decentralized fuzzy observer based output feedback control for nonlinear large scale systems an lmi approach this paper presents a decentralized fuzzy control problem for asymptotic stabilization of a class of nonlinear large scale systems that use an observer based output feedback scheme a takagi sugeno t s fuzzy model is adopted for the nonlinear large scale system which has unknown interconnection terms and a fuzzy controller is separately considered for measurable and nonmeasurable premise variable cases sufficient conditions are derived for both asymptotic stabilization and optimization of a maximum bound of interconnection and are formulated in terms of linear matrix inequalities finally numerical examples are provided to verify the effectiveness of the proposed techniques

h filtering for fuzzy systems with immeasurable premise variables an uncertain system approach this paper discusses a design of stable filters with h disturbance attenuation of takagi sugeno fuzzy systems with immeasurable premise variables when we consider the filter design of takagi sugeno fuzzy systems the selection of premise variables plays an important role if the premise variable is the state of the system then a fuzzy system describes a wide class of nonlinear systems in this case however a filter design of fuzzy systems based on parallel distributed compensator idea is infeasible to avoid such a difficulty we consider the premise variables uncertainties then we consider a robust h filtering problem for such an uncertain system a solution of the problem is given in terms of linear matrix inequalities lmis some numerical examples are given to illustrate our theory

low distortion embeddings for edit distance we show that 0 1 d endowed with edit distance embeds into e1 with distortion 2o slog d log log d we further show efficient implementation of the embedding that yield solutions to various computational problems involving edit distance these include sketching communication complexity nearest neighbor search for all these problems we improve upon previous bounds

on the impossibility of dimension reduction in l 1 the johnson lindenstrauss lemma shows that any n points in euclidean space i e n with distances measured under the e 2 norm may be mapped down to o log n e2 dimensions such that no pairwise distance is distorted by more than a 1 p e factor determining whether such dimension reduction is possible in e 1 has been an intriguing open question we show strong lower bounds for general dimension reduction in e 1 we give an explicit family of n points in e 1 such that any embedding with constant distortion d requires n 1 d2 dimensions this proves that there is no analog of the johnson lindenstrauss lemma for e 1 in fact embedding with any constant distortion requires n 1 dimensions further embedding the points into e 1 with 1pe distortion requires nh o e log 1 e dimensions our proof establishes this lower bound for shortest path metrics of series parallel graphs we make extensive use of linear programming and duality in devising our bounds we expect that the tools and techniques we develop will be useful for future investigations of embeddings into e 1

sums of two squares in analytic rings we study analytic singularities for which every positive semidefinite analytic function is a sum of two squares of analytic functions this is a basic useful property of the plane but difficult to check in other cases in particular what about z 2 xy z 2 yx 2 y 3 z 2 x 3 y 4 or z 2 x 3 xy 3 in fact the unique positive examples we can find are the brieskorn singularity the union of two planes in 3 space and the whitney umbrella conversely we prove that a complete intersection with that property other than the seven embedded surfaces already mentioned must be a very simple deformation of the two latter namely in particular except for the stems z 2 x 2 and z 2 yx 2 all singularities are real rational double points

fast approximate k nn graph construction for high dimensional data via recursive lanczos bisection nearest neighbor graphs are widely used in data mining and machine learning a brute force method to compute the exact knn graph takes dn2 time for n data points in the d dimensional euclidean space we propose two divide and conquer methods for computing an approximate knn graph in dnt time for high dimensional data large d the exponent t 1 2 is an increasing function of an internal parameter which governs the size of the common region in the divide step experiments show that a high quality graph can usually be obtained with small overlaps that is for small values of t a few of the practical details of the algorithms are as follows first the divide step uses an inexpensive lanczos procedure to perform recursive spectral bisection after each conquer step an additional refinement step is performed to improve the accuracy of the graph finally a hash table is used to avoid repeating distance calculations during the divide and conquer process the combination of these techniques is shown to yield quite effective algorithms for building knn graphs

