an algorithm to compute averages on matrix lie groups averaging is a common way to alleviate errors and random fluctuations in measurements and to smooth out data averaging also provides a way to merge structured data in a smooth manner the present paper describes an algorithm to compute averages on matrix lie groups in particular we discuss the case of averaging over the special orthogonal group of matrices the unitary group of matrices and the group of symmetric positive definite matrices

a combinatorial primal dual approach to semidefinite programs semidefinite programs sdps have been used in many recent approximation algorithms we develop a general primal dual approach to solve sdps using a generalization of the well known multiplicative weights update rule to symmetric matrices for a number of problems such as s parsest c ut and b alanced s eparator in undirected and directed weighted graphs m in u n c ut and m in 2cnf d eletion this yields combinatorial approximation algorithms that are significantly more efficient than interior point methods the design of our primal dual algorithms is guided by a robust analysis of rounding algorithms used to obtain integer solutions from fractional ones our ideas have proved useful in quantum computing especially the recent result of jain et al 2011 that qip e pspace

kernelization of matrix updates when and how abstract we define what it means for a learning algorithm to be kernelizable in the case when the instances are vectors asymmetric matrices and symmetric matrices respectively we can characterize kernelizability in terms of an invariance of the algorithm to certain orthogonal transformations if we assume that the algorithm s action relies on a linear prediction then we can show that in each case the linear parameter vector must be a certain linear combination of the instances we give a number of examples of how to apply our methods in particular we show how to kernelize multiplicative updates for symmetric instance matrices

delay range dependent robust stabilization for uncertain t s fuzzy control systems with interval time varying delays this paper is concerned with robust stabilization for a class of t s fuzzy control systems with interval time varying delays an approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities the main points of the approach are i two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria ii an appropriate lyapunov krasovskii functional is constructed by including both the lower and upper bounds of the interval time varying delays and iii neither model transformation nor free weighting matrices are employed in the theoretical result derivation as a result some improved sufficient stability criteria are derived and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem numerical examples are given to demonstrate the effectiveness of the proposed approach

learning the kernel matrix by maximizing a kfd based class separability criterion the advantage of a kernel method often depends critically on a proper choice of the kernel function a promising approach is to learn the kernel from data automatically in this paper we propose a novel method for learning the kernel matrix based on maximizing a class separability criterion that is similar to those used by linear discriminant analysis lda and kernel fisher discriminant kfd it is interesting to note that optimizing this criterion function does not require inverting the possibly singular within class scatter matrix which is a computational problem encountered by many lda and kfd methods we have conducted experiments on both synthetic data and real world data from uci and feret showing that our method consistently outperforms some previous kernel learning methods

polynomial fuzzy models for nonlinear control a taylor series approach classical takagi sugeno t s fuzzy models are formed by convex combinations of linear consequent local models such fuzzy models can be obtained from nonlinear first principle equations by the well known sector nonlinearity modeling technique this paper extends the sector nonlinearity approach to the polynomial case this way generalized polynomial fuzzy models are obtained the new class of models is polynomial both in the membership functions and in the consequent models importantly t s models become a particular case of the proposed technique recent possibilities for stability analysis and controller synthesis are also discussed a set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard t s approaches as the degrees of the involved polynomials increase

novel stabilization criteria for t s fuzzy systems with affine matched membership functions this paper presents a new parallel distributed compensation controller design approach for t s takagi sugeno fuzzy control systems with affine matched membership functions in the system and controller in the new fuzzy control affine transformed membership functions are adopted by scaling and biasing the original membership functions of the system stabilization and performance criterion of the closed loop t s fuzzy systems are obtained through a new parameterized linear matrix inequality which is rearranged by affine matched membership functions the conservativeness of stabilization condition for the t s fuzzy system is significantly relaxed by utilizing the constraints condition of the controllers membership functions which is determined from the difference of each transformed membership function in addition the controller gain is reconstructed by a decision variable separation technique with two different free weighting matrices without any scaling parameter the superiority of proposed method is verified through numerical examples

novel stability conditions for discrete time t s fuzzy systems this paper is concerned with the issue of developing a novel strategy to reduce the conservatism of stability conditions for discrete time takagi sugeno t s fuzzy systems unlike the previous ones which are almost quadratic with respect to the state vector a new class of lyapunov functions is proposed which is quadratic with respect to the kronecker products of the state vector thus including almost the existing ones found in the literature as special cases by combining the characterizations of homogeneous matrix polynomials and the properties of membership functions relaxed stability conditions are derived in the form of linear matrix inequalities which can be efficiently solved by the convex optimization techniques finally a numerical example is provided to illustrate the effectiveness of the proposed approach

