a newton cg augmented lagrangian method for semidefinite programming we consider a newton cg augmented lagrangian method for solving semidefinite programming sdp problems from the perspective of approximate semismooth newton methods in order to analyze the rate of convergence of our proposed method we characterize the lipschitz continuity of the corresponding solution mapping at the origin for the inner problems we show that the positive definiteness of the generalized hessian of the objective function in these inner problems a key property for ensuring the efficiency of using an inexact semismooth newton cg method to solve the inner problems is equivalent to the constraint nondegeneracy of the corresponding dual problems numerical experiments on a variety of large scale sdp problems with the matrix dimension n up to 4 110 and the number of equality constraints m up to 2 156 544 show that the proposed method is very efficient we are also able to solve the sdp problem fap36 with n 4 110 and m 1 154 467 in the seventh dimacs implementation challenge much more accurately than in previous attempts

direct updating of damping and stiffness matrices this note has outlined an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure the method minimizes the change in the damping and stiffness matrices with the constraint that the measured modal data is reproduced

semismoothness of solutions to generalized equations and the moreau yosida regularization we show that a locally lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point we present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible nonpolyhedral convex sets we prove that the semismoothness of solutions to the moreau yosida regularization of a lower semicontinuous proper convex function is implied by the semismoothness of the metric projector over the epigraph of the convex function

exact scaling in competitive growth models a competitive growth model cgm describes the aggregation of a single type of particle under two different growth rules with occurrence probabilities p and 1 p we explain the origin of the scaling behavior of the resulting surface roughness at small p for two cgm s which describe random deposition rd competing with ballistic deposition and rd competing with the edward wilkinson ew growth rule exact scaling exponents are derived the scaling behavior of the coefficients in the corresponding continuum equations are also deduced furthermore we suggest that in some cgm s the p dependence on the coefficients of the continuum equation that represents their universality class can be nontrivial in some cases the process cannot be represented by a unique universality class in order to show this we introduce a cgm describing rd competing with a constrained ew model this cgm shows a transition in the scaling exponents from rd to a kardar parisi zhang behavior when p is close to 0 and to a edward wilkinson one when p is close to 1 at practical time and length scales our simulation results are in excellent agreement with the analytic predictions

new methods for finite element model updating problems we consider two finite element model updating problems which incorporate the measured modal data into the analytical finite element model producing an adjusted model on the mass damping and stiffness that closely matches the experimental modal data we develop two efficient numerical algorithms for solving these problems the new algorithms are direct methods that require o nk2 and o nk2 k6 flops respectively and employ sparse matrix techniques when the analytic model is sparse here n is the dimension of the coefficient matrices defining the analytical model and k is the number of measured eigenpairs

periodic neural activity induced by network complexity we study a model for neural activity on the small world topology of watts and strogatz and on the scale free topology of barabasi and albert we find that the topology of the network connections may spontaneously induce periodic neural activity contrasting with nonperiodic neural activities exhibited by regular topologies periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger the average length of the periods increases with the square root of the network size

analysis of nonsmooth symmetric matrix valued functions with applications to semidefinite complementarity problems for any function f from mathbb r to mathbb r one can define a corresponding function on the space of n n block diagonal real symmetric matrices by applying f to the eigenvalues of the spectral decomposition we show that this matrix valued function inherits from f the properties of continuity local lipschitz continuity directional differentiability frechet differentiability continuous differentiability as well as rho order semismoothness our analysis uses results from nonsmooth analysis as well as perturbation theory for the spectral decomposition of symmetric matrices we also apply our results to the semidefinite complementarity problem addressing some basic issues in the analysis of smoothing semismooth newton methods for solving this problem

merit functions for semi definite complementarity problems merit functions such as the gap function the regularized gap function the implicit lagrangian and the norm squared of the fischer burmeister function have played an important role in the solution of complementarity problems defined over the cone of nonnegative real vectors we study the extension of these merit functions to complementarity problems defined over the cone of block diagonal symmetric positive semi definite real matrices the extension suggests new solution methods for the latter problems

