Ευσταθιος Αντωνίου

Δημοσιεύσεις

Περιοδικά

  1. E. N. Antoniou, A. I. G. Vardulakis, and N. P. Karampetakis, “A spectral characterization of the behavior of discrete time AR-representations over a finite time interval,” Kybernetika, vol. 34, no. 5, pp. 555–564, 1998, Accessed: Sep. 18, 2008. [Online]. Available: http://www.kybernetika.cz/content/1998/5/555. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.
  2. E. N. Antoniou and A. I. G. Vardulakis, “A note on the action of constant pseudostate feedback on the internal properness of an ARMA model,” Automatica, vol. 35, no. 8, pp. 1453–1456, 1999, Accessed: Sep. 18, 2008. [Online]. Available: http://dx.doi.org/10.1016/S0005-1098(99)00039-4. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this note we study the effect of constant pseudostate feedback on the internal properness of a linear multivariable system, described by an ARMA model. It is shown that the existence of a constant pseudostate feedback control law which makes the closed-loop system internally proper is equivalent to the absence of decoupling zeros at infinity of the open-loop system, a well-known result from the theory of descriptor systems.
  3. A. I. G. Vardulakis, E. N. Antoniou, and N. Karampetakis, “On the solution and impulsive behaviour of polynomial matrix descriptions of free linear multivariable systems,” International Journal of Control, vol. 72, no. 3, pp. 215–228, 1999, Accessed: Sep. 18, 2008. [Online]. Available: http://www.informaworld.com/smpp/ftinterface~content=a713805786~fulltext=713240930. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this note we examine the solution and the impulsive behaviour of autonomous linear multivariable systems whose pseudo-state β(t) obeys a linear matrix differential equation A(ρ)β(t) = 0 where A(ρ) is a polynomial matrix in the differential operator ρ := d/dt. We thus generalize to the general polynomial matrix case some results obtained by Verghese and colleagues which regard the impulsive behaviour of the generalized state vector x(t) of input free generalized state space systems.
  4. N. P. Karampetakis, J. Jones, and E. N. Antoniou, “Forward, backward, and symmetric solutions of discrete ARMA representations,” Circuits, Systems, and Signal Processing, vol. 20, no. 1, pp. 89–109, 2001, Accessed: Sep. 18, 2008. [Online]. Available: http://www.springerlink.com/content/r54835209x840718/fulltext.pdf. Πλήρες κέιμενο Περίληψη
    Περίληψη: The main objective of this paper is to determine a closed formula for the forward, backward, and symmetric solution of a general discrete-time Autoregressive Moving Average representation. The importance of this formula is that it is easily implemented in a computer algorithm and gives rise to the solution of analysis, synthesis, and design problems.
  5. A. I. G. Vardulakis and E. Antoniou, “Fundamental equivalence of discrete-time AR representations,” International Journal of Control, vol. 76, no. 11, pp. 1078–1088, 2003, Accessed: Sep. 18, 2008. [Online]. Available: http://dx.doi.org/10.1080/0020717031000123607. Πλήρες κέιμενο Περίληψη
    Περίληψη: We examine the problem of equivalence of discrete time auto-regressive representations (DTARRs) over a finite time interval. Two DTARRs are defined as fundamentally equivalent (FE) over a finite time interval [0, N] if their solution spaces or behaviours are isomorphic. We generalize the concept of strict equivalence (SE) of matrix pencils to the case of general polynomial matrices and in turn we show that FE of DTARRs implies SE of the underlying polynomial matrices.
  6. E. N. Antoniou and S. Vologiannidis, “A new family of companion forms of polynomial matrices,” Electronic Journal of Linear Algebra, vol. 11, pp. 78–87, 2004, Accessed: Sep. 18, 2008. [Online]. Available: http://repository.uwyo.edu/ela/vol11/iss1/8/. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. Furthermore, for the special class of self-adjoint polynomial matrices a particular member is shown to be self-adjoint itself.
  7. E. N. Antoniou, A. I. G. Vardulakis, and S. Vologiannidis, “Numerical computation of minimal polynomial bases: A generalized resultant approach,” Linear Algebra and its Applications, vol. 405, no. 1–3, pp. 264–278, 2005, doi: 10.1016/j.laa.2005.03.017. Πλήρες κέιμενο Περίληψη
    Περίληψη: We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F(s). The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be implemented using only orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coefficients. © 2005 Elsevier Inc. All rights reserved.