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

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

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

sums of squares on real algebraic curves given an affine algebraic variety v over with real points v compact and a non negative polynomial function f v with finitely many real zeros we establish a local global criterion for f to be a sum of squares in v we then specialize to the case where v is a curve the notion of virtual compactness is introduced and it is shown that in the local global principle compactness of v can be relaxed to virtual compactness the irreducible curves on which every non negative polynomial is a sum of squares are classified all results are extended to the more general framework of preorders moreover applications to the k moment problem from analysis are given in particular schmudgen s solution of the k moment problem for compact k is extended for dim k 1 to the case when k is virtually compact

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

finding structure with randomness probabilistic algorithms for constructing approximate matrix decompositions low rank matrix approximations such as the truncated singular value decomposition and the rank revealing qr decomposition play a central role in data analysis and scientific computing this work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low rank matrix approximation these techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets this paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions these methods use random sampling to identify a subspace that captures most of the action of a matrix the input matrix is then compressed either explicitly or implicitly to this subspace and the reduced matrix is manipulated deterministically to obtain the desired low rank factorization in many cases this approach beats its classical competitors in terms of accuracy robustness and or speed these claims are supported by extensive numerical experiments and a detailed error analysis the specific benefits of randomized techniques depend on the computational environment consider the model problem of finding the k dominant components of the singular value decomposition of an m times n matrix i for a dense input matrix randomized algorithms require bigo mn log k floating point operations flops in contrast to bigo mnk for classical algorithms ii for a sparse input matrix the flop count matches classical krylov subspace methods but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures iii for a matrix that is too large to fit in fast memory the randomized techniques require only a constant number of passes over the data as opposed to bigo k passes for classical algorithms in fact it is sometimes possible to perform matrix approximation with a single pass over the data

decentralized dynamic output feedback control for affine fuzzy large scale systems with measurement errors this paper investigates the decentralized output feedback control problem for affine fuzzy large scale systems with unknown interconnections a decentralized piecewise dynamic output feedback controller is constructed and the measurement errors between actual outputs and measured outputs are considered in control synthesis by introducing the s procedure and a cyclic small gain condition novel controller design conditions in terms of linear matrix inequalities lmis are derived which allow for reducing the worst case peak output due to measurement errors with satisfying an l norm constraint finally two examples are given to illustrate the effectiveness and superiority of the new results

finding correlations in subquadratic time with applications to learning parities and the closest pair problem given a set of n d dimensional boolean vectors with the promise that the vectors are chosen uniformly at random with the exception of two vectors that have pearson correlation coefficient hamming distance d 1 2 how quickly can one find the two correlated vectors we present an algorithm which for any constant 0 and constant 0 runs in expected time o n5 4 nd applications and extensions of this basic algorithm yield significantly improved algorithms for several other problems approximate closest pair for any sufficiently small constant 0 given n d dimensional vectors there exists an algorithm that returns a pair of vectors whose euclidean or hamming distance differs from that of the closest pair by a factor of at most 1 and runs in time o n2 the best previous algorithms including locality sensitive hashing have runtime o n2 o learning sparse parities with noise given samples from an instance of the learning parities with noise problem where each example has length n the true parity set has size at most k n and the noise rate is there exists an algorithm that identifies the set of k indices in time n 3 k poly 1 1 2 0 4 improves upon the results of grigorescu et al 2011 that give a runtime of n 1 2 2 o 1 k 2 poly 1 1 2 learning k juntas with noise given uniformly random length n boolean vectors together with a label which is some function of just k n of the bits perturbed by noise rate return the set of relevant indices leveraging the reduction of feldman et al 2009 our result for learning k parities implies an algorithm for this problem with runtime n 3 k poly 1 1 2 learning k juntas without noise given uniformly random length n boolean vectors together with a label which is some function of k n of the bits return the set of relevant indices using a modification of the algorithm of mossel et al 2004 and employing our algorithm for learning sparse parities with noise via the reduction of feldman et al 2009 we obtain an algorithm for this problem with runtime n 4 k poly n