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

generalized nonquadratic stability of continuous time takagi sugeno models this paper provides generalized nonquadratic stability conditions for continuous time nonlinear models in the takagi sugeno ts form obtained by sector nonlinearity approach should global quadratic stability fail for a given nonlinear model the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear matrix inequalities lmis which are efficiently solved by convex optimization techniques illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis

relaxed lmi based stability conditions for takagi sugeno fuzzy control systems using regional membership function shape dependent analysis approach this paper presents relaxed stability conditions for takagi sugeno t s fuzzy model based control systems it is assumed that the stability conditions are represented by some inequalities in the form of a p dimensional fuzzy summation to investigate the system stability the inequalities are expanded to n dimensional fuzzy summation n ges p the boundary and regional informations of membership functions are then utilized for relaxation of stability analysis results two analysis approaches are proposed in this paper the first approach is called the global membership function shape dependent approach in which the lower and upper bounds of the membership functions and its products from 2 to n in the full operating domain are considered in the stability analysis the second approach is named as the regional membership function shape dependent approach in which the operating region is partitioned to subregions and the boundary information of membership functions on each operating subregion is employed to facilitate the stability analysis in both approaches by the help of the boundary and or regional information of the membership functions some inequality constraints in the form of multidimensional fuzzy summation containing some slack matrices are constructed stability conditions in the form of linear matrix inequalities lmis are derived numerical examples are given to demonstrate the effectiveness of the proposed stability conditions

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

low rank decomposition meets kernel learning a generalized nystrom method abstract low rank matrix decomposition and kernel learning are two useful techniques in building advanced learning systems low rank decomposition can greatly reduce the computational cost of manipulating large kernel matrices however existing approaches are mostly unsupervised and do not incorporate side information such as class labels making the decomposition less effective for a specific learning task on the other hand kernel learning techniques aim at constructing kernel matrices whose structure is well aligned with the learning target which improves the generalization performance of kernel methods however most kernel learning approaches are computationally very expensive to obtain the advantages of both techniques and address their limitations in this paper we propose a novel kernel low rank decomposition formulation called the generalized nystrom method our approach inherits the linear time and space complexity via matrix decomposition while at the same time fully exploits partial label information in computing task dependent decomposition in addition the resultant low rank factors can generalize to arbitrary new samples rendering great flexibility in inductive learning scenarios we further extend the algorithm to a multiple kernel learning setup the experimental results on semi supervised classification demonstrate the usefulness of the proposed method

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

brief paper estimating the domain of attraction for non polynomial systems via lmi optimizations this paper proposes a strategy for estimating the domain of attraction da for non polynomial systems via lyapunov functions lfs the idea consists of converting the non polynomial optimization arising for a chosen lf in a polynomial one which can be solved via lmi optimizations this is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst case remainders in truncated taylor expansions moreover a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen lf and another condition is provided for establishing whether such an estimate has been found the proposed strategy can readily be exploited with variable lfs in order to search for optimal estimates lastly it is worth remarking that no other method is available to estimate the da for non polynomial systems via lmis

near optimal algorithms for online matrix prediction in several online prediction problems of recent interest the comparison class is composed of matrices for example in the online max cut problem the comparison class is matrices which represent cuts of a given graph and in online gambling the comparison class is matrices which represent permutations over n teams another important example is online collaborative filtering in which a widely used comparison class is the set of matrices with a small trace norm in this paper we isolate a property of matrices which we call beta tau decomposability and derive an efficient online learning algorithm that enjoys a regret bound of tilde o sqrt beta tau t for all problems in which the comparison class is composed of beta tau decomposable matrices by analyzing the decomposability of cut matrices low trace norm matrices and triangular matrices we derive near optimal regret bounds for online max cut online collaborative filtering and online gambling in particular this resolves i

brief paper local stability analysis using simulations and sum of squares programming the problem of computing bounds on the region of attraction for systems with polynomial vector fields is considered invariant subsets of the region of attraction are characterized as sublevel sets of lyapunov functions finite dimensional polynomial parametrizations for lyapunov functions are used a methodology utilizing information from simulations to generate lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed the suitability of lyapunov function candidates is assessed solving linear sum of squares optimization problems qualified candidates are used to compute invariant subsets of the region of attraction and to initialize various bilinear search strategies for further optimization we illustrate the method on small examples from the literature and several control oriented systems

