Wyniki wyszukiwania - BazTech

1

On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems

Vardulakis A. I. G., Karampetakis N. P., Antoniou E. N., Tictopoulou E.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 1

77-88

EN

We review the realization theory of polynomial (transfer function) matrices via 'pure' generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is defined and the mechanism of the 'cancellations' of 'decoupling zeros at infinity' is closely examined. The difference between the concepts of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts of dynamic and non-dynamic variables appearing in generalized state space realizations are also examined.

2

On schweizer-smital chaos

Pikula R.

Prace Naukowe Instytutu Matematyki Politechniki Wrocławskiej. Konferencje

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2001

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Vol. 24, nr 3

77-84

EN

It is shown that a minimal dynamical system chaotic in the sense of Schweizer-Smital may be monoergodic and have zero topological entropy. This paper provides also an example of system chaotic in the sense of Schweizer-Smital whose dynamics is very simple.

3

Optimality conditions and a classification of duality schemes in vector optimization

El Ghali B.

Control and Cybernetics

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2000

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Vol. 29, no 4

839-860

EN

Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x[0] belongs to A, w[0] belongs to Fx[0] such that w[0] is minimal in FA. To a family of vector minimization problems minimize[x belongs to X] F(x, y), y [belongs to] Y, one associates a Lagrange relation [L(x, [xi], y[0]) = union of sets y belongs to Y(F(x, y)-xi(y)+(y[0]))] where [xi] belongs to an arbitrary class [Xi] of mappings. For this type of problem, there exist several notions of solutions. Some useful characterizations of existential solutions are established and, consequently, some necessary conditions of optimality are derived. One result of intermediate duality is proved with the aid of the scalarization theory. Existence theorems for existential solutions are given and a comparison of several exact duality schemes is established, more precisely in the convex case it is shown that the majority of exact duality schemes can be obtained from one result of S. Dolecki and C. Malivert.

4

Effective tests for minimality in reduct generation

Susmaga R.

Foundations of Computing and Decision Sciences

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1998

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Vol. 23, No. 4

219-240

EN

The paper addresses the problem of checking for inclusion minimality in attribute reduction. Reduction of attributes information/decision tables is an important aspect of table analysis where so called reducts of attributes may successfully be applied. The reducts, however, are hard to generate because of high theoretical complexity of the problem. Especially difficult is the generation of all exact reducts for a given data set. This paper reports on a series of experiments with some advariced algorithms that allow to generate all reducts. Particular attention is paid to a family of algorithms based on the notion of discernibility matrix. The heaviest computing load of these algorithms lies in testing for minimality with regard to inclusion. The paper introduces a new minimality test that makes the algorithms even more effective. All the presented tests are evaluated in experiments with real-life data sets.