Minimum energy control of fractional positive electrical circuits

Open access

Abstract

Minimum energy control problem for the fractional positive electrical circuits is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by an example of fractional positive electrical circuit.

[1] Busłowicz M., Stability of linear continuous time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci. Tech. 56(4): 319-324 (2008).

[2] Dzieliński A., Sierociuk D., Sarwas G., Ultracapacitor parameters identification based on fractional order model, Proc ECC’09, Budapest (2009).

[3] Farina L., Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, NY, (2000).

[4] Kaczorek T., Polynomial approach to fractional descriptor electrical circuits, Computational Models for Business and Engineering Domains - ITHEA, Rzeszow, Poland (2014).

[5] Kaczorek T., Asymptotic stability of positive fractional 2D linear systems, Bull. Pol. Acad. Sci. Tech. 57(3): 289-292 (2009).

[6] Kaczorek T., Fractional positive continuous-time systems and their Reachability, Int. J. Appl. Math. Comput. Sci. 18(2): 223-228 (2008).

[7] Kaczorek T., Positive 1D and 2D systems, Springer Verlag, London (2001).

[8] Kaczorek T., Controllability and observability of linear electrical circuits, Electrical Review 87(9a): 248-254 (2011).

[9] Kaczorek T., Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 5(2): 42-51 (2011).

[10] Kaczorek T., Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems 58(6): 1203-1210 (2011).

[11] Kaczorek T., Practical stability of positive fractional discrete-time linear systems, Bull. Pol. Acad. Sci. Tech. 56(4): 313-317 (2008).

[12] Kaczorek T., Reachability and controllability to zero tests for standard and positive fractional discrete- time systems, Journal Européen des Systèmes Automatisés, JESA, 42(6-8): 769-787 (2008).

[13] Kaczorek T., Linear Control Systems, Research Studies Press and Wiley J., New York (1992).

[14] Kaczorek T., Minimum energy control of fractional positive continuous-time linear systems, submitted to Conf. MMAR (2013).

[15] Kaczorek T., Checking of the positivity of descriptor linear systems by the use of the shufflealgorithm, Archive of Control Sciences 21(3): 287-298 (2011).

[16] Kaczorek T., Minimum energy control of descriptor positive discrete-time linear systems, submitted to Compel, (2013).

[17] Kaczorek T., Minimum energy control of positive discrete-time linear systems with bounded inputs, Archives of Control Sciences 23(2): 205-211 (2013).

[18] Kaczorek T., Minimum energy control of positive continuous-time linear systems with bounded inputs, Archives of Electrical Engineering 63(1): 19-27 (2014).

[19] Kaczorek T., An extension of Klamka’s method of minimum energy control to fractional positive discrete- time linear systems with bounded inputs, Bull. Pol. Acad. Sci. Tech. 62(2): 227-231 (2014).

[20] Kaczorek T., Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin (2012).

[21] Kaczorek T., Klamka J., Minimum energy control of 2D linear systems with variable coefficients, Int. J. of Control 44(3): 645-650 (1986).

[22] Klamka J., Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht (1991).

[23] Klamka J., Minimum energy control of 2D systems in Hilbert spaces, System Sciences 9(1-2): 33-42 (1983).

[24] Klamka J., Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Trans. Autom. Contr. 21(4): 594-595 (1976).

[25] Klamka J., Controllability and minimum energy control problem of fractional discrete-time systems, Chapter in “New Trends in Nanotechology and Fractional Calculus”, Eds. Baleanu D., Guvenc Z.B., Tenreiro Machado J.A., Springer-Verlag, New York, 503-509 (2010).

[26] Oldham K. B., Spanier J., The Fractional Calculus, Academic Press, New York (1974).

[27] Ostalczyk P., Epitome of the fractional calculus: Theory and its Applications in Automatics, Wydawnictwo Politechniki Łódzkiej, Łódź (2008) (in Polish).

[28] Podlubny I., Fractional Differential Equations, Academic Press, San Diego (1999).

[29] Radwan A.G., Soliman A.M., Elwakil A.S., Sedeek A., On the stability of linear systems with fractional-order elements, Chaos, Solitones and Fractals 40(5): 2317-2328 (2009).

[30] Solteiro Pires E.J., Tenreiro Machado J.A., Moura Oliveira P.B., Fractional dynamics in genetic algorithms, Workshop on Fractional Differenation and its Application 2: 414-419 (2006).

Archives of Electrical Engineering

The Journal of Polish Academy of Sciences

Journal Information


CiteScore 2016: 0.71

SCImago Journal Rank (SJR) 2016: 0.238
Source Normalized Impact per Paper (SNIP) 2016: 0.535

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 147 146 12
PDF Downloads 64 63 4