method for higher order polynomial sugeno fuzzy inference systems a method for higher order polynomial sugeno fuzzy inference systems formation is presented compared to other existing higher order sugeno implementations it uses fewer parameters and compared to zero and 1st order sugeno fuzzy systems it has overall improved model performance while best models are not always obtained via a higher order representation in our proposed method it is possible to choose the polynomial order which best fits the desired data its input is a previously established model found by a clustering algorithm subtractive algorithm in this case afterward parameters of all higher order polynomials are adjusted using recursive least square algorithm for experimental validation multiple benchmark datasets are tested using hold out and k fold validation as well as data forecasting various performance measures are used although akaike information criterion is used as a primary measure to demonstrate that our proposed higher order polynomials have overall better model performance over zero and 1st order polynomials

online pca with optimal regret we investigate the online version of principle component analysis pca where in each trial t the learning algorithm chooses a k dimensional subspace and upon receiving the next instance vector xt suffers the compression loss which is the squared euclidean distance between this instance and its projection into the chosen subspace when viewed in the right parameterization this compression loss is linear i e it can be rewritten as tr wtxtxt where wt is the parameter of the algorithm and the outer product xtxt with xt 1 is the instance matrix in this paper generalize pca to arbitrary positive definite instance matrices xt with the linear loss tr wtxt we evaluate online algorithms in terms of their worst case regret which is a bound on the additional total loss of the online algorithm on all instances matrices over the compression loss of the best k dimensional subspace chosen in hindsight we focus on two popular online algorithms for generalized pca the gradient descent gd and matrix exponentiated gradient meg algorithms we show that if the regret is expressed as a function of the number of trials then both algorithms are optimal to within a constant factor on worst case sequences of positive definite instances matrices with trace norm at most one which subsumes the original pca problem with outer products this is surprising because meg is believed be suboptimal in this case we also show that when considering regret bounds as a function of a loss budget then meg remains optimal and strictly outperforms gd when the instance matrices are trace norm bounded next we consider online pca when the adversary is allowed to present the algorithm with positive semidefinite instance matrices whose largest eigenvalue is bounded rather than their trace which is the sum of their eigenvalues again we can show that meg is optimal and strictly better than gd in this setting

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

stability analysis of polynomial fuzzy models via polynomial fuzzy lyapunov functions in this paper the stability of continuous time polynomial fuzzy models by means of a polynomial generalization of fuzzy lyapunov functions is studied fuzzy lyapunov functions have been fruitfully used in the literature for local analysis of takagi sugeno models a particular class of the polynomial fuzzy ones based on a recent taylor series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space it is shown that a refinement of the polynomial lyapunov function so as to make it share the fuzzy structure of the model proves advantageous conditions thus obtained are tested via available sos software

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available

interactions of solitons in nonintegrable systems direct perturbation method and applications abstract problems of approximate description of soliton interaction in nonintegrable systems are discussed it is shown that in an arbitrary lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities a lagrangian may be introduced analogous to that for classical particles with a pair interaction potential a classification of possible types of soliton interaction is given and criteria of the existence of bound states are formulated a possibility of generalization of approximated description of soliton interaction in the multidimensional case is noted

control synthesis of discrete time t s fuzzy systems based on a novel non pdc control scheme this paper proposes relaxed stabilization conditions of discrete time nonlinear systems in the takagi sugeno t s fuzzy form by using the algebraic property of fuzzy membership functions a novel nonparallel distributed compensation non pdc control scheme is proposed based on a new class of fuzzy lyapunov functions thus relaxed stabilization conditions for the underlying closed loop fuzzy system are developed by applying a new slack variable technique in particular some existing fuzzy lyapunov functions and non pdc control schemes are special cases of the new lyapunov function and fuzzy control scheme respectively finally two numerical examples are provided to illustrate the effectiveness of the proposed method

on quantum statistical inference interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially in step with dramatic new developments in experimental techniques for studying small quantum systems furthermore developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory the present paper reviews this field and proposes and interrelates some new concepts for an extension of classical statistical inference to the quantum context

matrix exponentiated gradient updates for on line learning and bregman projection we address the problem of learning a symmetric positive definite matrix the central issue is to design parameter updates that preserve positive definiteness our updates are motivated with the von neumann divergence rather than treating the most general case we focus on two key applications that exemplify our methods on line learning with a simple square loss and finding a symmetric positive definite matrix subject to linear constraints the updates generalize the exponentiated gradient eg update and adaboost respectively the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector which in this context is a diagonal positive definite matrix with trace one the generalized updates use matrix logarithms and exponentials to preserve positive definiteness most importantly we show how the derivation and the analyses of the original eg update and adaboost generalize to the non diagonal case we apply the resulting matrix exponentiated gradient meg update and definiteboost to the problem of learning a kernel matrix from distance measurements