efficient clustering on riemannian manifolds reformulating computer vision problems over riemannian manifolds has demonstrated superior performance in various computer vision applications this is because visual data often forms a special structure lying on a lower dimensional space embedded in a higher dimensional space however since these manifolds belong to non euclidean topological spaces exploiting their structures is computationally expensive especially when one considers the clustering analysis of massive amounts of data to this end we propose an efficient framework to address the clustering problem on riemannian manifolds this framework implements random projections for manifold points via kernel space which can preserve the geometric structure of the original space but is computationally efficient here we introduce three methods that follow our framework we then validate our framework on several computer vision applications by comparing against popular clustering methods on riemannian manifolds experimental results demonstrate that our framework maintains the performance of the clustering whilst massively reducing computational complexity by over two orders of magnitude in some cases highlightswe propose a kernelised random projection framework for clustering manifold points we present three projection methods conforming to our proposed framework we contrast our proposal to clustering methods on manifolds in various vision tasks we show the proposal obtain significant speed up whilst maintaining the performance we analyse the parameters contributing to the speed up

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

a convex optimization model for finding non negative polynomials this paper presents a convex optimization model for the problem of finding some polynomials for which certain linear combinations are non negative polynomials this model is then applied to solve several filter design problems we first reformulate some low pass filter design problems with finite or infinite impulse response as optimization problems over non negative real or complex polynomials whose feasibility problems can be solved by applying our model the whole optimization problems are then solved by using a combination of a bisection search procedure on an appropriate parameter and our convex optimization model to solve the feasibility problems some numerical examples illustrate the method

pythagoras numbers of real irreducible algebroid curves and gram matrices abstract using elementary techniques of linear algebra in relation with gram matrices we bound the pythagoras number of a real irreducible algebroid curve by its multiplicity

exposed faces of semidefinitely representable sets a linear matrix inequality lmi is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite motivated by the fact that diagonal lmis define polyhedra the solution set of an lmi is called a spectrahedron linear images of spectrahedra are called semidefinitely representable sets part of the interest in spectrahedra and semidefinitely representable sets arises from the fact that one can efficiently optimize linear functions on them by semidefinite programming such as one can do on polyhedra by linear programming it is known that every face of a spectrahedron is exposed this is also true in the general context of rigidly convex sets we study the same question for semidefinitely representable sets lasserre proposed a moment matrix method to construct semidefinite representations for certain sets our main result is that this method can work only if all faces of the considered set are exposed this necessary condition complements sufficient conditions recently proved by lasserre helton and nie

efficient search for approximate nearest neighbor in high dimensional spaces we address the problem of designing data structures that allow efficient search for approximate nearest neighbors more specifically given a database consisting of a set of vectors in some high dimensional euclidean space we want to construct a space efficient data structure that would allow us to search given a query vector for the closest or nearly closest vector in the database we also address this problem when distances are measured by the l1 norm and in the hamming cube significantly improving and extending recent results of kleinberg we construct data structures whose size is polynomial in the size of the database and search algorithms that run in time nearly linear or nearly quadratic in the dimension depending on the case the extra factors are polylogarithmic in the size of the database

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

decentralized h fuzzy filter for nonlinear large scale sampled data systems with uncertain interconnections abstract this paper proposes a decentralized h fuzzy filter technique for nonlinear large scale interconnected systems that are based on the takagi sugeno fuzzy model the large scale system has unknown interconnection terms that are assumed to satisfy the quadratic bounds an error system between the nonlinear large scale system and the decentralized filter is constructed by using the fuzzy lyapunov technique sufficient conditions are proposed for both showing asymptotic stability and guaranteeing h fuzzy filter performance these sufficient conditions are derived in terms of linear matrix inequalities finally simulation examples are given to demonstrate the effectiveness of the proposed technique