  8. E. N. Antoniou and A. I. G. Vardulakis, “On the computation and parametrization of proper denominator assigning compensators for strictly proper plants,” IMA Journal of Mathematical Control and Information, vol. 22, no. 1, pp. 12–25, 2005, doi: 10.1093/imamci/dni002. Πλήρες κέιμενο Περίληψη
    Περίληψη: Given a right coprime MFD of a strictly proper plant P(s) = NR(S)DR(s)-1 with DR(s) column proper a simple numerical algorithm is derived for the computation of all polynomial solutions [XL(s), YL(s)] of the polynomial matrix Diophantine equation XL(s)DR(s) + YL(s)NR(s) = DC(s) which give rise to the class Φ(P, DC) of proper compensators C(s) := XL(s)-1 YL(s) that when employed in a unity feedback loop, result in closed-loop systems S(P, C) with a desired denominator Dc(s). The parametrization of the proper compensators C(s) ∈ Φ(P, DC) is obtained and the number of independent parameters in the parametrization is given. © Institute of Mathematics and its Applications 2005; all rights reserved.
  9. E. N. Antoniou and S. Vologiannidis, “Linearizations of polynomial matrices with symmetries and their applications,” Electronic Journal of Linear Algebra, vol. 15, pp. 107–114, 2006, Accessed: Sep. 18, 2008. [Online]. Available: http://repository.uwyo.edu/ela/vol15/iss1/7/. Πλήρες κέιμενο Περίληψη
    Περίληψη: In an earlier paper by the present authors, a new family of companion forms associated with a regular polynomial matrix was presented, generalizing similar results by M. Fiedler who considered the scalar case. This family of companion forms preserves both the finite and infinite elementary divisor structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. In this note, its applications on polynomial matrices with symmetries, which appear in a number of engineering fields, are examined.
  10. A. C. Pugh, E. N. Antoniou, and N. P. Karampetakis, “Equivalence of AR-representations in the light of the impulsive-smooth behaviour,” International Journal of Robust and Nonlinear Control, vol. 17, no. 8, pp. 769–785, 2007, doi: 10.1002/rnc.1135. Πλήρες κέιμενο Περίληψη
    Περίληψη: The paper presents a new notion of equivalence of non-regular AR-representations, based on the coincidence of the impulsive-smooth behaviours of the underlying systems. The proposed equivalence is characterized by a special case of the usual unimodular equivalence and a restriction of the matrix transformation of full equivalence (Int. J. Control 1988; 47(1):53-64). Copyright � 2006 John Wiley & Sons, Ltd.
  11. A.-I. G. Vardulakis, N. P. Karampetakis, E. N. Antoniou, and E. Tictopoulou, “On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems,” International Journal of Applied Mathematics and Computer Science, vol. 19, no. 1, pp. 77–88, 2009, Accessed: May 04, 2009. [Online]. Available: https://www.amcs.uz.zgora.pl/?action=paper&paper=421. Πλήρες κέιμενο Περίληψη
    Περίληψη: 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.
  12. N. P. Karampetakis, E. N. Antoniou, A. I. G. Vardulakis, and S. Vologiannidis, “Symbolic Computations on Rings of Rational Functions and Applications in Control Engineering,” in Computer Aided Systems Theory - EUROCAST 2009, vol. 5717, R. Moreno-Díaz, F. Pichler, and A. Quesada-Arencibia, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009, pp. 587–594. Πλήρες κέιμενο Περίληψη
    Περίληψη: A collection of algorithms implemented in Mathematica 7.0, freely available over the internet, and capable to manipulate rational functions and solve related control problems using polynomial analysis and design methods is presented. The package provides all the necessary functionality and tools in order to use the theory of Ω− stable functions, and is expected to provide the necessary framework for the development of several other algorithms that solve specific control problems.
  13. S. Vologiannidis and E. N. Antoniou, “A permuted factors approach for the linearization of polynomial matrices,” Mathematics of Control, Signals, and Systems, vol. 22, pp. 317–342, Apr. 2011, doi: 10.1007/s00498-011-0059-6. Πλήρες κέιμενο Περίληψη
    Περίληψη: In Antoniou and Vologiannidis (Electron J Linear Algebra 11:78–87, 2004; 15:107–114, 2006), a new family of companion forms associated with a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in Fiedler (Linear Algebra Its Appl 371:325–331, 2003) where the scalar case was considered. In this paper, extending this “permuted factors” approach, we present a broader family of companion-like linearizations, using products of up to n(n −1)/2 elementary matrices, where n is the degree of the polynomial matrix. Under given conditions, the proposed linearizations can be shown to consist of block entries where the coefficients of the polynomial matrix appear intact. Additionally, we provide a criterion for those linearizations to be block symmetric. We also illustrate several new block symmetric linearizations of the original polynomial matrix T (s), where in some of them the constraint of nonsingularity of the constant term and the coefficient of maximum degree are not a prerequisite.
