some sufficient conditions for the solvability of inverse eigenvalue problems abstract sufficient conditions for the solvability of additive and multiplicative inverse eigenvalue problems for hermitian matrices are considered the notion of majorization cauchy poincare interlacing inequalities and brouwer s fixed point theorem are applied

backward errors for the inverse eigenvalue problem backward errors for the symmetric matrix inverse eigenvalue problem with respect to an approximate solution are defined and explicit expressions of the backward errors are derived the expressions may be useful for testing the stability of practical algorithms

a note on the backward errors for hermite eigenvalue problems we discuss the backward error analysis of the hermite eigenproblems three kinds of problems are included generalized eigenproblem matrix polynomial eigenproblem and multiparameter eigenproblem in the case of the approximate eigenvalue being real these problems have already been solved by higham and higham siam j matrix anal 20 1998 493 tisseur lin alg appl 309 2002 339 and hachstenbach and plestenjak lin alg appl 375 2003 63 this note as a complement of their results considers the complex case

on the unsolvability of inverse eigenvalues problems almost everywhere abstract using sard s theorem we show that the inverse eigenvalue problems are unsolvable almost everywhere if too many of the eigenvalues are equal

stability of nonlinear elliptic systems with distributed parameters and variable boundary data in this paper nonlinear partial differential equations of the elliptic type with the dirichlet boundary data are investigated some sufficient conditions under which the solutions of considered equations depend continuously on parameters and boundary conditions are proved the proofs of main results are based on variational methods in the final part of the paper we give a short survey of the results and methods related to the question of stability of the boundary value problems

optimal control of harvesting in a nonlinear elliptic system arising from population dynamics the aim of this article is to study an optimal control problem for a system of nonlinear elliptic equations with dirichlet boundary conditions u x a x x c x u x eu x u x x x 1 1 x b x u x d x x f x u x x x u x x 0 on 1 2 the authors were supported in part by cicyt ministry of education and culture spain under grant pb98 1343 by junta de andalucia fqm116 and by eec contract human capital and mobility program erbchrxct 940494 also they thank o arino for suggesting the study of this control problem

self tuning regulators with explicit variance restrictions self tuning regulators with on line adaptation of the weights in a quadratic loss function are considered the criterion for control is to minimize the variances of one or several process variables design constraints are taken into account by introducing explicit state and input variance restrictions the algorithm solves the necessary optimality conditions of the variance constrained optimal control problem using a stochastic approximation method a particularly simple algorithm is obtained if the control is based on a single step loss function an example taken from multivariate cement kiln control shows however that there are practical situations when it is necessary to use a more complex algorithm which requires the on line solution of a riccati equation

stationary performance of linear stochastic systems under single step optimal control linear quadratic optimal control with finite time horizon is considered for the case of penalties on the squared inputs and outputs the relative weighting of these penalties is treated as a design parameter it is shown that for positive real systems the stationary variances of the input and the output vary monotonically with this design parameter

on the local convergence of an iterative approach for inverse singular value problems the purpose of this paper is to provide the convergence theory for the iterative approach given by m t chu numerical methods for inverse singular value problems siam j numer anal 29 1992 pp 885 903 in the context of solving inverse singular value problems we provide a detailed convergence analysis and show that the ultimate rate of convergence is quadratic in the root sense numerical results which confirm our theory are presented it is still an open issue to prove that the method is q quadratic convergent as claimed by m t chu

numerical methods for inverse singular value problems3 two numerical methods one continuous and the other discrete are proposed for solving inverse singular value problems the first method consists of solving an ordinary differential equation obtained from an explicit calculation of the projected gradient of a certain objective function the second method generalizes an iterative process proposed originally by friedland nocedal and overton siam j numer anal 24 1987 pp 634 667 for solving inverse eigenvalue problems with the geometry understood from the first method it is shown that the second method also the method proposed by friedland nocedal and overton for inverse eigenvalue problems is a variation of the newton method while the continuous method is expected to converge globally at a slower rate in finding a stationary point of the objective function the discrete method is proved to converge locally at a quadratic rate if there is a solution some numerical examples are presented

paper self tuning control of nonminimum phase systems the instability that arises from the pole zero cancellation of elementary self tuners and most mrac algorithms has given rise to a misapprehension that nonminimum phase systems can pose insoluble problems with the application of adaptive control since most practical processes exhibit some form of nonminimum phase behaviour particularly when controlled digitally this appeared to restrict the usefulness of self tuning methods however during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials the paper describes the practical features that a self tuning controller must possess and discusses how plant dead time and excess continuous time poles can lead to discrete time nonminimum phase zeros the source of instability of elementary self tuners is analysed and various suggested approaches for overcoming this problem are reviewed these include the use of a generalized minimum variance cost function incorporating control weighting factorization methods which avoid cancellation of the offending zeros adaptive control based on state space linear quadratic gaussian lqg theory and explicit pole placement via solution of a diophantine or bezoutian equation gawthrop s hybrid controller which avoids those nonminimum phase zeros due to continuous time pole excess is briefly discussed a series of simulations in which a nonminimum phase plant is subjected to a pattern of set point changes is presented to show some of the features of the algorithms in applications the order of the process is unlikely to be known or indeed be finite the pole placement algorithm which is particularly effective in the known order case is shown to lack robustness to underspecified order the use of a large control weighting however restores stability to the generalized minimum variance controller the conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum phase processes