a novel approach to h_ bm infty decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h infin decentralized output feedback controller for nonlinear interconnected systems this study introduces h infin decentralized fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear interconnected systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only a novel decoupled method is proposed in this study to transform the non linear matrix inequality non lmi conditions into some lmi forms by the proposed decoupled method the problem of h infin decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp with five prespecified scalars for each subsystem in general it is a difficult task to solve the evp with five prespecified scalars fortunately this special evp can be easily solved by using a genetic algorithm and an lmi based optimization method finally a simulation example is given to illustrate the design procedure and robust performance of the proposed methods

space time tradeoffs for approximate nearest neighbor searching nearest neighbor searching is the problem of preprocessing a set of n point points in d dimensional space so that given any query point q it is possible to report the closest point to q rapidly in approximate nearest neighbor searching a parameter e 0 is given and a multiplicative error of 1 e is allowed we assume that the dimension d is a constant and treat n and e as asymptotic quantities numerous solutions have been proposed ranging from low space solutions having space o n and query time o log n 1 ed 1 to high space solutions having space roughly o n log n ed and query time o log n e we show that there is a single approach to this fundamental problem which both improves upon existing results and spans the spectrum of space time tradeoffs given a tradeoff parameter where 2 1 e we show that there exists a data structure of space o n d 1 log 1 e that can answer queries in time o log n 1 e d 1 2 when e 2 this yields a data structure of space o n log 1 e that can answer queries in time o log n 1 e d 1 2 when e 1 e it provides a data structure of space o n ed 1 log 1 e that can answer queries in time o log n e our results are based on a data structure called a t e avd which is a hierarchical quadtree based subdivision of space into cells each cell stores up to t representative points of the set such that for any query point q in the cell at least one of these points is an approximate nearest neighbor of q we provide new algorithms for constructing avds and tools for analyzing their total space requirements we also establish lower bounds on the space complexity of avds and show that up to a factor of o log 1 e our space bounds are asymptotically tight in the two extremes e 2 and e 1 e

sums of squares in real rings let a be an excellent ring we show that if the real dimension of a is at least three then a has in finite pythagoras number and there exists a positive semidefinite element in a which is not a sum of squares in a

positive semidefinite germs in real analytic surfaces we find all real analytic surface germs in mathbb r 3 on which every positive semidefinite function germ is a sum of squares in fact of two squares of analytic function germs

optimal filtering with random sensor delay multiple packet dropout and uncertain observations this paper studies the problem of optimal filtering of discrete time systems with random sensor delay multiple packet dropout and uncertain observation the random sensor delay multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation a new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data based on a stochastic definition of the norm of a system with a stochastic parameter new relations for stochastic norm are derived the stochastic norm of the estimation error is used as a criterion for the filter design the relations derived for the new norm definition are used to obtain a set of linear matrix inequalities lmis to solve the filter design problems simulation examples show the effectiveness of the proposed method

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

the fast johnson lindenstrauss transform and approximate nearest neighbors we introduce a new low distortion embedding of ell 2 d into ell p o log n p 1 2 called the fast johnson lindenstrauss transform fjlt the fjlt is faster than standard random projections and just as easy to implement it is based upon the preconditioning of a sparse projection matrix with a randomized fourier transform sparse random projections are unsuitable for low distortion embeddings we overcome this handicap by exploiting the heisenberg principle of the fourier transform i e its local global duality the fjlt can be used to speed up search algorithms based on low distortion embeddings in ell 1 and ell 2 we consider the case of approximate nearest neighbors in ell 2 d we provide a faster algorithm using classical projections which we then speed up further by plugging in the fjlt we also give a faster algorithm for searching over the hypercube