  14. E. Antoniou and S. Vologiannidis, “On the characterization and parametrization of strong linearizations of polynomial matrices,” Electronic Journal of Linear Algebra, vol. 31, no. 1, pp. 610–619, Oct. 2016, doi: 10.13001/1081-3810.2950. Πλήρες κέιμενο Περίληψη
    Περίληψη: In the present note, a new characterization of strong linearizations, corresponding to a given regular polynomial matrix, is presented. A linearization of a regular polynomial matrix is a matrix pencil which captures the finite spectral structure of the original matrix, while a strong linearization is one incorporating its structure at infinity along with the finite one. In this respect, linearizations serve as a tool for the study of spectral problems where polynomial matrices are involved. In view of their applications, many linearization techniques have been developed by several authors in the recent years. In this note, a unifying approach is proposed for the construction of strong linearizations aiming to serve as a bridge between approaches already known in the literature.
  15. E. N. Antoniou, A. A. Pantelous, I. A. Kougioumtzoglou, and A. Pirrotta, “Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach,” Applied Mathematical Modelling, vol. 42, pp. 423–440, Feb. 2017, doi: 10.1016/j.apm.2016.10.025. Πλήρες κέιμενο Περίληψη
    Περίληψη: An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, based on the theoretical machinery of polynomial matrices, a closed form analytical solution is derived for the system response that involves non-singular matrices and relies on the use of a basis of the null space of the constraints matrix. Several structural/mechanical systems with singular matrices are included as examples for demonstrating the validity of the developed framework and for elucidating certain numerical aspects.
  16. L. Moysis, A. A. Pantelous, E. Antoniou, and N. P. Karampetakis, “Closed form solution for the equations of motion for constrained linear mechanical systems and generalizations: An algebraic approach,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1421–1445, Feb. 2017, doi: 10.1016/j.jfranklin.2016.11.027. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this paper, a mathematical methodology is presented for the determination of the solution of motion for linear constrained mechanical systems applicable also to systems with singular coefficients. For mathematical completeness and also to incorporate some other interesting cases, the methodology is formulated for a general class of higher order matrix differential equations. Thus, describing the system in an autoregressive moving average (ARMA) form, the closed form solution is derived in terms of the finite and infinite Jordan pairs of the system׳s polynomial matrix. The notion of inconsistent initial conditions is considered and an explicit formula for the homogeneous system is given. In this respect, the methodology discussed in the present note provides an alternative view to the problem of computation of the response of complex multi-body systems. Two interesting examples are provided and applications of the equation to such systems are illustrated.
  17. L. Moysis, N. Karampetakis, and E. Antoniou, “Observability of linear discrete-time systems of algebraic and difference equations,” International Journal of Control, vol. 92, no. 2, pp. 339–355, 2019, doi: 10.1080/00207179.2017.1354399. Πλήρες κέιμενο Περίληψη
    Περίληψη: ABSTRACTThe notion of observability for higher order discrete-time systems of algebraic and difference equations is studied. Such systems are also known as polynomial matrix descriptions . Attention is first given to a special form of descriptor systems with a state lead in the output. This system is transformed into its causal and noncausal subsystems and observability criteria are given in terms of the subsystem's matrices, and the fundamental matrix sequence of the matrix pencil (σE − A). Afterwards, the higher order system is studied. By transforming it into a first-order descriptor system of the above form, an observability criterion is provided for the higher order system in terms of the Laurent expansion at infinity of the system's polynomial matrix. In addition, observability is connected with the coprimeness of the polynomial matrices of the higher order system and the coprimeness of the matrix pencils of the descriptor system.
