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Kurzweil integral representation of interacting Prandtl-Ishlinskii operators
1. | Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1 |
2. | Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030 |
3. | MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland |
4. | Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75025, United States |
References:
[1] |
, The Science of Hysteresis (eds. I. Mayergoyz and G. Bertotti),, Elsevier, (2005).
|
[2] |
F. Al-Bender, V. Lampaert and J. Swevers, The generalized Maxwell-slip model: A novel model for friction simulation and compensation, IEEE Trans. Automat. Control, 50 (2005), 1883-1887.
doi: 10.1109/TAC.2005.858676. |
[3] |
G. Aumann, Reelle Funktionen, (German) [Real Functions], Springer, Berlin, 1954. |
[4] |
A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008.
doi: 10.1017/CBO9780511791383. |
[5] |
G. Bertotti, V. Basso, M. LoBue and A. Magni, Thermodynamics, hysteresis, and micromagnetics, in The Science of Hysteresis (eds. I. Mayergoyz and G. Bertotti), Elsevier, (2006), Vol. II, Chapter 1, 1-106.
doi: 10.1016/B978-012480874-4/50012-9. |
[6] |
M. Brokate, On the moving Preisach model, Math. Methods Appl. Sci., 15 (1992), 145-157.
doi: 10.1002/mma.1670150302. |
[7] |
M. Brokate, P. Krejčí and D. Rachinskii, Some analytical properties of the multidimensional continuous Mroz model of plasticity, Control Cybernet, 27 (1998), 199-215. |
[8] |
M. Brokate, A. Pokrovskii and D. Rachinskii, Asymptotic stability of continuum sets of periodic solutions to systems with hysteresis, J. Math. Anal. Appl., 319 (2006), 94-109.
doi: 10.1016/j.jmaa.2006.02.060. |
[9] |
M. Brokate, A. Pokrovskii, D. Rachinskii and O. Rasskazov, Differential equations with hysteresis via a canonical example, in The Science of Hysteresis (eds. I. Mayergoyz and G. Bertotti), Elsevier, 1 (2006), 125-291.
doi: 10.1016/B978-012480874-4/50005-1. |
[10] |
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, 1996.
doi: 10.1007/978-1-4612-4048-8. |
[11] |
D. Davino, P. Krejčí and C. Visone, Fully coupled modeling of magneto-mechanical hysteresis through 'thermodynamic' compatibility, Smart Mater. Struct., 22 (2013), 095009.
doi: 10.1088/0964-1726/22/9/095009. |
[12] |
M. A. Janaideh, S. Rakheja and C.-Y. Su, An analytical generalized Prandtl-Ishlinskii model inversion for hysteresis compensation in micropositioning control, IEEE/ASME Trans. Mechatronics, 16 (2011), 734-744.
doi: 10.1109/TMECH.2010.2052366. |
[13] |
M. Krasnosel'skii and A. Pokrovskii, Systems with Hysteresis, Springer, 1989.
doi: 10.1007/978-3-642-61302-9. |
[14] |
A. Krasnosel'skii and D. Rachinskii, Bifurcation of forced periodic oscillations for equations with Preisach hysteresis, J. Phys.: Conf. Ser., 22 (2005), 93-102.
doi: 10.1088/1742-6596/22/1/006. |
[15] |
A. Krasnosel'skii and D. Rachinskii, On a bifurcation governed by hysteresis nonlinearity, NoDEA Nonlinear Differ. Equ. Appl., 9 (2002), 93-115.