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

semi supervised domain adaptation on manifolds in real life problems the following semi supervised domain adaptation scenario is often encountered we have full access to some source data which is usually very large the target data distribution is under certain unknown transformation of the source data distribution meanwhile only a small fraction of the target instances come with labels the goal is to learn a prediction model by incorporating information from the source domain that is able to generalize well on the target test instances we consider an explicit form of transformation functions and especially linear transformations that maps examples from the source to the target domain and we argue that by proper preprocessing of the data from both source and target domains the feasible transformation functions can be characterized by a set of rotation matrices this naturally leads to an optimization formulation under the special orthogonal group constraints we present an iterative coordinate descent solver that is able to jointly learn the transformation as well as the model parameters while the geodesic update ensures the manifold constraints are always satisfied our framework is sufficiently general to work with a variety of loss functions and prediction problems empirical evaluations on synthetic and real world experiments demonstrate the competitive performance of our method with respect to the state of the art

selective hbox scr h _2 and hbox scr h _ infty stabilization of takagi sugeno fuzzy systems this paper presents new results concerning the stability analysis and design of state feedback controllers for continuous time takagi sugeno t s fuzzy systems via fuzzy lyapunov functions the membership functions of the t s fuzzy systems are modeled in a space that is defined by the cartesian product of simplexes called a multisimplex if the time derivatives of the membership functions are bounded the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions linear matrix inequality lmi relaxations that are based on polynomial matrices are provided for stability analysis and controller design extensions for the design of control laws that minimize upper bounds to h2 and h norms are also given the main novelty of this method is that it allows one to synthesize control gains which depends only on some premise variables that are selected by the designer numerical experiments illustrate the flexibility and advantages of the proposed method

learning in an uncertain world mimo covariance matrix optimization with imperfect feedback in this paper we present a distributed learning algorithm for the optimization of signal covariance matrices in gaussian multiple input and multiple output mimo multiple access channel with imperfect and possibly delayed feedback the algorithm is based on the method of matrix exponential learning mxl and it has the same information and computation requirements as distributed water filling however unlike water filling the proposed algorithm converges to the system s optimum signal covariance profile even under stochastic uncertainty and imperfect feedback moreover the algorithm also retains its convergence properties in the presence of user update asynchronicities random delays and or ergodically changing channel conditions our theoretical analysis is complemented by extensive numerical simulations which illustrate the robustness and scalability of mxl in realistic network conditions in particular the algorithm retains its convergence speed even for large numbers of users and or antennas per user

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

linear algorithms for online multitask classification we introduce new perceptron based algorithms for the online multitask binary classification problem under suitable regularity conditions our algorithms are shown to improve on their baselines by a factor proportional to the number of tasks we achieve these improvements using various types of regularization that bias our algorithms towards specific notions of task relatedness more specifically similarity among tasks is either measured in terms of the geometric closeness of the task reference vectors or as a function of the dimension of their spanned subspace in addition to adapting to the online setting a mix of known techniques such as the multitask kernels of evgeniou et al our analysis also introduces a matrix based multitask extension of the p norm perceptron which is used to implement spectral co regularization experiments on real world data sets complement and support our theoretical findings

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

stabilization for t s model based uncertain stochastic systems this paper considers the stabilization problem of a class of uncertain ito stochastic fuzzy systems driven by a multidimensional wiener process the uncertainty modeled in the systems is of the linear fractional type which includes the norm bounded uncertainty as a special case the objective is to design a state feedback fuzzy controller such that the closed loop system is robustly asymptotically stable under a stochastic setting by using a stochastic lyapunov approach sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique the derived stability conditions are then employed to design controllers which stabilize the uncertain ito stochastic fuzzy systems two simulation examples are given to illustrate the effectiveness of the approaches proposed