  18. E. N. Antoniou, A. Araújo, M. D. Bustamante, and A. Gibali, “Physically feasible decomposition of Engino® toy models: A graph-theoretic approach,” European Journal of Applied Mathematics, vol. 30, no. 2, pp. 278–297, Apr. 2019, doi: 10.1017/S0956792518000086. Πλήρες κέιμενο Περίληψη
    Περίληψη: During the 125th European Study Group with Industry held in Limassol, Cyprus, 5–9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets – the Engino® toy sets – consisting of a number of building blocks, which can be assembled by pupils to compose toy models. Depending on the contents of a particular toy set, the company has developed a number of models that can be built utilizing the blocks present in the set; however, the production of a step-by-step assembly manual for each model could only be done manually. The goal of the challenge posed by the company was to implement a procedure to automatically generate the assembly instructions for a given toy. In the present paper, we propose a graph-theoretic approach to model the problem and provide a series of results to solve it by employing modified versions of well-established algorithms in graph theory. An algorithmic procedure to obtain a hierarchical, physically feasible decomposition of a given toy model, from which a series of step-by-step assembly instructions can be recovered, is proposed.
  19. E. Antoniou and S. Vologiannidis, “On the reduction of 2-D polynomial systems into first order equivalent models,” Multidim Syst Sign Process, vol. 31, no. 1, pp. 249–268, Jan. 2020, doi: 10.1007/s11045-019-00661-8. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this paper we propose a novel approach for the reduction of a 2-D rectangular polynomial matrix of arbitrary degree, to first-order matrix pencils of the form $$sE_{1}+zE_{2}+A$$sE1+zE2+A, utilizing the framework of zero coprime equivalence (ZC-E). The proposed approach is in turn employed to derive a series of ZC-E matrix pencils, which can be obtained “by inspection” of the coefficients of the original bivariate polynomial matrix. Improving similar constructions of first order pencils available in the literature, our approach results in matrix pencils whose size increases linearly with the degrees of the indeterminates of the original polynomial matrix. From a system-theoretic point of view, the proposed method, provides the algebraic tools to transform a high order bivariate linear system, into a zero coprime system equivalent first order representation. Notably, one of the proposed transformation techniques gives rise to generalized 2$$-D$$-D Roesser models.
  20. S. Vologiannidis and E. Antoniou, “On the reduction of repetitive processes into singular and non-singular Roesser models,” Multidim Syst Sign Process, Jan. 2021, doi: 10.1007/s11045-020-00750-z. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent singular and non-singular 2-D state space representations. Particularly, a zero coprime system equivalence transformation resulting in a singular Roesser state space model, preserving the core algebraic structure of the original system matrix, is proposed. As a second step utilizing the singular Roesser model introduced, we further reduce the system to a non-singular, zero coprime system equivalent Roesser model. Both models are constructed by inspection or by applying elementary matrix manipulations and have significantly smaller dimensions compared to similar reductions found in the literature.
  21. S. Vologiannidis, E. N. Antoniou, N. P. Karampetakis, and A. I. G. Vardulakis, “Polynomial matrix equivalences: system transformations and structural invariants,” IMA Journal of Mathematical Control and Information, vol. 38, no. 1, pp. 54–73, Mar. 2021, doi: 10.1093/imamci/dnw065. Πλήρες κέιμενο Περίληψη
    Περίληψη: The present article is a survey on linear multivariable systems equivalences. We attempt a review of the most significant forms of system equivalence having as a starting point matrix transformations preserving certain aspects of their spectral structure. From a system theoretic point of view, the need for a variety of forms of polynomial matrix equivalences, arises from the fact that different types of spectral invariants give rise to different types of dynamics of the underlying linear system. A historical perspective of the key results and their contributors is also given.
  22. E. Karapalidou, N. Alexandris, E. Antoniou, S. Vologiannidis, J. Kalomiros, and D. Varsamis, “Implementation of a Sequence-to-Sequence Stacked Sparse Long Short-Term Memory Autoencoder for Anomaly Detection on Multivariate Timeseries Data of Industrial Blower Ball Bearing Units,” Sensors, vol. 23, no. 14, p. 6502, Jan. 2023, doi: 10.3390/s23146502. Πλήρες κέιμενο Περίληψη
    Περίληψη: The advent of Industry 4.0 introduced new ways for businesses to evolve by implementing maintenance policies leading to advancements in terms of productivity, efficiency, and financial performance. In line with the growing emphasis on sustainability, industries implement predictive techniques based on Artificial Intelligence for the purpose of mitigating machine and equipment failures by predicting anomalies during their production process. In this work, a new dataset that was made publicly available, collected from an industrial blower, is presented, analyzed and modeled using a Sequence-to-Sequence Stacked Sparse Long Short-Term Memory Autoencoder. Specifically the right and left mounted ball bearing units were measured during several months of normal operational condition as well as during an encumbered operational state. An anomaly detection model was developed for the purpose of analyzing the operational behavior of the two bearing units. A stacked sparse Long Short-Term Memory Autoencoder was successfully trained on the data obtained from the left unit under normal operating conditions, learning the underlying patterns and statistical connections of the data. The model was evaluated by means of the Mean Squared Error using data from the unit’s encumbered state, as well as using data collected from the right unit. The model performed satisfactorily throughout its evaluation on all collected datasets. Also, the model proved its capability for generalization along with adaptability on assessing the behavior of equipment similar to the one it was trained on.

