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The generalized S- and σ-inverse – a comparative case study for right- and left-invertible plants

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Języki publikacji
EN
Abstrakty
EN
In this paper, an advanced study covering the comparison between two classes of generalized inverses is conducted. Two sets of instances, strictly derived from the recently introduced nonunique S- and σ-inverse, are analyzed, especially in terms of degrees of freedom-oriented interchangeable application in different engineering tasks. Henceforth, the respective collections of right and left inverses can be combined in order to achieve a complex tool for robustification of a plethora of real processes. The great potential of two S- and σ-inverse, in particular in robust control and signal recovery as well as complex optimal tasks, is confirmed in the manuscript and supported by the recently carried out research investigations.
Rocznik
Strony
1517--1523
Opis fizyczny
Bibliogr. 24 poz., rys.
Twórcy
autor
  • Opole University of Technology, ul. Prószkowska 76, 45-758 Opole, Poland
autor
  • Opole University of Technology, ul. Prószkowska 76, 45-758 Opole, Poland
Bibliografia
  • [1] X. Yang, D. Zhou, D. Liu, and R. Yang, “Moving cast shadow detection using block nonnegative matrix factorization”, Bull. Pol. Ac.: Tech. 66 (2), 229–234 (2018).
  • [2] J. Klamka, “Constrained controllability of semilinear systems with delayed controls”, Bull. Pol. Ac.: Tech. 56 (4), 333–337 (2008).
  • [3] S. Vologiannidis and N. Karampetakis, “Inverses of multivariable polynomial matrices by Discrete Fourier Transforms”, Multidimens. Syst. Signal Process. 15 (4), 341–361 (2004).
  • [4] M.D. Petković, P.S. Stanimirović, and M.B. Tasić, “Effective partitioning method for computing weighted Moore-Penrose inverse”, Comput. Math. Appl. 55 (8), 1720–1734 (2008).
  • [5] S. Vologiannidis, E. Antoniou, N. Karampetakis, and A. Vardulakis, “Polynomial matrix equivalences: system transformations and structural invariants”, IMA J. Math. Control Inf. 32, 1–20, (2016).
  • [6] W.P. Hunek and M. Krok, “A study on a new criterion for minimum-energy perfect control in the state-space framework”, Proc. Inst. Mech. Eng. Part I – J. Syst. Control Eng. 233 (7), 779–787 (2019).
  • [7] W.P. Hunek and P. Majewski, “Perfect reconstruction of signal – a new polynomial matrix inverse approach”, EURASIP J. Wirel. Commun. Netw. 2018 (107), 1–8 (2018).
  • [8] W.P. Hunek and P. Dzierwa, “New results in generalized minimum variance control of computer networks”, Inf. Technol. Control 43 (3), 315–320 (2014).
  • [9] A.K. Alhejji and M.R. Sayeh, “Dynamical neural networks-based inverse optimal sliding mode controller”, Proc. of the 3rd International Conference on Control, Decision and Information Technologies (CoDiT’2016), Saint Julian’s, Malta, 2016, pp. 417–424.
  • [10] P.W. Aitchison, “Generalized inverse matrices and their applications”, Int. J. Math. Educ. Sci. Technol. 13 (1), 99–109 (1982).
  • [11] A.B. Israel and T.N.E. Grevill, “Generalized Inerses, Theory and Applications”, in CMS Books in Mathematics, Springer-Verlag, New York, 2003.
  • [12] R. Shukla, S. Khoram, E. Jorgensen, J. Li, M. Lipasti, and S. Wright, “Computing generalized matrix inverse on spiking neural substrate”, Front. Neurosci. 12, 115 (2018).
  • [13] P.S. Stanimirović and M.D. Petković, “Computing generalized inverse of polynomial matrices by interpolation”, Appl. Math. Comput. 172, 508–523 (2006).
  • [14] C.M. Fonseca and J. Petronilho, “Explicit inverses of some tridiagonal matrices”, Linear Alg. Appl. 325 (13), 721 (2001).
  • [15] N.P. Karampetakis and P. Tzekis, “On the computation of the generalized inverse of a polynomial matrix”, IMA J. Math. Control Inf. 18 (1), 83–97 (2001).
  • [16] W.P. Hunek and P. Majewski, “Relationship between S- and σ -inverse for some class of nonsquare matrices – an initial study”, Proc. of the IEEE 15th International Conference on Control and Automation (ICCA), Edinburgh, Scotland, 2019, 1156–1160.
  • [17] L. Noueili, W. Chagra, and M. Ksouri, “New Iterative Learning Control Algorithm using Learning Gain Based on σ Inversion for Nonsquare MIMO Systems”, Hindawi: Model. Simul. Eng. 2018, 4195938 (2018).
  • [18] T. Zhang, H.G. Li, Z.Y. Zhong, and G.P. Cai, “Hysteresis model and adaptive vibration suppression for a smart beam with time delay”, J. Sound Vibr. 358, 35–47 (2015).
  • [19] T. Zhang, B.T. Yang, H.G. Li, and G. Meng, “Dynamic modeling and adaptive vibration control study for giant magnetostrictive actuators”, Sens. Actuator A-Phys. 190, 96–105 (2013).
  • [20] T. Zhang, H.G. Li, and G.P. Cai, “Hysteresis identification and adaptive vibration control for a smart cantilever beam by a piezo-electric actuator”, Sens. Actuator A-Phys. 203, 168–175 (2013).
  • [21] S. Dadhich and W. Birk, “Analysis and control of an extended quadruple tank process”, Proc. of the 13th IEEE European Control Conference (ECC’2014), 2014, pp. 838–843.
  • [22] A.M. Almeida, M. Kaminski Lenzi, and E. Kaminski-Lenzi, “A survey of fractional order calculus applications of multiple-input, multiple-output (MIMO) process control”, Fractal and Fractional 4 (22), 32 (2020).
  • [23] P. Navrátil, L. Pekař and R. Matušů, “Control of a multivariable system using optimal control pairs: a quadruple-tank process”, IEEE Access 8, 2537–2563 (2020).
  • [24] M. Jiang, B. Jiang, and Q. Wang, “Internal model control for rank-deficient system with time delays based on damped pseudo-inverse”, Processes 7 (5), 264, 15 (2019).
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-05408538-e95e-486a-998b-55b6b2d463b8
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