sphere is determined by resorting to only a few primitive operations in the integer domain the symmetry of its quadraginta octants provides an added advantage by confining the computation to its prima quadraginta octant detailed theoretical analysis and experimental results have been furnished to demonstrate its simplicity and elegance

stability analysis of discrete time recurrent neural networks we address the problem of global lyapunov stability of discrete time recurrent neural networks rnns in the unforced unperturbed setting it is assumed that network weights are fixed to some values for example those attained after training based on classical results of the theory of absolute stability we propose a new approach for the stability analysis of rnns with sector type monotone nonlinearities and nonzero biases we devise a simple state space transformation to convert the original rnn equations to a form suitable for our stability analysis we then present appropriate linear matrix inequalities lmis to be solved to determine whether the system under study is globally exponentially stable unlike previous treatments our approach readily permits one to account for non zero biases usually present in rnns for improved approximation capabilities we show how recent results of others on the stability analysis of rnns can be interpreted as special cases within our approach we illustrate how to use our approach with examples though illustrated on the stability analysis of recurrent multilayer perceptrons the approach proposed can also be applied to other forms of time lagged rnns

exponential h synchronization and state estimation for chaotic systems via a unified model in this paper h synchronization and state estimation problems are considered for different types of chaotic systems a unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems such as hopfield neural networks cellular neural networks chua s circuits unified chaotic systems qi systems chaotic recurrent multilayer perceptrons etc based on the h performance analysis of this unified model using the linear matrix inequality approach novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the state estimation problem is then studied for the same unified model where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level the parameters of these controllers and filters are obtained by solving the eigenvalue problem most chaotic systems can be transformed into this unified model and h synchronization controllers and state estimators for these systems are designed in a unified way three numerical examples are provided to show the usefulness of the proposed h synchronization and state estimation conditions

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

exponential stabilization of neural networks with various activation functions and mixed time varying delays this paper presents some results on the global exponential stabilization for neural networks with various activation functions and time varying continuously distributed delays based on augmented time varying lyapunov krasovskii functionals new delay dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities a numerical example is given to illustrate the feasibility of our results

robust local stability of multilayer recurrent neural networks we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers the stability condition follows from linking theories about linearization robustness analysis of linear systems under nonlinear perturbation and matrix inequalities a characterization of the basin of attraction of the origin is given in terms of the level set of a quadratic lyapunov function similar to the nl sub q theory the local stability is imposed around the origin and the apparent basin of attraction is made large by applying the criterion while the proven basin of attraction is relatively small due to conservatism of the criterion modification of the dynamic backpropagation by the new stability condition is discussed and illustrated by simulation examples

approximating euclidean circles by neighbourhood sequences in a hexagonal grid in this paper the nodes of the hexagonal grid are used as points there are three types of neighbours on this grid therefore neighbourhood sequences contain values 1 2 3 the grid is coordinatized by three coordinates in a symmetric way digital circles are classified based on digital distances using neighbourhood sequences they can be triangle hexagon enneagon and dodecagon their corners and side lengths are computed such as their perimeters and areas the radius of a digital disk is usually not well defined i e the same disk can have various radii according to the neighbourhood sequence used therefore the non compactness ratio is used to measure the quality of approximation of the euclidean circles the best approximating neighbourhood sequence is presented it is shown that the approximation can be improved using two neighbourhood sequences in parallel comparisons to other approximations are also shown

asymptotically log fano varieties abstract motivated by the study of fano type varieties we define a new class of log pairs that we call asymptotically log fano varieties and strongly asymptotically log fano varieties we study their properties in dimension two under an additional assumption of log smoothness and give a complete classification of two dimensional strongly asymptotically log smooth log fano varieties based on this classification we formulate an asymptotic logarithmic version of calabi s conjecture for del pezzo surfaces for the existence of kahler einstein edge metrics in this regime we make some initial progress towards its proof by demonstrating some existence and non existence results among them a generalization of matsushima s result on the reductivity of the automorphism group of the pair and results on log canonical thresholds of pairs one by product of this study is a new conjectural picture for the small angle regime and limit which reveals a rich structure in the asymptotic regime of which a folklore conjecture concerning the case of a fano manifold with an anticanonical divisor is a special case

on stabilization of stochastic cohen grossberg neural networks with mode dependent mixed time delays and markovian switching the globally exponential stabilization problem is investigated for a general class of stochastic cohen grossberg neural networks with both markovian jumping parameters and mixed mode dependent time delays the mixed time delays consist of both discrete and distributed delays this paper aims to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive delay dependent criteria for the exponential stabilization problem three numerical examples are carried out to demonstrate the feasibility of our delay dependent stabilization criteria

reconstruction of a digital circle abstract since digitization always causes some loss of information reconstruction of the original figure from a given digitization is a challenging task reconstruction of digital circles has already been addressed in the literature however an in depth analysis of an obq image of a continuous circle as well as a solution to its domain construction problem is still lacking in this paper a detailed analysis of digital circles has been carried out a modified i r method is formulated to numerically compute the domain of each digital quarter circle for a given radius several properties of the obq image of a circle reveal that in many cases it is possible to split a digital circle into four digital quarter circles such that the domains of the individual quarter circles can be combined to obtain the domain of the full circle moreover the domain of a quarter circle is geometrically characterized