Συνέδρια

  1. N. P. Karampetakis, J. Jones, and S. N. Antoniou, “Forward, Backward and Symmetric solutions of discrete time ARMA representations,” Brussels, Belgium, 1997.
  2. S. N. Antoniou, A. I. G. Vardulakis, and N. Karampetakis, “A spectral characterization of the behavior of discrete time AR-representations over a finite time interval,” Brussels, Belgium, Jul. 1997.
  3. J. Vlioras, S. N. Antoniou, and A. I. G. Vardulakis, “Implementation of some Linear Multivariable Systems Algorithms via Maple,” Brussels, Belgium, Jul. 1997.
  4. S. Antoniou, N. Karampetakis, and A. I. G. Vardulakis, “A Classification of the Solutions of non-regular, discrete-time Descriptor Systems,” San Diego, USA, Dec. 1997.
  5. A. I. G. Vardulakis and E. N. Antoniou, “Fundamental Equivalence of Discrete-time AR-representations,” Prague, Czech Republic, 2001.
  6. A. I. Vardulakis, N. P. Karampetakis, E. Antoniou, P. Tzekis, and S. Vologiannidis, “A Descriptor Systems Package for Mathematica,” Rhodes, Greece, Jun. 2003.
  7. E. N. Antoniou and A. I. G. Vardulakis, “A numerical method for the computation of proper denominator assigning compensators for strictly proper plants,” Rhodes, Greece, Jun. 2003.
  8. P. Kujan, M. Hromcik, M. Sebek, N. P. Karampetakis, E. N. Antoniou, and S. Vologiannidis, “Effective computations with 2-variable polynomial matrices in MATHEMATICA,” Kusadasi, Aydin, Turkey, Jun. 2004.
  9. E. N. Antoniou, A. I. G. Vardulakis, and S. Vologiannidis, “On the Computation of Minimal Polynomial Bases,” Kusadasi, Aydin, Turkey, Jun. 2004.
  10. E. Antoniou, S. Vologiannidis, and N. Karampetakis, “Linearizations of Polynomial Matrices with Symmetries and Their Applications.,” in Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005., Jun. 2005, pp. 159–163, doi: 10.1109/.2005.1467008. Πλήρες κέιμενο Περίληψη
    Περίληψη: In E.N. Antoniou and S. Vologiannidis ( 2004), a new family of companion forms associated to a regular polynomial matrix has been presented generalizing similar results presented by M. Fiedler in M. Fiedler (2003) where the scalar case was considered. This family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. In this note we examine its applications on polynomial matrices with symmetries which appear in a number of engineering fields
  11. A. C. Pugh, E. N. Antoniou, and N. P. Karampetakis, “Equivalence of AR-Representations in the Light of the Impulsive-Smooth Behavior,” in Proceedings of the 44th IEEE Conference on Decision and Control, Dec. 2005, pp. 1547–1552, doi: 10.1109/CDC.2005.1582378. Πλήρες κέιμενο Περίληψη
    Περίληψη: The paper presents a new notion of equivalence of non-regular AR- representations, based on the coincidence of the impulsive-smooth behaviors of the underlying systems. The proposed equivalence is characterized by a special case of the usual unimodular equivalence and a restriction of the matrix transformation of full equivalence [21].
  12. A. I. G. Vardulakis, N. P. Karampetakis, and E. N. Antoniou, “On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems,” in 2007 European Control Conference (ECC), Jul. 2007, pp. 4532–4539, doi: 10.23919/ECC.2007.7068426. Πλήρες κέιμενο Περίληψη
    Περίληψη: We review the realization theory of polynomial (transfer function) matrices via “pure” generalized state space 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. Finally the isomorphism between the zeros at infinity of the “infinite pole pencil” and the Rosenbrock system matrix of an irreducible at infinity generalized state space realization of a polynomial matrix and the pole and zero structure at infinity of such a polynomial matrix is examined.