fuzzy gain scheduling controller and observer design based on lyapunov method and convex optimization addresses model based fuzzy control a constructive and automated method for the design of a gain scheduling controller is presented based on a given takagi sugeno fuzzy model of the plant the controller is designed such that stability and prescribed performance of the closed loop are guaranteed these properties are valid in a wide working range around an equilibrium without restrictions to slowly varying trajectories the synthesis is based on linear matrix inequalities and convex optimization techniques if required a fuzzy state estimator and an extended controller can be included providing a zero steady state error in the presence of disturbances and modeling errors the proposed method has been applied to a control of a laboratory liquid level process hence the performance has been evaluated in simulations as well as in real time control

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

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

roughness exponent in the domany kinzel cellular automaton we propose a method to detect phase transitions in discrete lattice models based on the roughness exponent this approach is applied to the one dimensional domany kinzel cellular automaton ca our results obtained by numerical simulations show that the roughness exponent method detects the frozen active phase transition directly from the ca spatio temporal configurations without any reference to thermodynamical potentials order parameters or response functions

semidefinite inverse eigenvalue problems with prescribed entries and partial eigendata in this paper we study the semidefinite inverse eigenvalue problem of reconstructing a real n by n matrix c such that it is nearest to the original pre estimated real n by n matrix c o in the frobenius norm and satisfies the measured partial eigendata where the required matrix c should preserve the symmetry positive semidefiniteness and the prescribed entries of the pre estimated matrix c o we propose the alternating direction method of multipliers for solving the semidefinite inverse eigenvalue problem where three related iterative algorithms are presented we also extend our method to the case of lower bounds numerical experiments are reported to illustrate the efficiency of the proposed method for solving semidefinite inverse eigenvalue problems

h spl infin decentralized fuzzy model reference tracking control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h sub spl infin decentralized controller for nonlinear interconnected systems the model reference tracking control problem of nonlinear interconnected systems is studied via h sub spl infin decentralized fuzzy control method first the nonlinear interconnected system is represented by an equivalent takagi sugeno type fuzzy model a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the h spl infin model reference tracking performance is achieved furthermore the stability of the nonlinear interconnected systems is also guaranteed if states are not all available a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control consequently a fuzzy observer based state feedback decentralized fuzzy controller is proposed to solve the h sub spl infin tracking control design problem for nonlinear interconnected systems the problem of h sub spl infin decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp the evp can be solved very efficiently using convex optimization techniques finally simulation examples are given to illustrate the tracking performance of the proposed methods

improving the interpretability of tsk fuzzy models by combining global learning and local learning the fuzzy inference system proposed by takagi sugeno and kang known as the tsk model in fuzzy system literature provides a powerful tool for modeling complex nonlinear systems unlike conventional modeling where a single model is used to describe the global behavior of a system tsk modeling is essentially a multimodel approach in which simple submodels typically linear models are combined to describe the global behavior of the system most existing learning algorithms for identifying the tsk model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model although these algorithms can generate a tsk model with good global performance i e the model is capable of approximating the given system with arbitrary accuracy provided that sufficient rules are used and sufficient training data are available they cannot guarantee the resulting model to have a good local performance often the submodels in the tsk model may exhibit an erratic local behavior which is difficult to interpret since one of the important motivations of using the tsk model also other fuzzy models is to gain insights into the model it is important to investigate the interpretability issue of the tsk model we propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework this algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics but remains the component of global fitting in the existing learning algorithms the algorithm is capable of adjusting its parameters based on the user s preference generating models with good tradeoff in terms of global fitting and local interpretation we illustrate the performance of the proposed algorithm using a motorcycle crash modeling example