doi: 10.1007/s00030-002-8120-2. |
[16] |
P. Krejčí, The Kurzweil integral with exclusion of negligible sets, Math. Bohem., 128 (2003), 277-292. |
[17] |
P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakkōtosho, 1996. |
[18] |
P. Krejčí and K. Kuhnen, Inverse control of systems with hysteresis and creep, IEE P-Contr. Theor. Ap., 148 (2001), 185-192. |
[19] |
P. Krejčí and J. Kurzweil, A nonexistence result for the Kurzweil integral, Math. Bohem., 127 (2002), 571-580. |
[20] |
P. Krejčí, H. Lamba, S. Melnik and D. Rachinskii, Analytical solution for a class of network dynamics with mechanical and financial applications, Phys. Rev. E, 90 (2014), 032822. |
[21] |
P. Krejčí and Ph. Laurençot, Generalized variational inequalities, J. Convex Anal., 9 (2002), 159-183. |
[22] |
P. Krejčí, J. P. O'Kane, A. Pokrovskii and D. Rachinskii}, Properties of solutions to a class of differential models incorporating Preisach hysteresis operator, Phys. D, 241 (2012), 2010-2028.
doi: 10.1016/j.physd.2011.05.005. |
[23] |
P. Krejčí, J. P. O'Kane, A. Pokrovskii and D. Rachinskii, Stability results for a soil model with singular hysteretic hydrology, J. Phys.: Conf. Ser. 268 (2011), 012016. |
[24] |
K. Kuhnen, Modeling, identification and compensation of complex hysteretic nonlinearities: A modified Prandtl-Ishlinskii approach, Eur. J. Control, 9 (2003), 407-418.
doi: 10.3166/ejc.9.407-418. |
[25] |
J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J., 7 (1957), 418-449. |
[26] |
Lemaitre and J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, Cambridge, 1990. |
[27] |
I. Mayergoyz, Mathematical Models of Hysteresis and Their Applications, Elsevier, 2003. |
[28] |
L. Prandtl, Ein Gedankenmodell zur kinetischen Theorie der festen Körper, (German) [A model for kinetic theory of solid bodies], ZAMM Z. Ang. Math. Mech., 8 (1928), 85-106. |
[29] |
Š. Schwabik, On a modified sum integral of Stieltjes type, Časopis Pěst. Mat., 98 (1973), 274-277. |
[30] |
M. Tvrdý, Regulated functions and the Perron-Stieltjes integral, Časopis Pêst. Mat., 114 (1989), 187-209. |
[31] |
A. Visintin, Differential Models of Hysteresis, Springer, 1994.
doi: 10.1007/978-3-662-11557-2. |
show all references
References:
[1] |
, The Science of Hysteresis (eds. I. Mayergoyz and G. Bertotti),, Elsevier, (2005).
|
[2] |
F. Al-Bender, V. Lampaert and J. Swevers, The generalized Maxwell-slip model: A novel model for friction simulation and compensation, IEEE Trans. Automat. Control, 50 (2005), 1883-1887.
doi: 10.1109/TAC.2005.858676. |
[3] |
G. Aumann, Reelle Funktionen, (German) [Real Functions], Springer, Berlin, 1954. |
[4] |
A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008.
doi: 10.1017/CBO9780511791383. |
[5] |
G. Bertotti, V. Basso, M. LoBue and A. Magni, Thermodynamics, hysteresis, and micromagnetics, in The Science of Hysteresis (eds. I. Mayergoyz and G. Bertotti), Elsevier, (2006), Vol. II, Chapter 1, 1-106.
doi: 10.1016/B978-012480874-4/50012-9. |
[6] |
M. Brokate, On the moving Preisach model, Math. Methods Appl. Sci., 15 (1992), 145-157.
doi: 10.1002/mma.1670150302. |
[7] |
M. Brokate, P. Krejčí and D. Rachinskii, Some analytical properties of the multidimensional continuous Mroz model of plasticity, Control Cybernet, 27 (1998), 199-215. |
[8] |
M. Brokate, A. Pokrovskii and D. Rachinskii, Asymptotic stability of continuum sets of periodic solutions to systems with hysteresis, J. Math. Anal. Appl., 319 (2006), 94-109.
doi: 10.1016/j.jmaa.2006.02.060. |
[9] |
M. Brokate, A. Pokrovskii, D. Rachinskii and O. Rasskazov, Differential equations with hysteresis via a canonical example, in The Science of Hysteresis (eds. I. Mayergoyz and G. Bertotti), Elsevier, 1 (2006), 125-291.