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

brief paper delay dependent robust stability of uncertain fuzzy large scale systems with time varying delays this paper addresses the stability problem of fuzzy large scale systems flsss with uncertainties and arbitrary time varying delays the stability conditions which are less conservative and more applicable than the existing results are derived by a novel lyapunov krasovskii functional method and expressed in terms of linear matrix inequalities lmis two examples are given to demonstrate the correctness and advantage of our theoretical results

h sub 2 norm optimization with constrained dynamic output feedback controllers decentralized and reliable control this paper addresses some open problems in the area of dynamic output feedback control design the first one is the structurally constrained decentralized control problem and the second is related to robust and reliable control a necessary and sufficient condition for decentralized and quadratic stabilizability is given and used to provide a solution to the h sub 2 norm optimization problem a numerical cross decomposition algorithm is developed and satisfactorily applied to find the solution of some illustrative examples a comprehensive benchmark validates the results

fuzzy based interaction prediction approach for hierarchical control of large scale systems this paper presents a fuzzy based interaction prediction approach f ipa for two level optimal control of large scale systems the design procedure uses a decomposition coordination framework of hierarchical structures at the first level the system is decomposed into subsystems for which subproblems are formed at the second level a fuzzy coordinator is used to predict the coordination parameters needed to coordinate the solutions of the first level subproblems the fuzzy coordinator uses a critic vector to evaluate its performance and learn its parameters by minimizing an energy function the proposed control scheme is implemented on a two degrees of freedom 2dof model of robot manipulator with parallel links and two inverted pendulums on cars simulation results are obtained and compared with the gradient based interaction prediction approach g ipa and a centralized optimization

on the positive extension property and hilbert s 17th problem for real analytic sets in this work we study the positive extension pe property and hilbert s 17th problem for real analytic germs and sets a real analytic germ x 0 of r 0 n has the pe property if every positive semidefinite analytic function germ on x 0 has a positive semidefinite analytic extension to r 0 n analogously one states the pe property for a global real analytic set x in an open set q of r 0 n these pe properties are natural variations of hilbert s 17th problem here we prove that 1 a real analytic germ x 0 subset of r 0 3 has the pe property if and only if every positive semidefinite analytic function germ on x 0 is a sum of squares of analytic function germs on x 0 and 2 a global real analytic set x of dimension 2 and local embedding dimension 3 has the pe property if and only if it is coherent and all its germs have the pe property if that is the case every positive semidefinite analytic function on x is a sum of squares of analytic functions on x moreover we classify the singularities with the pe property

sum of squares length of real forms for n d ge 1 let p n 2d denote the smallest number p such that every sum of squares of degree d forms in mathbb r x 1 ldots x n is a sum of p squares we establish lower bounds for p n 2d that are considerably stronger than the bounds known so far combined with known upper bounds they give p 3 2d in d 1 d 2 in the ternary case assuming a conjecture of iarrobino kanev on dimensions of tangent spaces to catalecticant varieties we show that p n 2d sim const cdot d n 1 2 for d rightarrow infty and all n ge 3 for ternary sextics and quaternary quartics we determine the exact value of the invariant showing p 3 6 4 and p 4 4 5

is the k nn classifier in high dimensions affected by the curse of dimensionality abstract there is an increasing body of evidence suggesting that exact nearest neighbour search in high dimensional spaces is affected by the curse of dimensionality at a fundamental level does it necessarily mean that the same is true for k nearest neighbours based learning algorithms such as the k nn classifier we analyse this question at a number of levels and show that the answer is different at each of them as our first main observation we show the consistency of a k approximate nearest neighbour classifier however the performance of the classifier in very high dimensions is provably unstable as our second main observation we point out that the existing model for statistical learning is oblivious of dimension of the domain and so every learning problem admits a universally consistent deterministic reduction to the one dimensional case by means of a borel isomorphism

decentralized pdc for large scale t s fuzzy systems this paper studies the decentralized stabilization problem for a large scale system the considered large scale system comprises of a number of subsystems and each subsystem is represented by a takagi sugeno t s fuzzy model the interconnection between any two subsystems may be nonlinear and satisfies some matching condition by the concept of parallel distributed compensation pdc the decentralized fuzzy control for each subsystem is synthesized in which the control gain depends on the strength of interconnections maximal number of the fired rules in each subsystem and the common positive matrix p sub i based on lyapunov criterion and riccati inequality some sufficient conditions are derived and the common p sub i is solved by linear matrix inequalities lmi so that the whole closed loop large scale fuzzy system with the synthesized fuzzy control is asymptotically stable finally a numerical example is given to illustrate the control synthesis and its effectiveness