a discrete method to study stochastic growth equations a cellular automata perspective using cellular automata dynamics a discrete technique to study stochastic growth equations sge is presented by analogy to deposition models in which the growth rule depends on height differences between neighbours we introduce an interface growth process with synchronous updating in which the transition probability for a given site i to receive a particle at a time t is defined as pi t exp i t and are the model parameters and i t is a function which depends on the height of the site i and its neighbours and its functional form is specified through discretization of the deterministic part of the growth equation associated with a given deposition process to validate the method we study its application to two linear sge the edwards wilkinson equation and the mullins herring equation and a nonlinear one the kardar parisi zhang equation the statistical analysis of the height distributions in simulations recovered the correct values for roughening exponents confirming that the processes generated are indeed in the universality classes of the original growth equations we also observed a crossover from random deposition to the correlated regime when the parameter is varied in each case studied

neural network based optimal fuzzy controller design for nonlinear systems a neural learning fuzzy technique is proposed for t s fuzzy model identification of model free physical systems further an algorithm with a defined modelling index is proposed to integrate and to guarantee that the proposed neural based optimal fuzzy controller can stabilize physical systems the modelling index is defined to denote the modelling error evolution and to ensure that the training data for neural learning can describe the physical system behavior very well the algorithm which integrates the neural based fuzzy modelling and optimal fuzzy controlling process can implement off line modelling and on line optimal control for model free physical systems the neural fuzzy inference network is a self organizing inference system to learn fuzzy membership functions and fuzzy subsystems parameters as data feeding in based on the generated t s fuzzy models for the continuous mass spring damper system and chua s chaotic circuit discrete time model car system and articulated vehicle their corresponding fuzzy controllers are formulated from both local concept and global concept fuzzy approach respectively the simulation results demonstrate the performance of the proposed neural based fuzzy modelling technique and of the integrated algorithm of neural based optimal fuzzy control structure

complementarity and nondegeneracy in semidefinite programming primal and dual nondegeneracy conditions are defined for semidefinite programming given the existence of primal and dual solutions it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution the converses hold if strict complementarity is assumed primal and dual nondegeneracy assumptions do not imply strict complementarity as they do in lp the primal and dual nondegeneracy assumptions imply a range of possible ranks for primal and dual solutions x and z this is in contrast with lp where nondegeneracy assumptions exactly determine the number of variables which are zero it is shown that primal and dual nondegeneracy and strict complementarity all hold generically numerical experiments suggest probability distributions for the ranks of x and z which are consistent with the nondegeneracy conditions

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

universal behavior of the coefficients of the continuous equation in competitive growth models the competitive growth models cgm involving only one kind of particles are a mixture of two processes one with probability p and the other with probability 1 p the p dependence produce crossovers between two different regimes we demonstrate that the coefficients of the continuous equation describing their universality classes are quadratic in p or 1 p we show that the origin of such dependence is the existence of two different average time rates thus the quadratic p dependence is a universal behavior of all the cgm we derive analytically the continuous equations for two cgm in 1 1 dimensions from the microscopic rules using a regularization procedure we propose generalized scalings that reproduce the scaling behavior in each regime in order to verify the analytic results and the scalings we perform numerical integrations of the derived analytical equations the results are in excellent agreement with those of the microscopic cgm presented here and with the proposed scalings

computing a nearest symmetric positive semidefinite matrix the nearest symmetric positive semidefinite matrix in the frobenius norm to an arbitrary real matrix a is shown to be b h 2 where h is the symmetric polar factor of b a at 2 in the 2 norm a nearest symmetric positive semidefinite matrix and its distance 2 a from a are given by a computationally challenging formula due to halmos we show how the bisection method can be applied to this formula to compute upper and lower bounds for 2 a differing by no more than a given amount a key ingredient is a stable and efficient test for positive definiteness based on an attempted choleski decomposition for accurate computation of 2 a we formulate the problem as one of zero finding and apply a hybrid newton bisection algorithm some numerical difficulties are discussed and illustrated by example

