identification of physical parameters in structures systems abstract linear time invariant systems with a limited number of unknowns corresponding to physical component values often exhibit certain structural conditions on the way in which these values appear in the transfer functions in this paper the problem of identifying these unknowns is considered the structure translates to an associated identification problem which is multilinear in the unknowns this is exploited in the design of two algorithms which use measurements of input and output and knowledge of the polynomial coefficients of the multilinear combinations of the system parameters conditions are established for the uniform asymptotic stability of these algorithms

a regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its l norm the i th singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one we show that near a local maximum however the largest singular value has a lipschitz second derivative but need not have a third derivative using this regularity result we give a quadratically convergent algorithm for computing the l norm of a transfer matrix

unified convergence results on a minimax algorithm for finding multiple critical points in banach spaces a minimax method for finding multiple critical points in banach spaces is successfully developed in x yao and j zhou siam j sci comput 26 2005 pp 1796 1809 by using a projected pseudogradient as a search direction since several different techniques can be used to compute a projected pseudogradient the uniform stepsize and the continuity of a search direction two key properties for the convergence results in y li and j zhou siam j sci comput 24 2002 pp 865 885 get lost in this paper instead of proving convergence results of the algorithm for each technique unified convergence results are obtained with a weaker stepsize assumption an abstract existence convergence result is also established it is independent of the algorithm and explains why function values always converge faster than their gradients do the weaker stepsize assumption is then verified for several different cases as an illustration to the new results the banach space w 0 1 p omega is considered and the conditions posed in the new results are verified for a quasi linear elliptic pde

characterization and construction of the nearest defective matrix via coalescence of pseudospectral components let a be a matrix with distinct eigenvalues and let w a be the distance from a to the set of defective matrices using either the 2norm or the frobenius norm define the pseudospectrum of a to be the set of points in the complex plane which are eigenvalues of matrices a e with kek and let c a be the supremum of all with the property that has n distinct components demmel and wilkinson independently observed in the 1980s that w a c a and equality was established for the 2 norm by alam and bora in 2005 we give new results on the geometry of the pseudospectrum near points

a graphical characterization of structurally controllable linear systems with dependent parameters one version of the concept of structural controllability defined for single input systems by lin and subsequently generalized to multi input systems by others states that a parameterized matrix pair a b whose nonzero entries are distinct parameters is structurally controllable if values can be assigned to the parameters that cause the resulting matrix pair to be controllable in this paper the concept of structural controllability is broadened to allow for the possibility that a parameter may appear in more than one location in the pair a b subject to a certain condition on the parameterization called the binary assumption an explicit graph theoretic characterization of such matrix pairs is derived

identification of linearly overparametrized nonlinear systems often a dynamical model is nonlinear in the unknown parameters but it can be transformed into an overparametrized linear regression model where the components of the overparametrization vector are nonlinear functions of the smaller number of unknown parameters an algorithm that directly identifies the unknown parameters is presented and the authors characterize the convergence domains under two different sets of assumptions on the excitation of the signals the corresponding convergence rates are computed

robust stability of polynomials with multilinear parameter dependence abstract the problem is studied of testing for stability a class of real polynomials in which the coefficients depend on a number of variable parameters in a multilinear way we show that the testing for real unstable roots can be achieved by examining the stability of a finite number of corner polynomials obtained by setting parameters at their extreme values while checking for unstable complex roots normally involves examining the real solutions of up to m 1 simultaneous polynomial equations where m is the number of parameters when m 2 this is an especially simple task

a formula for the 2 norm distance from a matrix to the set of matrices with multiple eigenvalues we prove that the 2 norm distance from an n times n matrix a to the matrices that have a multiple eigenvalue lambda is equal to where the singular values sigma k are ordered nonincreasingly therefore the 2 norm distance from a to the set of matrices with multiple eigenvalues is