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

fault detection filtering for nonlinear switched stochastic systems in this note the fault detection filtering problem is solved for nonlinear switched stochastic system in the t s fuzzy framework our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with brownian motion based on observer based fault detection fuzzy filter as a residual generator the proposed fault detection is formulated as a fuzzy filtering problem by the utilization of the average dwell time technique and the piecewise lyapunov function technique the fuzzy parameter dependent fault detection filters are designed that guarantee the resulted error system to be mean square exponential stable with a weighted mathcal h infty error performance then the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique finally simulation has been presented to show the effectiveness of the proposed fault detection technique

polynomial time approximation schemes for geometric min sum median clustering the johnson lindenstrauss lemma states that n points in ahigh dimensional hilbert space can be embedded with smalldistortion of the distances into an o log n dimensional space by applying a random linear transformation weshow that similar though weaker properties hold for certainrandom linear transformations over the hamming cube we use thesetransformations to solve np hard clustering problems in the cube aswell as in geometric settings more specifically we address thefollowing clustering problem given n points in a larger set e g d endowed with a distance function e g l2 distance we would like to partition the dataset into k disjoint clusters each with a cluster center so as to minimize the sum over all data points of the distancebetween the point and the center of the cluster containing thepoint the problem is provably np hard in some high dimensionalgeometric settings even for k 2 we give polynomial timeapproximation schemes for this problem in several settings including the binary cube 0 1 d with hamming distance and d either with l1 distance or with l2 distance or with the square ofl2 distance in all these settings the bestprevious results were constant factor approximation guarantees wenote that our problem is similar in flavor to the k medianproblem and the related facility location problem which has beenconsidered in graph theoretic and fixed dimensional geometricsettings where it becomes hard when k is part of the input in contrast we study the problem when k is fixed but thedimension is part of the input

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

eigenvalues of symmetric matrices over integral domains abstract given an integral domain a we consider the set of all integral elements over a that can occur as an eigenvalue of a symmetric matrix over a we give a sufficient criterion for being such an element in the case where a is the ring of integers of an algebraic number field this sufficient criterion is also necessary and we show that the size of matrices grows linearly in the degree of the element the latter result settles a questions raised by bass estes and guralnick

weighted sums of squares in local rings and their completions i let a be an excellent regular local ring of dimension two let t be a finitely generated preordering in a and let widehat t be the preordering generated by t in the completion widehat a of a we study the question when the property of being saturated descends from widehat t to t and establish conditions of geometric nature which allow to decide this question as an application we classify all principal preorderings in a of degree 3 which are saturated in the case where a has a real closed residue field these results have direct implications for nonnegativity certificates for real polynomials on two dimensional semi algebraic sets

the computational hardness of estimating edit distance we prove the first nontrivial communication complexity lower bound for the problem of estimating the edit distance aka levenshtein distance between two strings to the best of our knowledge this is the first computational setting in which the complexity of estimating the edit distance is provably larger than that of hamming distance our lower bound exhibits a trade off between approximation and communication asserting for example that protocols with o 1 bits of communication can obtain only approximation alpha geq omega log d log log d where d is the length of the input strings this case of o 1 communication is of particular importance since it captures constant size sketches as well as embeddings into spaces like l 1 and squared l 2 two prevailing algorithmic approaches for dealing with edit distance indeed the known nontrivial communication upper bounds are all derived from embeddings into l 1 by excluding low communication protocols for edit distance we rule out a strictly richer class of algorithms than previous results furthermore our lower bound holds not only for strings over a binary alphabet but also for strings that are permutations aka the ulam metric for this case our bound nearly matches an upper bound known via embedding the ulam metric into l 1 our proof uses a new technique that relies on fourier analysis in a rather elementary way