effective optimization for fuzzy model predictive control this paper addresses the optimization in fuzzy model predictive control when the prediction model is a nonlinear fuzzy model nonconvex time consuming optimization is necessary with no guarantee of finding an optimal solution a possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control i e quadratic programming for long range predictive control however the influence of the linearization error may significantly deteriorate the performance in our approach this is remedied by linearizing the fuzzy model along the predicted input and output trajectories one can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories four different methods for the construction of the optimization problem are proposed making difference between the cases when a single linear model or a set of linear models are used by choosing an appropriate method the user can achieve a desired tradeoff between the control performance and the computational load the proposed techniques have been tested and evaluated using two simulated industrial benchmarks ph control in a continuous stirred tank reactor and a high purity distillation column

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

application of the alternating direction method for an inverse monic quadratic eigenvalue problem abstract this paper shows that the alternating direction method can be used to solve the inverse monic quadratic eigenvalue problem imqep with the semidefiniteness and sparsity requirements the results of numerical examples show that the proposed method works well

analysis and design of an affine fuzzy system via bilinear matrix inequality a novel analysis and design method for affine fuzzy systems is proposed both continuous time and discrete time cases are considered the quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities bmis two diffeomorphic state transformations one is linear and the other is nonlinear are introduced to convert the plant into more tractable affine form the conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality lmi technique the bias terms of the fuzzy controller are solved simultaneously together with the gains finally the applicability of the suggested method is demonstrated via an example and computer simulation

spontaneous emergence of spatio temporal order in class 4 automata abstract we report surprisingly regular behaviors observed for a class 4 cellular automaton the totalistic rule 20 starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in space this is the first evidence that different types of spatio temporal order can emerge under specific conditions out of disorder in the same discrete rule based algorithm

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

optimal fuzzy controller design local concept approach in this paper we present a global optimal and stable fuzzy controller design method for both continuous and discrete time fuzzy systems under both finite and infinite horizons first a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers based on this sufficient condition we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory the stability of the entire closed loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller the optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant feedback continuous fuzzy system possesses an infinite gain margin that is its stability is guaranteed no matter how large the feedback gain becomes two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties

optimal fuzzy controller design in continuous fuzzy system global concept approach we propose a design method for a global optimal fuzzy controller to control and stabilize a continuous fuzzy system with free or fixed end point under finite or infinite horizon time a linear like global system representation of continuous fuzzy system is first proposed by viewing a continuous fuzzy system in global concept and unifying the individual matrices into synthetical matrices based on this the optimal control law which can achieve global minimum effect is developed theoretically the nonlinear segmental two point boundary value problem is derived for the finite horizon problem and a forward riccati like differential equation for the infinite horizon problem the stability of the closed loop fuzzy system can be ensured by the designed optimal fuzzy controller the optimal closed loop fuzzy system cannot only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant closed loop fuzzy system possesses an infinite gain margin

robust stability constraints for fuzzy model predictive control this paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the takagi sugeno t s type resulting in a stable closed loop control system conditions are given that guarantee closed loop robust asymptotic stability for open loop bounded input bounded output bibo stable processes with an additive l sub 1 norm bounded model uncertainty the idea is closely related to small gain based l sub 1 control theory but due to the time varying approach the resulting robust stability constraints are less conservative therefore the fuzzy model is viewed as a linear time varying system rather than a nonlinear one the goal is to obtain constraints on the control signal and its increment that guarantee robust stability robust global asymptotic stability and offset free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances

synchronization universality classes and stability of smooth coupled map lattices we study two problems related to spatially extended systems the dynamical stability and the universality classes of the replica synchronization transition we use a simple model of one dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class while stable chaos implies that the synchronization transition belongs to the directed percolation universality class