doi: 10.1016/B978-012480874-4/50005-1. |
[10] |
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, 1996.
doi: 10.1007/978-1-4612-4048-8. |
[11] |
D. Davino, P. Krejčí and C. Visone, Fully coupled modeling of magneto-mechanical hysteresis through 'thermodynamic' compatibility, Smart Mater. Struct., 22 (2013), 095009.
doi: 10.1088/0964-1726/22/9/095009. |
[12] |
M. A. Janaideh, S. Rakheja and C.-Y. Su, An analytical generalized Prandtl-Ishlinskii model inversion for hysteresis compensation in micropositioning control, IEEE/ASME Trans. Mechatronics, 16 (2011), 734-744.
doi: 10.1109/TMECH.2010.2052366. |
[13] |
M. Krasnosel'skii and A. Pokrovskii, Systems with Hysteresis, Springer, 1989.
doi: 10.1007/978-3-642-61302-9. |
[14] |
A. Krasnosel'skii and D. Rachinskii, Bifurcation of forced periodic oscillations for equations with Preisach hysteresis, J. Phys.: Conf. Ser., 22 (2005), 93-102.
doi: 10.1088/1742-6596/22/1/006. |
[15] |
A. Krasnosel'skii and D. Rachinskii, On a bifurcation governed by hysteresis nonlinearity, NoDEA Nonlinear Differ. Equ. Appl., 9 (2002), 93-115.
doi: 10.1007/s00030-002-8120-2. |
[16] |
P. Krejčí, The Kurzweil integral with exclusion of negligible sets, Math. Bohem., 128 (2003), 277-292. |
[17] |
P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakkōtosho, 1996. |
[18] |
P. Krejčí and K. Kuhnen, Inverse control of systems with hysteresis and creep, IEE P-Contr. Theor. Ap., 148 (2001), 185-192. |
[19] |
P. Krejčí and J. Kurzweil, A nonexistence result for the Kurzweil integral, Math. Bohem., 127 (2002), 571-580. |
[20] |
P. Krejčí, H. Lamba, S. Melnik and D. Rachinskii, Analytical solution for a class of network dynamics with mechanical and financial applications, Phys. Rev. E, 90 (2014), 032822. |
[21] |
P. Krejčí and Ph. Laurençot, Generalized variational inequalities, J. Convex Anal., 9 (2002), 159-183. |
[22] |
P. Krejčí, J. P. O'Kane, A. Pokrovskii and D. Rachinskii}, Properties of solutions to a class of differential models incorporating Preisach hysteresis operator, Phys. D, 241 (2012), 2010-2028.
doi: 10.1016/j.physd.2011.05.005. |
[23] |
P. Krejčí, J. P. O'Kane, A. Pokrovskii and D. Rachinskii, Stability results for a soil model with singular hysteretic hydrology, J. Phys.: Conf. Ser. 268 (2011), 012016. |
[24] |
K. Kuhnen, Modeling, identification and compensation of complex hysteretic nonlinearities: A modified Prandtl-Ishlinskii approach, Eur. J. Control, 9 (2003), 407-418.
doi: 10.3166/ejc.9.407-418. |
[25] |
J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J., 7 (1957), 418-449. |
[26] |
Lemaitre and J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, Cambridge, 1990. |
[27] |
I. Mayergoyz, Mathematical Models of Hysteresis and Their Applications, Elsevier, 2003. |
[28] |
L. Prandtl, Ein Gedankenmodell zur kinetischen Theorie der festen Körper, (German) [A model for kinetic theory of solid bodies], ZAMM Z. Ang. Math. Mech., 8 (1928), 85-106. |
[29] |
Š. Schwabik, On a modified sum integral of Stieltjes type, Časopis Pěst. Mat., 98 (1973), 274-277. |
[30] |
M. Tvrdý, Regulated functions and the Perron-Stieltjes integral, Časopis Pêst. Mat., 114 (1989), 187-209. |
[31] |
A. Visintin, Differential Models of Hysteresis, Springer, 1994.
doi: 10.1007/978-3-662-11557-2. |
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