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

strong stabilizability of systems with multiaffine uncertainties and numerator denominator coupling this paper considers a set of proper transfer functions whose numerator and denominator polynomial coefficients display dependent multiaffine parametric uncertainties it is shown that provided no member transfer function has positive real pole zero cancellations all members satisfy the parity interlacing property iff all corner members do the same notice that while this implies that each member is strongly stabilizable it does not imply the existence of a single stable controller that stabilizes the whole set the paper also shows that whenever the numerator and denominator polynomials lie in dependent polytopes the task of verifying the absence of positive real pole zero cancellations can be accomplished by checking the edges

spectral conditioning and pseudospectral growth using the language of pseudospectra we study the behavior of matrix eigenvalues under two scales of matrix perturbation first we relate lidskii s analysis of small perturbations to a recent result of karow on the growth rate of pseudospectra then considering larger perturbations we follow recent work of alam and bora in characterizing the distance from a given matrix to the set of matrices with multiple eigenvalues in terms of the number of connected components of pseudospectra

persistence of excitation conditions for partially known systems abstract this note derives persistence of excitation conditions on the input for systems with partially known transfer functions the assumed transfer function model is p 0 s k t p s q 0 s k t q s where k is the unknown parameter vector p 0 s q 0 s are known scalar polynomials and p s and q s are known vector polynomials

an indirect prediction error method for system identification abstract a new form of prediction error method pem is developed it is applicable to the case where the model structure of interest can be imbedded in a larger model structure whose estimation is relatively easy an optimal way of reducing the larger model to the smaller model structure is presented and various interpretations of this reduction are given the proposed method will have the same asymptotic statistical properties as the standard pem but it can be implemented by a more efficient algorithm the properties of the method are illustrated by the means of some simulated examples

a local minimax characterization for computing multiple nonsmooth saddle critical points this paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design most characterizations for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax problems thus they are not helpful for numerical algorithm design inspired by the results on computational theory and methods for finding multiple smooth saddle critical points in 14 15 19 21 23 a local minimax characterization for multiple nonsmooth saddle critical points in either a hilbert space or a reflexive banach space is established in this paper to provide a mathematical justification for numerical algorithm design a local minimax algorithm for computing multiple nonsmooth saddle critical points is presented by its flow chart

a minimax method for finding multiple critical points and its applications to semilinear pdes most minimax theorems in critical point theory require one to solve a two level global optimization problem and therefore are not for algorithm implementation the objective of this research is to develop numerical algorithms and corresponding mathematical theory for finding multiple saddle points in a stable way in this paper inspired by the numerical works of choi mckenna and ding costa chen and the idea to define a solution submanifold some local minimax theorems are established which require us to solve only a two level local optimization problem based on the local theory a new local numerical minimax method for finding multiple saddle points is developed the local theory is applied and the numerical method is implemented successfully to solve a class of semilinear elliptic boundary value problems for multiple solutions on some nonconvex non star shaped and multiconnected domains numerical solutions are illustrated by their graphics for visualization in a subsequent paper y li and j zhou convergence results of a minimax method for finding critical points in review we establish some convergence results for the algorithm

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

level set methods for finding critical points of mountain pass type abstract computing mountain passes is a standard way of finding critical points we describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case we apply these techniques to describe a strategy for addressing the wilkinson problem of calculating the distance from a matrix to a closest matrix with repeated eigenvalues finally we relate critical points of mountain pass type to nonsmooth and metric critical point theory

estimation of the persistence of strain from experimental recordings from cardiac tissue abstract the persistence of strain 2 has been ported from fluid mechanics into nonlinear dynamics as a measure of the geometry of attracting sets that reflects both stretching sensitivity to initial conditions and folding we outline a method for estimating 2 from experimental time series and apply it to electrical and mechanical signals recorded from the surface of the heart during experimentally induced ventricular fibrillation

constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems a new numerical algorithm for solving semilinear elliptic problems is presented a variational formulation is used and critical points of a c1 functional subject to a constraint given by a level set of another c1 functional or an intersection of such level sets of finitely many functionals are sought first constrained local minima are looked for then constrained mountain pass points the approach is based on the deformation lemma and the mountain pass theorem in a constrained setting several examples are given showing new numerical solutions in various applications