discrete time optimal fuzzy controller design global concept approach proposes a systematic and theoretically sound way to design a global optimal discrete time fuzzy controller to control and stabilize a nonlinear discrete time fuzzy system with finite or infinite horizon time a linear like global system representation of a discrete time fuzzy system is first proposed by viewing such a system in a global concept and unifying the individual matrices into synthetic matrices then based on this kind of system representation a discrete time optimal fuzzy control law which can achieve a global minimum effect is developed theoretically a nonlinear two point boundary value problem tpbvp is derived as a necessary and sufficient condition for the nonlinear quadratic optimal control problem to simplify the computation a multi stage decomposition of the optimization scheme is proposed and then a segmental recursive riccati like equation is derived moreover in the case of time invariant fuzzy systems we show that the optimal controller can be obtained by just solving discrete time algebraic riccati like equations based on this several fascinating characteristics of the resultant closed loop fuzzy system can easily be elicited the stability of the closed loop fuzzy system can be ensured by the designed optimal fuzzy controller the optimal closed loop fuzzy system can not only be guaranteed to be exponentially stable but also stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant closed loop fuzzy system possesses an infinite gain margin i e its stability is guaranteed no matter how large the feedback gain becomes an example is given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proven stability properties

optimal tracking design for stochastic fuzzy systems in general fuzzy control design for stochastic nonlinear systems is still difficult since the fuzzy bases are stochastic so as to increase the difficulty and complexity of the fuzzy tracking control design in this study a fuzzy stochastic moving average model with control input fuzzy armax model is introduced to describe nonlinear stochastic systems from the fuzzy armax model a fuzzy one step ahead prediction model is developed based on a fuzzy one step ahead prediction stochastic model optimal design algorithms are proposed to achieve the optimal tracking of nonlinear stochastic systems in this study the minimum variance tracking control generalized minimum variance tracking control and the optimal model reference tracking control are developed for stochastic fuzzy systems we construct some basic stability conditions for general stochastic fuzzy systems and use these conditions to verify the stability of the fuzzy tracking control systems finally two simulation examples are given to indicate the performance of the proposed methods

stability analysis and synthesis for an affine fuzzy control system via lmi and ilmi a continuous case a new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper the method suggested is based on the numerical convex optimization techniques in analysis the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities lmis the emphasis of this paper however is on the synthesis of fuzzy controller based on the derived stability condition in the synthesis the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains continuous iterative lmi ilmi approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system

sensitivity analysis of optimization problems under second order regular constraints we present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition this is a technical condition that is always satisfied in the case of semi definite optimization we derive lipschitz and holder expansions of approximate optimal solutions under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem we show how the theory applies to semi infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds and discuss the differentiability of metric projections as well as the moreau yosida regularization finally we show how the theory applies to semi definite optimization

an augmented lagrangian dual optimization approach to the h weighted model updating problem abstract model updating for the quadratic eigenvalue problem aims to update the model q 2 m c k by given eigendata in this paper we consider the h weighted model updating problem which can not only preserve the symmetry and definiteness of the original model but also express our confidence in the original model through assigning different confidence weights we propose an augmented lagrangian dual method for the h weighted model updating problem under some mild assumptions our method is shown to converge at least linearly numerical results illustrate the effectiveness of our method in addition we compare our method with the semi definite programming sdp method numerical results illustrate that when the scale of the model becomes large our method still works but the sdp method failed to converge

fault detection and isolation for affine fuzzy systems with sensor faults this paper investigates the fault detection and isolation fdi problem for a class of nonlinear systems with sensor outage faults the considered nonlinear systems are described as affine fuzzy models and the system outputs are chosen as the premise variables of fuzzy models different from the existing results the influence of sensor faults on premise variables is considered as a result the well known parallel distributed compensation scheme cannot be used for fdi filters design by using the structural information encoded in the fuzzy rules the affine fuzzy system is represented by multiple operating regime based models in fault free case and faulty cases in the multiple model scheme a bank of piecewise fdi filters are constructed each of them is based on the affine fuzzy model that describes the system in the presence of a specified fault the fault dependent residual signals generated from the filters are used for detecting and isolating the specified fault the fdi filter design conditions are obtained in the formulation of linear matrix inequalities finally a numerical example is given to illustrate the effectiveness and merits of the proposed method

a dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure the inverse quadratic eigenvalue problem iqep arises in the field of structural dynamics it aims to find three symmetric matrices known as the mass the damping and the stiffness matrices such that they are closest to the given analytical matrices and satisfy the measured data the difficulty of this problem lies in the fact that in applications the mass matrix should be positive definite and the stiffness matrix positive semidefinite based on an equivalent dual optimization version of the iqep we present a quadratically convergent newton type method our numerical experiments confirm the high efficiency of the proposed method

h controller design for affine fuzzy systems based on piecewise lyapunov functions in finite frequency domain this paper studies the problem of state feedback controller design for a class of nonlinear systems described by continuous time affine fuzzy models based on a piecewise continuous lyapunov function combined with s procedure and some matrix decoupling techniques a novel control law is derived in the formulation of linear matrix inequalities lmis in finite frequency domain first a so called finite frequency h performance index is defined which extends the standard h performance then a sufficient condition is derived such that the fuzzy closed loop system satisfies a finite frequency h performance by introducing the s procedure and adding slack variables piecewise controllers are designed to deal with disturbances in the low middle and high frequency domain respectively the proposed piecewise controller design method can get a better disturbance attenuation performance when the frequency ranges of disturbances are known beforehand finally two examples are given to illustrate the effectiveness and superiority of the new results

analysis and design for a class of complex control systems part i fuzzy modelling and identification this paper is the first of two dealing with the analysis and design of a class of complex control systems this part deals with fuzzy modelling and identification the second paper is concerned with fuzzy controller design we believe that these two papers show a way to analyze and design complex control systems using a combination of fuzzy logic and modern control theory the complex systems studied in these two papers can be represented by a fuzzy aggregation of a set of local linear models the identification can be divided into two procedures the first procedure is the identification of the membership functions including the determination of the number of fuzzy rules and the estimation of the parameters in the membership functions the second is the identification of the local linear models including the determination of the structure and the parameters of the local rule maps and the global rule interpolation two examples are used to demonstrate the application of the modelling method

exact quantification of the complexity of spacewise pattern growth in cellular automata we analyze the two possible ways of simulating complex systems with cellular automata by using the familiar timewise updating or by using the complementary spacewise updating both updating algorithms operate on identical sets of initial conditions defining the state of the automaton while timewise growth generally probes just vanishingly small sets of initial conditions producing statistical samples of the asymptotic attractors spacewise growth operates with much restricted sets which allow one to simulate them all exhaustively our main result is the derivation of an exact analytical formula to quantify precisely one of the two sources of algorithmic complexity of spacewise detection of the complete set of attractors for elementary 1d cellular automata with generic non periodic architectures of any arbitrary size the formula gives the total number of initial conditions that need to be investigated to locate rigorously all possible patterns for any given rule as simple applications we illustrate how this knowledge may be used i to uncover missing patterns in previous classifications in the literature and ii to obtain surprisingly novel patterns that are totally unreachable with the time honored technique of artificially imposing spatially periodic boundary conditions

semismooth matrix valued functions matrix valued functions play an important role in the development of algorithms for semidefinite programming problems this paper studies generalized differential properties of such functions related to nonsmooth smoothing newton methods the first part of this paper discusses basic properties such as the generalized derivative rademacher s theorem b derivative directional derivative and semismoothness the second part shows that the matrix absolute value function the matrix semidefinite projection function and the matrix projective residual function are strongly semismooth