  13. A. I. Vardulakis, N P Karampetakis, E. Antoniou, and S. Vologiannidis, “Descriptor Systems Toolbox : A Mathematica-Based Package for Descriptor Systems,” San Antonio, Texas (USA), 2008.
  14. S. Vologiannidis and E. Antoniou, “A permuted factors approach for the linearization of polynomial matrices,” presented at the Applied Linear Algebra (ALA) 2010, Novi Sad, Serbia, May 2010.
  15. S. Vologiannidis, E. Antoniou, and M. Kasidiaris, “Zero coprime equivalent matrix pencils of a 2 - D polynomial matrix,” in Proceedings of the 7th International Workshop on Multidimensional (nD) Systems, Poitiers, France, 2011, pp. 1–5, doi: 10.1109/nDS.2011.6076868. Πλήρες κέιμενο
  16. P. A. Tzekis, E. Antoniou, and S. Vologiannidis, “Computation of the general solution of a multivariate polynomial matrix Diophantine equation,” in 2013 21st Mediterranean Conference on Control Automation (MED), Jun. 2013, pp. 677–682, doi: 10.1109/MED.2013.6608796. Πλήρες κέιμενο Περίληψη
    Περίληψη: The algorithm presented in [21] provides a method for the computation of the general solution of a polynomial matrix Diophantine equation. In this work we extend this algorithm for the n-D PMDE. We present a method to efficiently address the division of multivariate polynomials. The theory is implemented via illustrative examples.
  17. A. I. G. Vardulakis, N. Karampetakis, E. Antoniou, and S. Vologiannidis, “Notions of equivalence for linear multivariable systems,” in 2013 21st Mediterranean Conference on Control Automation (MED), Jun. 2013, pp. 794–800, doi: 10.1109/MED.2013.6608814. Πλήρες κέιμενο Περίληψη
    Περίληψη: The present paper is a survey on linear multivariable systems equivalences. We attempt a review of the most significant types of system equivalence having as a starting point matrix transformations preserving certain types of their spectral structure. From a system theoretic point of view, the need for a variety of forms of polynomial matrix equivalences, arises from the fact that different types of spectral invariants give rise to different types of dynamics of the underlying linear system. A historical perspective of the key results and their contributors is also given.
  18. E. Antoniou, A. Pantelous, and P. Tzekis, “On the Computation of the Response of Perturbed Discrete Time Descriptor Systems,” in IFAC Proceedings Volumes, Jan. 2014, vol. 47, pp. 9522–9527, doi: 10.3182/20140824-6-ZA-1003.02027. Πλήρες κέιμενο Περίληψη
    Περίληψη: Descriptor systems provide the natural framework for the study of a wide variety of physical, electrical, mechanical, economical and social systems. In this paper, the response of a Linear Time Invariant (LTI), descriptor system in discrete-time over a finite time interval is examined, whose coefficient matrix on the right hand side of the descriptor equation has been perturbed by a constant matrix. The response of the perturbed system is explicitly computed using a modified version of the well known Weierstrass canonical form and a simplified approximation formula is derived. A numerical example illustrates the findings.
  19. E. N. Antoniou and S. Vologiannidis, “On the parametrization of linearizations of polynomial matrices,” in 22nd Mediterranean Conference on Control and Automation, Jun. 2014, pp. 316–321, doi: 10.1109/MED.2014.6961390. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this note we propose a new approach for the construction of a parametrization of the linearizations corresponding to a given polynomial matrix. A linearization of a polynomial matrix is a first order polynomial matrix which is in a certain sense equivalent to the original one. The main advantage of linearization techniques, is that in most cases, a linearization can be easily constructed from the coefficients of the polynomial matrix. In view of their advantages and applications many linearization techniques have been developed by several authors in the recent years. In the present paper we propose a unifying approach aiming to serve as a bridge between the two main linearization approaches already known in the literature.
  20. P. Tzekis, E. Antoniou, and A. Pantelous, “On the response of linear time invariant higher order systems with perturbed coefficients,” in Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA), Liverpool, UK, Jul. 2014, pp. 1039–1046. Περίληψη
    Περίληψη: We provide a new approach towards the analysis of the response of higher order systems whose coefficients are subject to norm bounded perturbations. Based on the magnitudes of the perturbations, we obtain bounds of the response of the system. The first order case, that is state space or more generally descriptor systems, has been extensively studied in the past using a variety of approaches and many results have been produced. On the other hand, a very popular strategy to overcome the difficulty of high order systems, is to reduce them to first order equivalents. Our approach utilizes the aforementioned techniques to study the response of polynomial systems under perturbations.