exponential rm h _ infty synchronization of general discrete time chaotic neural networks with or without time delays this brief studies exponential h synchronization of a class of general discrete time chaotic neural networks with external disturbance on the basis of the drive response concept and h control theory and using lyapunov krasovskii or lyapunov functional state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays but also reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities most discrete time chaotic systems with or without time delays such as hopfield neural networks cellular neural networks bidirectional associative memory networks recurrent multilayer perceptrons cohen grossberg neural networks chua s circuits etc can be transformed into this general chaotic neural network to be h synchronization controller designed in a unified way finally some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

how delays affect neural dynamics and learning we investigate the effects of delays on the dynamics and in particular on the oscillatory properties of simple neural network models we extend previously known results regarding the effects of delays on stability and convergence properties we treat in detail the case of ring networks for which we derive simple conditions for oscillating behavior and several formulas to predict the regions of bifurcation the periods of the limit cycles and the phases of the different neurons these results in turn can readily be applied to more complex and more biologically motivated architectures such as layered networks in general the main result is that delays tend to increase the period of oscillations and broaden the spectrum of possible frequencies in a quantifiable way simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior adaptable delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics accordingly we derive recurrent backpropagation learning formulas for the adjustment of delays and other parameters in networks with delayed interactions and discuss some possible applications

on fujita s log spectrum conjecture we prove fujita s log spectrum conjecture it follows from the acc of a suitable set of pseudo effective thresholds

neural network based dobc for a class of nonlinear systems with unmatched disturbances in this brief the problem of composite anti disturbance tracking control for a class of strict feedback systems with unmatched unknown nonlinear functions and external disturbances is investigated a disturbance observer based control dobc in combination with a neural network scheme and back stepping method is developed to achieve a composite anti disturbance controller design that provides guaranteed performance in the proposed method a conventional disturbance observer and a radial basis function neural network rbfnn are combined into a new disturbance observer to estimate the unmatched disturbances as compared with conventional dobc methods the primary merit of the proposed method is that the unknown nonlinear functions are approximated using the rbfnn technique and not regarded as part of the disturbances or estimated by a conventional disturbance observer hence the proposed method can obtain higher control accuracy than the conventional dobc methods this advantage is validated by simulation studies

mld s vs thresholds and flips minimal log discrepancies mld s are related not only to termination of log flips 22 and thus to the existence of log flips 11 but also to the ascending chain condition acc of some global invariants and invariants of singularities in the log minimal model program lmmp in this paper we draw clear links between several central conjectures in the lmmp more precisely our main result states that the lmmp the acc conjecture for mld s and the boundedness of canonical morifano varieties in dimension d imply the following the acc conjecture for a lc thresholds in particular for canonical and log canonical lc thresholds in dimension d the acc conjecture for lc thresholds in dimension d 1 termination of log flips in dimension d 1 for effective pairs and existence of pl flips in dimension d 2 this also gives new proofs of some well known and new results in the field in low dimensions the acc conjecture holds for a lc thresholds of surfaces the acc conjecture holds for lc thresholds of 3 folds termination of 3 fold log flips holds for effective pairs and the existence of 4 fold pl flips holds

neural network based control design an lmi approach we address a neural network based control design for a discrete time nonlinear system our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin a linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state feedback control law for the nonlinear system based on the certainty equivalence principle the control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal further the stability of the closed loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed loop system converges finally a simple example is presented so as to illustrate our control design procedure

designing fuzzy controllers from a variable structures standpoint a procedure is presented for designing fuzzy controllers based upon variable structures techniques three such controllers are presented the fuzzy equivalents of sliding mode controllers saturating controllers and tanh controllers by using an approach based upon variables structures vss techniques the stability of each of these controllers is assured by using a sliding surface the order of the rule base is reduced to size r spl times m where r is the number of inputs and m is the number of fuzzification levels this combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties to illustrate the proposed design procedure fuzzy controllers are designed for a ball and beam system it is demonstrated that in spite of this system being a fourth order unstable system the proposed design procedure results in simple stable fuzzy controllers

nonlinear system identification using neural state space models applicable to robust control design prediction error learning algorithms for neural state space models are developed both for the deterministic case and the stochastic case with measurement and process noise for the stochastic case a predictor with direct parametrization of the kalman gain by a neural net architecture is proposed expressions for the gradients are derived by applying narendra s sensitivity model approach finally a linear fractional transformation representation is given for neural state space models which makes it possible to use these models obtained from input output measurements on a plant in a standard robust performance control scheme

digitized circular arcs characterization and parameter estimation the digitization of a circular arc causes an inherent loss of geometrical information arcs with slightly different local curvature or position may lead to exactly the same digital pattern in this paper the authors give a characterization of all centers and radii of circular arcs yielding the same digitization pattern the radius of the arcs varies over the set however only one curvature or radius estimate can be assigned to the digital pattern the authors derive an optimal estimator and give expressions for the bound on the precision of estimation this bound due to digitization is the deterministic equivalent of the cramer rao bound known from parameter estimation theory consider the estimation of the local curvature and local radius of a smooth object typically such parameters are estimated by moving a window along the digital boundary methods in literature show a poor precision in estimating curvature values relative errors of over 40 are often found from the definition of curvature it follows that locally the curve can be considered a circular arc and hence the method presented in this paper can be applied to the pattern in the window giving estimates with optimal precision and a measure for the remaining error on the practical side the authors present examples of the residual error due to the discrete grid the estimation of the radius or curvature of a circular arc at random position with an estimation window containing 10 points coded with nine freemancodes has a relative deviation exceeding 2 for a full disk the deviation is below 1 when the radius r exceeds four grid units the presented method is particularly useful for problems where some prior knowledge on the distribution of radii is known and where there is a noise free sampling