approximation theory of fuzzy systems spl minus siso case in this paper the approximation properties of mimo fuzzy systems generated by the product inference are discussed we first give an analysis of fuzzy basic functions fbf s and present several properties of fbf s based on these properties of fbf s we obtain several basic approximation properties of fuzzy systems 1 basic approximation property which reveals the basic approximation mechanism of fuzzy systems 2 uniform approximation bounds which give the uniform approximation bounds between the desired control or decision functions and fuzzy systems 3 uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions and 4 universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect the similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds

roughening of the interfaces in 1 1 dimensional two component surface growth with an admixture of random deposition we simulate competitive two component growth on a one dimensional substrate of l sites one component is a poisson type deposition that generates kardar parisi zhang kpz correlations the other is random deposition rd we derive the universal scaling function of the interface width for this model and show that the rd admixture acts as a dilatation mechanism to the fundamental time and height scales but leaves the kpz correlations intact this observation is generalized to other growth models it is shown that the flat substrate initial condition is responsible for the existence of an early nonscaling phase in the interface evolution the length of this initial phase is a nonuniversal parameter but its presence is universal we introduce a method to measure the length of this initial nonscaling phase in application to parallel and distributed computations the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete event simulations it is shown that such algorithms are generally scalable in a ring communication topology

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

do integrable cellular automata have the confinement property we analyse a criterion introduced by joshi and lafortune for the integrability of cellular automata obtained from discrete systems through the ultradiscretization procedure we show that while this criterion can be used in order to single out integrable ultradiscrete systems there do exist cases where the system is nonintegrable and still the criterion is satisfied conversely we show that for ultradiscrete systems that are derived from linearizable mappings the criterion is not satisfied we investigate this phenomenon further in the case of a mapping which includes a linearizable subcase and show how the violation of the criterion comes to be finally we comment on the growth properties of ultradiscrete systems

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

semismooth homeomorphisms and strong stability of semidefinite and lorentz complementarity problems based on an inverse function theorem for a system of semismooth equations this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular stable we show further that for a parametric complementarity problem of this kind if a solution corresponding to a base parameter is strongly stable then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution similar results are also derived for a complementarity problem defined on the lorentz cone the analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the lorentz cone

affine ts model based fuzzy regulating servo control design an affine t s fuzzy system is derived naturally from linearizing a nonlinear system or from some data driven identification techniques for example cluster based algorithms or soft computation learning structures little research is proposed for the intrinsic analysis of an affine type fuzzy system further the controllers to regulate or to achieve servo control of affine ts based nonlinear systems are also few both affine type fuzzy regulation and servo control design scheme are theoretically derived a simple lyapunov based stability criterion and some extra conditions are proposed to guarantee the global stability of the generated closed loop fuzzy systems the exponential stability of the feedback fuzzy system is ensured under some conditions the performance of the proposed fuzzy controllers and fuzzy servo controllers is examined by three case studies simulation results show that the proposed controllers can stabilize these affine fuzzy systems and the proposed servomechanism can adapt itself to various incoming signals in very short time spans

decentralized state feedback control of uncertain affine fuzzy large scale systems with unknown interconnections this paper investigates the problem of the decentralized state feedback controller design for a class of nonlinear large scale systems described by uncertain affine fuzzy models with unknown interconnections first based on the structural information encoded in the fuzzy rules the affine fuzzy large scale system is represented by multiple operating regime based models then a decentralized state feedback controller is designed and a cyclic small gain condition is introduced to address the unknown interconnections such that the resulting closed loop system is asymptotically stable with the disturbance attenuation by constructing a piecewise lyapunov function combined with s procedure and adding slack matrix variables a convex decentralized controller design condition is derived in the formulation of linear matrix inequalities where the system matrix is separated from lyapunov matrix such that the controller parameterization is independent of the lyapunov matrix in contrast with the existing results the derived stabilizability condition loosens restrictions on the decentralized controller design and can be applied to handle the nonlinear large scale systems without satisfying the matching condition finally an example is given to illustrate the effectiveness and superiority of the new results