  21. A. Pantelous and E. Antoniou, “Linear Descriptor Differential Equations and its Application to Constrained Mechanical Systems,” presented at the 7th International Conference on Dynamic Systems and Applications & 5th International Conference on Neural, Parallel and Scientific Computations, Atlanta, USA, May 2015.
  22. E. N. Antoniou, A. Pantelous, and P. Tzekis, “A new approach for the formulation of the equations of motion of constrained mechanical systems and its application to linear systems,” presented at the Modern Mathematical Methods in Science and Technology (M3ST), Kalamata, Greece, Aug. 2015.
  23. E. N. Antoniou, A. Pantelous, I. Kougioumtzoglou, and A. Pirrotta, “A Polynomial Matrix Theory Approach for Determining the Response of Structural Systems with Singular Coefficient Matrices,” in Proceedings of the 12th International Conference on Structural Safety & Reliability (ICOSSAR 2017), TU Wienn, Vienna, Austria, Aug. 2017, pp. 1224--1231. Περίληψη
    Περίληψη: Polynomial matrix theory is shown to be a valuable tool for the analysis of the equations of motion of multi-degree-of-freedom (MDOF) linear structural systems involving singular coefficient matrices. Singular mass coefficient matrices in such systems may appear either due to the use redundant coordinates or due to the introduction of massless bodies used to facilitate the modeling process. The equations of motion in such cases are a set of algebraic – differential equations involving a singular mass matrix, which makes the determination of the acceleration, a rather complicated task. By employing tools from polynomial matrix theory, this difficulty can be overcome, and a closed form analytical solution is derived along with conditions guaranteeing continuity of the response.
  24. S. Vologiannidis and E. Antoniou, “A new approach on the linearization of 2-D polynomial matrices,” in 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), Apr. 2019, pp. 171–175, doi: 10.1109/CoDIT.2019.8820594. Πλήρες κέιμενο Περίληψη
    Περίληψη: In this paper we propose a generic approach to reduce a 2-L square polynomial matrix of arbitrary degree(s), to first-order matrix pencils of the form sE1+zE2+A, utilizing the framework of zero coprime equivalence (ZC-E). This generic approach is in turn employed to derive a series of ZC-E matrix pencils, which can be obtained “by inspection” of the coefficients of the original bivariate polynomial matrix. Improving similar constructions of first order pencils in the literature, our approach results in matrix pencils whose size increases linearly with the degrees of the indeterminates of the original polynomial matrix.
  25. M. D. Bustamante, E. N. Antoniou, A. Araújo, and A. Gibali, “Physically feasible decomposition of Engino® toy models: A graph-theoretic approach,” presented at the British Applied Mathematics Colloquium 2019, Bath, UK, Apr. 2019, [Online]. Available: https://www.bath.ac.uk/events/british-applied-mathematics-colloquium-2019/. Πλήρες κέιμενο Περίληψη
    Περίληψη: During the 125th European Study Group with Industry held in Limassol, Cyprus, 5-9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets -- the Engino® toy sets - consisting of a number of building blocks which can be assembled by pupils to compose toy models. Depending on the contents of a particular toy set, the company has developed a number of models that can be built utilising the blocks present in the set. However, the production of a step-by-step assembly manual for each model could only be done manually. The goal of the challenge posed by the company was to implement a procedure to automatically generate the assembly instructions for a given toy. In the present paper we propose a graph-theoretic approach to model the problem and provide a series of results to solve it by employing modified versions of well established algorithms in graph theory. An algorithmic procedure to obtain a hierarchical, physically feasible decomposition of a given toy model, from which the assembly instructions can be recovered, is proposed.