stability in semilinear problems abstract in the paper we derive results concerning a continuous dependence of solutions on the right hand side for a semilinear operator equation lu g u by assuming that l d l h h h a hilbert space is self adjont with a closed range and g h r is continuous convex on h and g teaux differentiable on d l using these results we obtain theorems on the continuous dependence of solutions on functional parameters for a semilinear problem of the second order u au d u f t u t 0 a e with the dirichlet boundary conditions u 0 u 0 where a 1 and is a functional parameter

sufficient conditions for the solvability of an algebraic inverse eigenvalue problem abstract let a a1 a2 an be given n n hermitian matrices and 1 2 n be given real numbers we present new sufficient conditions under which there exist real numbers c1 c2 cn such that the matrix a nt 1 ctat has eigenvalues 1 2 n

sufficient conditions for the solubility of inverse eigenvalue problems abstract we define an inverse eigenvalue problem which contains as special cases the classical additive and multiplicative inverse eigenvalue problems using some results on the distance of eigenvalues from matrix diagonal elements and brouwer s fixed point theorem we give sufficient conditions for the solubility of the problem

a backward error for the inverse singular value problem a backward error for inverse singular value problems with respect to an approximate solution is defined and an explicit expression for the backward error is derived by extending the approach described in j g sun backward errors for the inverse eigenvalue problem numer math 82 1999 339 349 the expression may be useful for testing the stability of practical algorithms

brief paper variance constrained self tuning control a self tuning regulator for a variance constrained optimal control problem is given the criterion for control is to minimize the stationary variance of the output in the cases when the regulator which gives minimum variance requires too large control signals an inequality constraint on the input variance is introduced in practice it is easier to select a constraint on the variance of the input than to choose the relative weights in a quadratic loss function the self tuning regulator applies the robbins monro scheme to adjust the lagrange multiplier of the variance constrained control problem the behaviour of the algorithm is illustrated by a simulated example the asymptotic behaviour of the regulator is studied using a set of associated ordinary differential equations

existence of optimal controls via continuous dependence on parameters abstract we consider a system of elliptic equations and derive sufficient conditions for solutions of the system to depend continuously on parameters these conditions are employed to obtain an existence result for an optimal control problem

an algorithm for symmetric generalized inverse eigenvalue problems abstract using qr like decomposition with column pivoting and least squares techniques we propose a new and efficient algorithm for solving symmetric generalized inverse eigenvalue problems and give its locally quadratic convergence analysis we also present some numerical experiments which illustrate the behaviour of our algorithm

adaptive predictive control with mean square input constraint abstract convergence properties of a self tuning regulator incorporating an input mean square constraint are studied an algorithm derived from the long range controller musmar is considered for this algorithm using the ode method for analysing stochastic recursive algorithms and singularly perturbed ode theory a local convergence result is proved this result characterizes possible convergence points of the algorithm as the constrained minima of the underlying steady state quadratic cost the actual convergence of the algorithm to the possible equilibrium points predicted by theory is verified by means of simulation examples including unmodelled plant dynamics

a backward error for the symmetric generalized inverse eigenvalue problem abstract in this paper we discuss the backward error for the symmetric generalized inverse eigenvalue problem which extends the result of sun 1999 10 the optimal backward error is defined for symmetric generalized inverse eigenvalue problem with respect to an approximate solution and the upper and lower bounds are derived for the optimal backward error the expressions may be useful for testing the stability of practical algorithms

inexact newton methods for inverse eigenvalue problems in this paper we survey some of the latest development in using inexact newton methods for solving inverse eigenvalue problems these methods require the solutions of nonsymmetric and large linear systems i e the large jacobian equations one can solve these systems by iterative methods inner iterations however iterative methods usually oversolve the problem in the sense that they require far more inner iterations than is required for the convergence of the newton outer iterations the inexact methods can avoid the oversolving problem and hence improve the efficiency the convergence rate of the inexact methods are superlinear and a good tradeoff between the required inner and outer iterations can be obtained

on solvability of inverse eigenvalue problems with hermitian matrices abstract taking advantages of krylov bogoljubov and weinstein s and temple s theories and schur s majorization theorem we present new sufficient conditions for the solvability of multiplicative inverse eigenvalue problems and so called generalized inverse eigenvalue problems with hermitian matrices

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations