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Bifurcation structure of steady-states for bistable equations with nonlocal constraint
Existence of sliding motions for nonlinear evolution equations in Banach spaces
1. | Free University of Bolzano/Bozen, Piazza Università 1, 39100 Bolzano, Italy |
References:
[1] |
G. Bartolini and T. Zolezzi, Control of nonlinear variable structure systems,, J. Math. Anal. Appl., 118 (1986), 42.
|
[2] |
S. Drakunov and Ü. Özgüner, Generalized sliding modes for manifold control of distributed parameter systems,, in, 193 (1994), 109. Google Scholar |
[3] |
S. V. Drakunov and V. I. Utkin, Sliding mode control in dynamic systems,, Internat. J. Control, 55 (1992), 1029.
|
[4] |
A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides,", Mathematics and its Applications (Soviet Series), (1988).
|
[5] |
P. Grisvard, "Elliptic Problems in Nonsmooth Domains,", Monographs and Studies in Mathematics, (1985).
|
[6] |
L. Levaggi, Infinite dimensional systems' sliding motions,}, Eur. J. Control, 8 (2002), 508. Google Scholar |
[7] |
L. Levaggi, Sliding modes in Banach spaces,, Differ. Integral Equ., 15 (2002), 167.
|
[8] |
L. Levaggi, High-gain feedback and sliding modes in infinite dimensional systems,, Control Cybernet., 33 (2004), 33.
|
[9] |
L. Levaggi, Variable structure control for parabolic evolution equations,, in, (2005), 1234. Google Scholar |
[10] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires,", (French) Dunod; Gauthier-Villars, (1969).
|
[11] |
J. L. Lions, "Optimal Control of Systems Governed by Partial Differential Equations,", Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, (1971).
|
[12] |
Y. Orlov, Discontinuous unit feedback control of uncertain infinite-dimensional systems,, IEEE Trans. Automat. Control, 45 (2000), 834.
|
[13] |
Y. Orlov and D. Dochain, Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor,, IEEE Trans. Automat. Control, 47 (2002), 1293.
|
[14] |
Y. Orlov, Y. Lou and Panagiotis D. Christofides, Robust stabilization of infinite-dimensional systems using sliding-mode output feedback control,, Internat. J. Control, 77 (2004), 1115.
|
[15] |
Y. Orlov, A. Pisano and E. Usai, Continuous state-feedback tracking of an uncertain heat diffusion process,, Systems Control Lett., 59 (2010), 754.
|
[16] |
Y. Orlov and V. Utkin, Use of sliding modes in distributed system control problems,, Automat. Remote Control, 43 (1982), 1127.
|
[17] |
Y. Orlov and V. Utkin, Sliding mode control in indefinite-dimensional systems,, Automatica J. IFAC, 23 (1987), 753.
|
[18] |
Y. Orlov and V. Utkin, Unit sliding mode control in infinite-dimensional systems,, Adaptive learning and control using sliding modes. Appl. Math. Comput. Sci., 8 (1998), 7.
|
[19] |
A. Pisano, Y. Orlov and E. Usai, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques,, SIAM J. Control Optim., 49 (2011), 363.
|
[20] |
R. E. Showalter, "Monotone Operators in Banach Space and Nonlinear Partial Differential Equations,", Mathematical Surveys and Monographs, (1997).
|
[21] |
V. Utkin, "Sliding Modes in Control and Optimization,", Communications and Control Engineering Series, (1992).
|
[22] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. II/A,", Linear monotone operators. Translated from the German by the author and Leo F. Boron. Springer-Verlag, (1990).
|
[23] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. II/B,", Nonlinear monotone operators. Translated from the German by the author and Leo F. Boron. Springer-Verlag, (1990).
|
[24] |
T. Zolezzi, Variable structure control of semilinear evolution equations,, in, (1989), 997.
|
show all references
References:
[1] |
G. Bartolini and T. Zolezzi, Control of nonlinear variable structure systems,, J. Math. Anal. Appl., 118 (1986), 42.
|
[2] |
S. Drakunov and Ü. Özgüner, Generalized sliding modes for manifold control of distributed parameter systems,, in, 193 (1994), 109. Google Scholar |
[3] |
S. V. Drakunov and V. I. Utkin, Sliding mode control in dynamic systems,, Internat. J. Control, 55 (1992), 1029.
|
[4] |
A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides,", Mathematics and its Applications (Soviet Series), (1988).
|
[5] |
P. Grisvard, "Elliptic Problems in Nonsmooth Domains,", Monographs and Studies in Mathematics, (1985).
|
[6] |
L. Levaggi, Infinite dimensional systems' sliding motions,}, Eur. J. Control, 8 (2002), 508. Google Scholar |
[7] |
L. Levaggi, Sliding modes in Banach spaces,, Differ. Integral Equ., 15 (2002), 167.
|
[8] |
L. Levaggi, High-gain feedback and sliding modes in infinite dimensional systems,, Control Cybernet., 33 (2004), 33.
|
[9] |
L. Levaggi, Variable structure control for parabolic evolution equations,, in, (2005), 1234. Google Scholar |
[10] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires,", (French) Dunod; Gauthier-Villars, (1969).
|
[11] |
J. L. Lions, "Optimal Control of Systems Governed by Partial Differential Equations,", Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, (1971).
|
[12] |
Y. Orlov, Discontinuous unit feedback control of uncertain infinite-dimensional systems,, IEEE Trans. Automat. Control, 45 (2000), 834.
|
[13] |
Y. Orlov and D. Dochain, Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor,, IEEE Trans. Automat. Control, 47 (2002), 1293.
|
[14] |
Y. Orlov, Y. Lou and Panagiotis D. Christofides, Robust stabilization of infinite-dimensional systems using sliding-mode output feedback control,, Internat. J. Control, 77 (2004), 1115.
|
[15] |
Y. Orlov, A. Pisano and E. Usai, Continuous state-feedback tracking of an uncertain heat diffusion process,, Systems Control Lett., 59 (2010), 754.
|
[16] |
Y. Orlov and V. Utkin, Use of sliding modes in distributed system control problems,, Automat. Remote Control, 43 (1982), 1127.
|
[17] |
Y. Orlov and V. Utkin, Sliding mode control in indefinite-dimensional systems,, Automatica J. IFAC, 23 (1987), 753.
|
[18] |
Y. Orlov and V. Utkin, Unit sliding mode control in infinite-dimensional systems,, Adaptive learning and control using sliding modes. Appl. Math. Comput. Sci., 8 (1998), 7.
|
[19] |
A. Pisano, Y. Orlov and E. Usai, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques,, SIAM J. Control Optim., 49 (2011), 363.
|
[20] |
R. E. Showalter, "Monotone Operators in Banach Space and Nonlinear Partial Differential Equations,", Mathematical Surveys and Monographs, (1997).
|
[21] |
V. Utkin, "Sliding Modes in Control and Optimization,", Communications and Control Engineering Series, (1992).
|
[22] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. II/A,", Linear monotone operators. Translated from the German by the author and Leo F. Boron. Springer-Verlag, (1990).
|
[23] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. II/B,", Nonlinear monotone operators. Translated from the German by the author and Leo F. Boron. Springer-Verlag, (1990).
|
[24] |
T. Zolezzi, Variable structure control of semilinear evolution equations,, in, (1989), 997.
|
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