  26. E. Karapalidou, A. Efraimidis, S. Vologiannidis, and E. Antoniou, “Modeling the Health Status of a Ball Bearing for Predictive Maintenance Purposes,” in 2023 9th International Conference on Control, Decision and Information Technologies (CoDIT), Rome, Italy, Jul. 2023. Περίληψη
    Περίληψη: Modern industries are constantly aiming to maximize utilization and performance of their machine equipment and minimize costly and unscheduled downtime. In the recent years, this was made possible with the advancement of technology and the coming of the fourth industrial revolution, also known as Industry 4.0, which introduced the Internet of Things and Artificial Intelligence systems in industrial applications. This allowed the employment of predictive maintenance methods able to assess the health of the equipment and diagnose possible future failures. In this work, an experimental assembly was constructed comprised by an electrical motor, a reduction gear, an axle, a coupler, a bearing and a vibration sensor attached to the latter. Three types of experiments were conducted for the purpose of producing a labeled dataset based on vibration measurements. Specifically, measurements were made during the bearing’s working in normal operating state, one with lack and one with excess amount of grease. A preliminary statistical analysis was performed while a Multilayer Perceptron model was employed to automatically predict the status of the bearing. The dataset is freely available at the Zenodo data repository.

Κεφάλαια σε συλλογικούς τόμους

  1. E. Antoniou, I. Kafetzis, and S. Vologiannidis, “A Review of Linearization Methods for Polynomial Matrices and their Applications,” in Analysis, Geometry, Nonlinear Optimization and Applications, in Series on Computers and Operations Research, no. Volume 9, vol. Volume 9. WORLD SCIENTIFIC, 2022, pp. 157–188. doi: 10.1142/9789811261572_0006. Πλήρες κέιμενο

Βιβλία

  1. Β. Κώστογλου and Ε. Αντωνίου, ΠΙΘΑΝΟΤΗΤΕΣ ΚΑΙ ΣΤΑΤΙΣΤΙΚΗ, Θεωρία – Εφαρμογές – Χρήση του SPSS, 1η έκδοση. Θεσσαλονίκη: Επιστημονικές Εκδόσεις Τζιόλα, 2021. [Online]. Available: https://www.tziola.gr/book/pithanotites-k-statistiki Πλήρες κέιμενο Περίληψη
    Περίληψη: Περιέχει: Μέρος Ι - Θεωρία Πιθανοτήτων, Εισαγωγικές έννοιες, Διακριτή πιθανότητα και συνδυαστική, Δεσμευμένη Πιθανότητα - Ανεξαρτησία, Διακριτές Τυχαίες Μεταβλητές, Συνεχείς Τυχαίες Μεταβλητές, Πολυδιάστατες τυχαίες μεταβλητές, Μέρος ΙΙ - Στατιστική, Περιγραφική Στατιστική, Εκτιμητική και Διαστήματα Εμπιστοσύνης, Έλεγχοι Υποθέσεων, Ανάλυση Διασποράς, Γραμμική Παλινδρόμηση, Εφαρμογή με χρήση του SPSS, Στατιστικοί πίνακες, Λύσεις Ασκήσεων, Βιβλιογραφία

Διδακτορική διατριβή

  1. Ε. Ν. Αντωνίου, “Ανάλυση ιδιαζόντων γραμμικών συστημάτων διαρκιτού χρόνου,” Διδακτορική Διατριβή, Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης, Τμήμα Μαθηματικών, 2000. Πλήρες κέιμενο Περίληψη
    Περίληψη: Το αντικείμενο της παρούσας διδακτορικής διατριβής είναι τα ιδιάζοντα γραμμικά συστήματα διακριτού χρόνου. Η περίπτωση των πρωτοβάθμιων κανονικών συστημάτων έχει μελετηθεί στο παρελθόν από διάφορους συγγραφείς, κυρίως σε επίπεδο αλγεβρικής και γεωμετρικής ανάλυση. Κύριος στόχος της παρούσας έρευνας είναι η επέκταση των αποτελεσμάτων αυτών προς τρεις κατευθύνσεις. Συγκεκριμένα η ανάλυση μη-κανονικών πρωτοβάθμιων ιδιαζόντων συστημάτων, η μελέτη της δομής του χώρου λύσεων (συμπεριφορά) κανονικών αυτοπαλλίνδρομων (AR) παραστάσεων και η μέθοδος επίλυσης αυτοπαλλίνδρομων παραστάσεων κινούμενου μέσου (ARMA) με τη χρήση του θεμελιώδους πίνακα. Η δομή των χώρων λύσεων που μελετήθηκαν συσχετίστηκε άμεσα με την αλγεβρική δομή των πολυωνυμικών πινάκων που περιγράφουν τα αντίστοιχα συστήματα και ιδιαίτερο βάρος δόθηκε στην αλγεβρική δομή των τελευταίων στο άπειρο.