exponentiated gradient versus gradient descent for linear predictors we consider two algorithm for on line prediction based on a linear model the algorithms are the well known gradient descent gd algorithm and a new algorithm which we call eg they both maintain a weight vector using simple updates for the gd algorithm the update is based on subtracting the gradient of the squared error made on a prediction the eg algorithm uses the components of the gradient in the exponents of factors that are used in updating the weight vector multiplicatively we present worst case loss bounds for eg and compare them to previously known bounds for the gd algorithm the bounds suggest that the losses of the algorithms are in general incomparable but eg has a much smaller loss if only a few components of the input are relevant for the predictions we have performed experiments which show that our worst case upper bounds are quite tight already on simple artificial data

predicting a switching sequence of graph labelings we study the problem of predicting online the labeling of a graph we consider a novel setting for this problem in which in addition to observing vertices and labels on the graph we also observe a sequence of just vertices on a second graph a latent labeling of the second graph selects one of k labelings to be active on the first graph we propose a polynomial time algorithm for online prediction in this setting and derive a mistake bound for the algorithm the bound is controlled by the geometric cut of the observed and latent labelings as well as the resistance diameters of the graphs when specialized to multitask prediction and online switching problems the bound gives new and sharper results under certain conditions

finite time h asynchronous state estimation for discrete time fuzzy markov jump neural networks with uncertain measurements abstract this paper is concerned with the problem of the h asynchronous state estimation for fuzzy markov jump neural networks fmjnns with uncertain measurements over a finite time interval in terms of a bernoulli distributed white sequence the phenomenon of the randomly occurring uncertainties in the output equation is represented by exploiting a random variable with known occurrence probabilities the main focus of this paper is to present a state estimator such that the resulting error system is finite time bounded and satisfies an h performance requirement then by employing the stochastic analysis technique sufficient conditions are provided to ensure that the state estimator is designed by means of solving a convex optimization problem an example is finally given to explain the effectiveness and potentiality of the proposed design method

polynomial fuzzy model based control systems stability analysis via piecewise linear membership functions this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems using the sum of squares sos approach the pfmb control system under consideration requires that the polynomial fuzzy model and polynomial fuzzy controller share neither the same premise membership functions nor the same number of fuzzy rules this class of pfmb control systems offers a greater design flexibility to the polynomial fuzzy controller however due to the imperfectly matched membership functions it usually produces more conservative stability conditions by following the traditional stability analysis approach for the fmb control systems to facilitate the stability analysis piecewise linear membership functions plmfs are proposed which offer a nice property that the grades of membership are governed by a finite number of sample points thus it allows the plmfs to be brought to the sos based stability conditions which are applied to the pfmb control systems with the specified plmfs rather than any shapes the system stability can be examined by checking only the pfmb control system at the sample points it is worth mentioning that the plmfs which are not necessarily implemented physically are a mathematical tool to carry out the stability analysis to verify the stability analysis result a simulation example is given to demonstrate the effectiveness of the proposed approach

novel delay dependent stability criterion for time varying delay systems with parameter uncertainties and nonlinear perturbations this study proposes a novel approach to obtain less conservative conditions for the robust stability analysis for time varying delay systems with parameter uncertainties and nonlinear perturbations specifically first we divide the time varying delay into non uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms more exactly second novel delay derivation dependent stability criteria are derived by introducing a parameter c in the lyapunov krasovskii functional third we define some new variables to deal with uncertain parameters finally two numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results

improvement on nonquadratic stabilization of discrete time takagi sugeno fuzzy systems multiple parameterization approach this paper presents the relaxed nonquadratic stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this we propose a new fuzzy controller and lyapunov function by generalizing the nonparallel distributed compensation non pdc control law and nonquadratic lyapunov function respectively by exploiting po lya s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions an infinite family of sufficient conditions for the asymptotic stabilizability is derived these conditions are formulated in the format of linear matrix inequalities lmis and hence are numerically tractable via convex programming techniques finally an example is given to illustrate advantages of the proposed method

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

dynamics of spiral waves in non equilibrium media in this paper the spiral waves in two dimensional nonequilibrium media are studied on the basis of the two dimensional ginzburg landau equation in the general case the perturbation of origin spiral waves leads to the spiral rotation and to the motion of spiral cores motion in media with hard and soft excitation is analysed separately

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise lyapunov function based switching fuzzy controller this paper proposes the minimum type piecewise lyapunov function based switching fuzzy controller that switches accompanying the piecewise lyapunov function by applying this switching fuzzy controller with the minimum type piecewise lyapunov function the relaxed stabilization criterion is obtained for continuous takagi sugeno t s fuzzy systems some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities bmis which contain some bilinear terms as the product of a full matrix and a scalar according to the literature the path following method is very effective for this kind of bmi problem hence it is utilized to obtain solutions of the criterion xie et al in 1997 chose two types i e minimum type and maximum type of piecewise lyapunov functions as the lyapunov function candidates the reasons for why this study only chooses the minimum type piecewise lyapunov function as the lyapunov function candidate are illustrated moreover the numerical example shows the relaxation of the proposed criterion

fuzzy resilient energy to peak filtering for continuous time nonlinear systems the problem of resilient energy to peak filtering for a class of uncertain continuous time nonlinear systems is investigated in this paper a takagi sugeno fuzzy model with norm bounded uncertainties is used to represent the nonlinear plant attention is focused on the design of an energy to peak filter such that the filtering error system is asymptotically stable and the prescribed energy to peak filtering performance is guaranteed where the designed filter is assumed to have additive gain variations the proposed design is aimed at all filter matrices with gain variations which improves the existing results on resilient energy to peak filtering for continuous time systems a simulation example is provided to show the effectiveness of the proposed methods

a membership function dependent approach for stability analysis and controller synthesis of takagi sugeno models this paper presents a new approach for stability analysis and controller design of takagi sugeno ts models the analysis considers information derived from existing or induced order relations among the membership functions partitioning of the state space and the use of piecewise lyapunov functions pwlf arise naturally as a consequence of induced order relations conditions under the novel approach can be expressed as linear matrix inequalities lmis facilitating the inclusion of performance design examples are provided to show the advantages over the classical quadratic approach

membership function dependent stability analysis of fuzzy model based control systems using fuzzy lyapunov functions this paper investigates the stability of fuzzy model based fmb control system formed by a t s fuzzy model and a fuzzy controller connected in a close loop based on a fuzzy lyapunov function a general fmb control system that the t s fuzzy model and fuzzy controller not sharing the same premise membership functions and or the same number of fuzzy rules is considered a membership function dependent stability analysis approach is proposed to consider the membership functions of both the t s fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities as the stability conditions are membership function dependent they are dedicated to the fmb control system with the specified membership functions under consideration it is thus the membership function dependent stability conditions are more relaxed compared to the existing membership function independent stability conditions a fuzzy lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work in this paper this criterion is not required and thus the stability conditions can be further relaxed some simulation examples are given to demonstrate the merits of the proposed approach

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

an approach to observer design of continuous time takagi sugeno fuzzy model with bounded disturbances this paper addresses the problem of designing the observer for a class of nonlinear systems by using the t s takagi sugeno fuzzy model first two lemmas are obtained to demonstrate how to design the observer then based on the non quadratic lyapunov function a new method is proposed to locally stabilize the t s fuzzy system the new method can be applied to any t s models no matter whether the rules are even or odd naturally the new method is extended to get some lmis linear matrix inequalities to design the observer for practical reason the disturbances considered in this paper are bounded by magnitude and energy finally three examples are given to illustrate the effectiveness of the new approach

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods

the em algorithm for kernel matrix completion with auxiliary data in biological data it is often the case that observed data are available only for a subset of samples when a kernel matrix is derived from such data we have to leave the entries for unavailable samples as missing in this paper the missing entries are completed by exploiting an auxiliary kernel matrix derived from another information source the parametric model of kernel matrices is created as a set of spectral variants of the auxiliary kernel matrix and the missing entries are estimated by fitting this model to the existing entries for model fitting we adopt the em algorithm distinguished from the em algorithm of dempster et al 1977 based on the information geometry of positive definite matrices we will report promising results on bacteria clustering experiments using two marker sequences 16s and gyrb

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

spiral waves in reaction diffusion equations we consider the reaction diffusion system begin gathered r t nabla 2 r r left 1 r 2 vec nabla theta cdot vec nabla theta right hfill r theta t r nabla 2 theta 2 vec nabla r cdot vec nabla theta qr 3 hfill end gathered this system governs the solutions of reaction diffusion systems near a hopf bifurcation point in two spatial dimensions we use formal asymptotic expansions to contruct one armed and multi armed archimedean spiral waves for small values of the parameter q we then show that the one armed spiral waves are probably stable and the multi armed ones are unstable for q small next by numerical continuation methods we construct spiral waves for all q these calculations show that the one armed spiral waves are unstable when q 1 397 cdots we also find the explicit one dimensional analogues of spiral waves for all q and show that they are unstable for q small

new relaxed stability and stabilization conditions for continuous time t s fuzzy models this paper deals with the problems of stability and stabilization for continuous time takagi sugeno t s models by employing the order relation information of the membership functions mfs the transformation matrix and the pseudo mf vector are obtained the conventional continuous time t s fuzzy model is then transformed to a new compact t s model based on which relaxed stability and stabilization conditions are derived in the form of linear matrix inequalities an improved approach to constructing the transformation matrix is presented which could take full advantage of the order relation information of the mfs and further reduce the conservatism numerical examples are provided to illustrate the effectiveness of the proposed approach

on the interaction of spiral waves in non equilibrium media abstract we show that the asymptotic interaction of spirals in two dimensionally oscillating continuous media falls off exponentially and can be attractive as well as repulsive depending on the parameters of the system but not on the topological charges the exponent is in qualitative agreement with simulations for moderate distances the simulations show that spirals may form a stable bound state pairs with opposite topological charges drift with constant velocity and like charged spirals rotate around each other with constant frequency this is in contrast with the stationary non oscillating case where the interaction of vortices or dislocations is long range and monotonical and depends on topological charges

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

local stability analysis of continuous time takagi sugeno fuzzy systems a fuzzy lyapunov function approach this paper proposes a strategy to estimate invariant subsets of the domain of attraction da for asymptotically stable zero equilibrium points of continuous time takagi sugeno t s fuzzy systems specifically by using lyapunov s stability theory and the linear matrix inequality lmi technique sufficient conditions for proving the local stability are provided in terms of single parameter minimization problems subject to lmi constraints or eigenvalue problems which are solvable via convex optimizations the fuzzy lyapunov functions flfs expressed by the so called multi dimensional fuzzy summations are employed to characterize invariant subsets of the da as sublevel sets of the flfs to compute a larger inner estimate of the da an iterative lmi algorithm is also developed finally illustrative examples show the efficacy of the approach

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

brief paper approaches to extended non quadratic stability and stabilization conditions for discrete time takagi sugeno fuzzy systems this paper provides simple and effective linear matrix inequality lmi characterizations for the stability and stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this more general classes of non parallel distributed compensation non pdc control laws and non quadratic lyapunov functions are presented unlike the conventional non quadratic approaches using only current time normalized fuzzy weighting functions we consider not only the current time fuzzy weighting functions but also the l step past l 0 and one step ahead ones when constructing the control laws and lyapunov functions consequently by introducing additional decision variables it can be shown that the proposed conditions include the existing ones found in the literature as particular cases examples are given to demonstrate the effectiveness of the approaches

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

sliding mode fuzzy control for takagi sugeno fuzzy systems with bilinear consequent part subject to multiple constraints this paper investigated the multiple performance constrained sliding mode fuzzy control problem for continuous time stochastic nonlinear systems with multiplicative noises the stochastic nonlinear systems considered in this paper are represented by takagi sugeno t s fuzzy models with a bilinear consequent part to simultaneously satisfy stability passivity and variance constraints sufficient conditions are derived in terms of linear matrix inequalities based on lyapunov theory by solving the corresponding sufficient conditions a parallel distributed compensation based fuzzy controller is obtained to ensure the stability of the closed loop nonlinear systems subject to variance and passivity performance constraints the main contribution of this paper is a sliding mode fuzzy controller developed such that the considered multiple performance constraints can be satisfied for the t s fuzzy systems with a bilinear consequent part finally a numerical example for controlling a ship steering system is provided to demonstrate the validity and effectiveness of the proposed sliding mode fuzzy control method

positive semidefinite metric learning using boosting like algorithms the success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data it is often beneficial to learn such a metric from the input training data instead of using a default one such as the euclidean distance in this work we propose a boosting based technique termed boostmetric for learning a quadratic mahalanobis distance metric learning a valid mahalanobis distance metric requires enforcing the constraint that the matrix parameter to the metric remains positive semidefinite semidefinite programming is often used to enforce this constraint but does not scale well and is not easy to implement boostmetric is instead based on the observation that any positive semidefinite matrix can be decomposed into a linear combination of trace one rank one matrices boostmetric thus uses rank one positive semidefinite matrices as weak learners within an efficient and scalable boosting based learning process the resulting methods are easy to implement efficient and can accommodate various types of constraints we extend traditional boosting algorithms in that its weak learner is a positive semidefinite matrix with trace and rank being one rather than a classifier or regressor experiments on various data sets demonstrate that the proposed algorithms compare favorably to those state of the art methods in terms of classification accuracy and running time

