Showing papers in "Kybernetika in 1996"

On a class of perimeter-type distances of probability distributions.

Abstract: The class If , p G ( l ,oo] , of /-divergences investigated in this paper generalizes an /-divergence introduced by the author in [9] and applied there and by Reschenhofer and Bomze [11] in different areas of hypotheses testing. The main result of the present paper ensures that, for every p € (1, oo), the square root of the corresponding divergence defines a distance on the set of probability distributions. Thus it generalizes the respecting statement for p = 2 made in connection with Example 4 by Kafka, Osterreicher and Vincze in [6]. From the former literature on the subject the maximal powers of /-divergences defining a distance are known for the subsequent classes. For the class of Hellinger-divergences given in terms of p\u) = 1 + u — (u -\-u~) , s £ (0,1) , already Csiszar and Fischer [3] have shown that the maximal power is min(s, 1 — s). For the following two classes the maximal power coincides with their parameter. The class given in terms of f(a)(u) = | l — u \ , a € (0,1], was investigated by Boekee [2]. The previous class and this one have the special case s = a = \ in common. This famous case is attributed to Matusita [8]. The class given by

Kalman filter sensitivity with respect to parametric noises uncertainty

Abstract: The influence of the noises uncertainty on the Kalman filter performance is characterized by sensitivity functions. Relationships for computing these functions are derived and used both for synthesizing a Kalman filter with reduced sensitivity (KFRS) and a self-tuning Kalman filter (SKF). The results are illustrated by examples.

On the Morgan problem with stability

Abstract: where the polynomial matrices Ni(s) and D(s) form a normal external description (NED) of (C, A H ) ; see [11]. The matrices N(s) := CNx(s) and D(s) then form, not necessarily coprime, a matrix fraction description (MFD) of (C,A,B). Recall that Ni(s) and D(s) are right coprime with D(s) being column reduced. The column degrees, Cj := degciD(s), i = 1,2,... ,m, are the controllability indices of (C, A, B). We shall further assume (see [8] for more details) that V* = TV, where TV denotes the maximal controllability subspace lying in Ker C and V* is the maximal (A,B)invariant subspace contained in Ker C.

Optimization of dynamical systems.

Abstract: Consider an optimization problem where the objective function is an integral contain­ ing the solution of a system of ordinary differential equations. Suppose we have efficient optimization methods available as well as efficient methods for initial value problems for ordinary differential equations. The main purpose of this paper is to show how these methods can be efficiently applied to a considered problem. First, the general procedures for the evaluation of gradients and Hessian matrices are described. Furthermore, the new efficient Gauss-Newton-like approximation of the Hessian matrix is derived for the special case when the objective function is an integral of squares. This approximation is used for deriving the Gauss-Newton-like trust region method, with which global and superlinear convergence properties are proved. Finally several optimization methods are proposed and computational experiments illustrating their efficiency are shown.

Decoupling in singular systems: a polynomial equation approach

Abstract: In this paper, the row by row decoupling problem by static state feedback is studied for regularizable singular square systems. The problem is handled in matrix polynomial equation setting. The necessary and sufficient conditions on decouplabilit y are introduced and an algorithm for calculation of feedback gains is presented. A structural interpretation is also given for decoupled systems.

Explicit conditions for ripple-free dead-beat control

Abstract: A generalized and systematic approach to the problem of dead-beat response to polyno­ mial time-domain inputs is presented Necessary and sufficient conditions for the impulse response coefficients of the system, in the form of a set of linear equations, are derived For the case of minimum prototype systems, a formula for the explicit computation of the overall pulse transfer function of the system is deduced and their properties are fur­ ther studied, together with their ability to track complex inputs It is also presented an analytical study of the system's control sequence, which plays an important role for the inter sample activity of the plant By eliminating possible oscillations that may be present in this sequence, necessary and sufficient conditions for ripple-free dead-beat response are derived

One method for robust control of uncertain systems: theory and practice

Abstract: We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov stability theory. The uncertainties, which are deterministic, are characterized by certain structural conditions and known as well as unknown bounds. As a consequence of the Lyapunov approach, the methodology is not restricted to linear or time-invariant systems. The robustness of these controllers in the presence of singular perturbations is considered. The situation in which the full state of the system is not available for measurement is also considered as are other generalizations. Applications of the proposed discussed in the complete version of the paper.

An empirical investigation of Cressie and Read tests for the hypothesis of independence in three-way contingency tables

Abstract: This paper is concerned with comparison of Cressie and Read tests for the hypothesis of independence in three-way contingency tables. A Monte Carlo study is done to empirically compare the power of some members of the family of these tests under various spike alternatives.

Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems

Abstract: New parallel algorithms for solving initial and boundary value problems for linear ODEs and their systems on large parallel MIMD computers are proposed. The proposed algorithms are based on dividing a problem in similar so-called local problems, which can be solved independently and in parallel using any known (sequential or parallel) method. The solution is then built as a linear combination of the local solutions. The recurrence relationships (for the case of non-homogeneo us equations) and explicit expressions (for the case of homogeneous equations) for the coefficients of that linear com­ bination are obtained. Three elementary examples, illustrating the idea of the proposed approach, are given. The majority of parallel algorithms were developed for solving algebraic problems and boundary value problems for partial differential equations (PDEs). With the exception of the parallelization of methods of the Runge-Kutta type and their modi­ fications, almost no attention was paid to the development of parallel algorithms for ordinary differential equations (ODEs), and the available literature reflects this state [l]-[5]. However, not every parallel algorithm for solving PDEs is applicable for solving ODEs. Some new parallel algorithms for solving initial and boundary value problems for linear ODEs and their systems are described and illustrated in this paper. The proposed approach is based on two main ideas. 1. The first idea is that, in fact, we always deal with finite intervals when we look for the numerical solution of any initial value problem. Even when the given interval (in the formulation of a problem) is infinite, we can obtain the numerical solution of a problem only for the finite subinterval of the given original infinite interval. So it seems to be natural to apply numerical methods directly to the finite (sub)interval of the researcher's interest.

Balancing of systems with periodic jumps.

Abstract: In this paper we study the balancing and model-reduction of linear systems with discrete jumps at periodic time instants. These systems arise in the study of linear systems with sampled data control and filtering problems. We study the balancing for the case of fixed and infinite intervals. We show that the system balancing can be used to obtain a reduced order-model of the system with the properties of the original system. An example is provided to illustrate the procedure.

On a method of estimating parameters in non-negative ARMA models

Abstract: The purpose of this paper is to introduce a method of estimating parameters in nonnegative ARMA processes. The method is a generalization of the procedures which were derived for autoregressive and moving-average processes. The estimates are constructed in the form of minima of certain fractions or some functions of these minima. A theorem concerning the strong consistence of these estimates is proved and its applications to the models ARMA(1,1), ARMA(2,1) and ARMA(p,l), p > 2 are demonstrated.

Inverse updated systolic RLS algorithm with regularized exponential forgetting

Abstract: A systolic algorithm for the Recursive Least Squares identification with covariance up­ date, using the block-accumulated regularization mechanism to increase numerical stability of the algorithm with respect to weakly informative data, is presented. The advantages over standard sequential implementation are that the sampling period of estimator is sig­ nificantly reduced even with the robustifying modification of algorithm and that it is made independent of order of the identified system.

An extension of the root perturbation $m$-dimensional polynomial factorization method

Abstract: In this paper, an extension of an m-D (multidimensional or multivariable) polynomial factorization method is investigated. The method is the \"root perturbation method\" which is recently proposed by the author. According to this method, one sets to zero all complex variables, except one variable, and factorizes the 1-D polynomial. Furthermore, the values of these variables vary properly. In this way, one can \"built\" the m-dimensional polynomial in its factorized form. However, in the \"root perturbation method\", an assumption is that the 1-D polynomial must have discrete roots. In this paper, a solution is given in the case that the 1-D polynomial may have multiple roots. This is achieved by a proper transformation of the complex variables. The present method is summarized by way of algorithm. A numerical (3-D) example is presented.

A computational method for reduced-order observers in linear systems.

Abstract: A Computationally stable method for reduced-order observers of linear systems is proposed. This method is based on orthogonal transformations and adopts Diophantine matrix polynomial equations

The invariant polynomial assignment problem for linear periodic discrete-time systems.

Abstract: Various classes of processes, such as periodically time-varying networks and filters (for example switched-capacitors circuits and multirate digital filters), chemical processes, multirate sampled-data systems, can be modeled through a linear periodic system (see, e. g., [2, 13] and references therein). Moreover, the study of linear periodic systems can be helpful even for the stabilization and control of time-invariant linear systems through a periodic controller [1, 8, 18, 19, 21, 27], and for the stabilization and control of a class of bilinear systems [10, 11, 12]. In the discrete-time case, a control theory is developing with the help of algebraic and geometric techniques and contributions on several control problem have been given, including eigenvalue assignment, state and output dead-beat control, disturbance decoupling, model matching, adaptive control, robust control and optimal H2/H∞ control (see, e. g., [3, 5, 7, 13, 15, 17, 22, 25, 26]). The aim of this paper is to analyze the invariant polynomial assignment problem for the class of discrete-time linear periodic systems. This problem generalizes the characteristic polynomial assignment, which, for the same class of systems, was solved by a geometric approach in [5, 15, 17, 22]. For time-invariant plants, the invariant polynomial assignment was considered in [19, 20, 23, 27]. The paper is organized in the following way. In Section 2 preliminary definitions and results are given. The problem considered in this paper is formally stated in Section 3, and conditions for its solvability are constructively established in Section 4.