physically based parameterizations for designing adaptive algorithms abstract structural properties are examined of systems with physical component values as parameters both state variable realizations and transfer function descriptions are investigated the transfer functions in particular are shown to be the ratios of polynomials with coefficients multilinear in the parameters these structures prove useful in formulating adaptive algorithms

computation of the frequency response of systems with uncertain parameters a simplification abstract computation of all possible frequency responses of a linear system that depends on m uncertain parameters is the subject of this paper using a brute force approach this computation could be carried out using an m l dimensional parameter sweep i e there is the usual frequency sweep plus one sweep for each uncertain parameter a much simpler computational alternative is possible if the uncertain system s transfer function has a linear dependence on the parameters and if the set of possible parameter values has a polytopic structure for this class of uncertain systems it has previously been shown that for a single fixed frequency all possible responses can be determined using several 1 dimensional sweeps thus for a range of frequencies the obvious extension would involve several 2 dimensional sweeps however this obvious extension is not the simplest way to carry out the computation indeed this paper will show that all possible responses for a range of frequencies can be determined

observer based parameter identifiers for nonlinear systems with parameter dependencies a class of nonlinear dynamical systems whose dynamics depend linearly on the unknown parameter vector is considered after reviewing a standard observer based identifier for estimating the unknown parameters we propose a family of new identifiers which exploit the a priori known parameter dependencies we then establish under mild assumptions on the dynamical system that 1 the proposed identifiers are stable and 2 the weighted norm of state parameter errors using the proposed identifiers are less than the corresponding errors using the standard identifier for a length of time after t 0 the main contribution of this paper is that it introduces a family of observer based identifiers which exhibit better transient performance than the standard identifier

convergence results of a local minimax method for finding multiple critical points in y li and j zhou siam j sci comput 23 2001 pp 840 865 a new local minimax method that characterizes a saddle point as a solution to a local minimax problem was established based on the local characterization a numerical minimax algorithm was designed for finding multiple saddle points numerical computations of many examples in semilinear elliptic pde were successfully carried out to solve for multiple solutions one of the important issues which remains unsolved is the convergence of the numerical minimax method in this paper first step 5 in the algorithm is modified with the design of a new stepsize rule that is easier to implement practically and with which convergence results of the numerical minimax method are established for isolated and nonisolated critical points the convergence results show that the algorithm indeed exceeds the scope of a minimax principle in the last section numerical multiple solutions to the henon equation and a sublinear elliptic equation subject to zero dirichlet boundary condition are presented to show their numerical convergence and profiles

on sensitivity of eigenvalues and eigendecompositions of matrices abstract the main purpose of this paper is to provide solutions of two problems on sensitivity of eigenvalues and eigendecompositions of matrices the first problem is due to wilkinson and it concerns finding the distance from an n n matrix with n distinct eigenvalues to the set of matrices having multiple eigenvalues we also describe how to construct a nearest matrix having a multiple eigenvalue the second problem concerns providing a characterization of the stability of eigendecompositions of matrices and is due to demmel

vertex results for the steady state analysis of uncertain systems it is shown that if a system is robustly stable and if the dependence on the uncertain parameters is to an extent multiaffine then the extreme values of the steady state response over the entire set of parameters is equal to the extreme values over just the vertices of the parameter set this vertex result is doubly useful because it is valid in both continuous time and discrete time

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

a high linking algorithm for sign changing solutions of semilinear elliptic equations where n is a bounded domain with regular boundary the operator can be replaced by a more general second order uniformly elliptical operator in divergence form the solutions we are interested in nding are of minimax type and sign changing nonlinear elliptic equations of type 1 1 arise naturally in physics engineering and mathematical biology it is known that many such equations have multiple solutions their study has attracted the attention of many pure and applied mathematicians during the past two decades let us assume that f satis es the following regularity and growth conditions a1 f x t is locally lipschitz continuous in