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

finite time synchronization of sampled data t s fuzzy complex dynamical networks subject to average dwell time approach abstract the problem of finite time synchronization for takagi sugeno t s fuzzy complex dynamical networks with coupling delays via sampled data control is presented in this paper to change the sampled data control system into a continuous time delayed system an input delay approach is applied based on the lyapunov stability theory a suitable lyapunov krasovskii functional lkf is constructed with the kronecker products furthermore by applying the average dwell time approach a novel sufficient condition is established to ascertain the finite time stabilization of fuzzy complex dynamical networks cdns with switching signals the proposed method is less conservative than conventional approaches since the newly developed time dependent fuzzy lkf is used the proposed sufficient condition can be represented in the form of linear matrix inequalities lmis finally the effectiveness and superiority of the proposed approach is validated through both numerical and practical examples

a kernel approach for semisupervised metric learning while distance function learning for supervised learning tasks has a long history extending it to learning tasks with weaker supervisory information has only been studied recently in particular some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information in this paper we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach the metric learning problem is thus formulated as an optimization problem for kernel learning an attractive property of the optimization problem is that it is convex and hence has no local optima while a closed form solution exists for the first special case the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically experimental results based on both synthetic and real world data show that this new kernel approach is promising for nonlinear metric learning

stability region analysis using polynomial and composite polynomial lyapunov functions and sum of squares programming we propose using bilinear sum of squares programming for obtaining inner bounds of roas for dynamical systems with polynomial vector fields we search for polynomial as well as composite lyapunov functions comprised of pointwise maximums of polynomial functions results for several examples from the literature are presented using the proposed methods and the penbmi solver

regression on fixed rank positive semidefinite matrices a riemannian approach the paper addresses the problem of learning a regression model parameterized by a fixed rank positive semidefinite matrix the focus is on the nonlinear nature of the search space and on scalability to high dimensional problems the mathematical developments rely on the theory of gradient descent algorithms adapted to the riemannian geometry that underlies the set of fixed rank positive semidefinite matrices in contrast with previous contributions in the literature no restrictions are imposed on the range space of the learned matrix the resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties we apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix good performance is observed on classical benchmarks

nonquadratic stabilization of continuous t s fuzzy models lmi solution for a local approach this paper is concerned with nonquadratic stabilization design problem for continuous time nonlinear models in the takagi sugeno t s form obtained by sector nonlinearity approach most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function by changing the paradigm of global stabilization for something less restrictive a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper it is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous nonquadratic attempts moreover conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities lmis which can be efficiently solved by convex optimization techniques simulation examples are given to demonstrate the validity and applicability of the proposed approaches

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

metric and kernel learning using a linear transformation metric and kernel learning arise in several machine learning applications however most existing metric learning algorithms are limited to learning metrics over low dimensional data while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points in this paper we study the connections between metric learning and kernel learning that arise when studying metric learning as a linear transformation learning problem in particular we propose a general optimization framework for learning metrics via linear transformations and analyze in detail a special case of our framework that of minimizing the logdet divergence subject to linear constraints we then propose a general regularized framework for learning a kernel matrix and show it to be equivalent to our metric learning framework our theoretical connections between metric and kernel learning have two main consequences 1 the learned kernel matrix parameterizes a linear transformation kernel function and can be applied inductively to new data points 2 our result yields a constructive method for kernelizing most existing mahalanobis metric learning formulations we demonstrate our learning approach by applying it to large scale real world problems in computer vision text mining and semi supervised kernel dimensionality reduction

further theoretical justification of the k samples variation approach for discrete time takagi sugeno fuzzy systems the recently developed k samples variation approach is known as a powerful way to reduce the conservativeness of existing stability and stabilization conditions for discrete time takagi sugeno t s fuzzy systems in this approach the lyapunov functions under consideration are not necessarily decreasing at every sample but are allowed to decrease every k samples which is evidently less restrictive than classical approaches consequently less conservative linear matrix inequality lmi conditions were derived in addition it was proved that for two positive integers k1 and k2 if the condition for k k1 is fulfilled then those corresponding to k k2 are also satisfied when k2 is the divisor of k1 in this letter we prove that if the condition for k k2 admits a solution then those corresponding to any k k2 are also solvable