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On observers and compensators for infinite dimensional semilinear systems
1. | Département de Mathématiques, Université Chouaib Doukkali, Faculté des Sciences, BP 20 El Jadida 24000, Morocco |
References:
[1] |
B. Abouzaid, M. E. Achhab and V. Wertz, Regulator problem for infinite-dimensional linear systems with constraints on control and its rate, European Journal of Control, 17 (2011), 183-190.
doi: 10.3166/ejc.17.183-190. |
[2] |
B. Abouzaid, M. E. Achhab and V. Wertz, Stabilization of a class of partially observed infinite-dimensional systems with control constraints, IMA Journal of Mathematical Control and Information, 26 (2009), 79-94.
doi: 10.1093/imamci/dnn014. |
[3] |
M. E. Achhab, M. Laabissi, J. Winkin and D. Dochain, State trajectory analysis of plug flow nonisothermal reactors using a nonlinear model, Proceedings of the 38th IEEE Conference on Decision and Control. Vol. 1, IEEE, Phoenix, AZ, USA, 1999, 663-667.
doi: 10.1109/CDC.1999.832862. |
[4] |
M. E. Achhab and M. Laabissi, Feedback stabilization of a class of distributed parameter systems with control constraints, Systems & Control Letters, 45 (2002), 163-171.
doi: 10.1016/S0167-6911(01)00171-2. |
[5] |
M. E. Achhab and V. Wertz, On stabilization of partially observed infinite-dimensional semilinear systems, in 1st IFAC Workshop on Control of Systems Modeled by Partial Differential Equations CPDE. Vol. 1, Paris, France, 2013, 161-166.
doi: 10.3182/20130925-3-FR-4043.00040. |
[6] |
I. Aksikas, J. Winkin and D. Dochain, Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor, Systems & Control Letters, 56 (2007), 122-132.
doi: 10.1016/j.sysconle.2006.08.012. |
[7] |
R. Al-Saphory and and A. El Jai, Sensors and asymptotic $\omega$-observer for distributed diffusion systems, Sensors, 1 (2001), 161-182. |
[8] |
B. Aylaj, M. E. Achhab and M. Laabissi, Asymptotic behaviour of state trajectories for a class of tubular reactor nonlinear models, IMA Journal of Mathematical Control and Information, 24 (2007), 163-175.
doi: 10.1093/imamci/dnl013. |
[9] |
N. Barje, M. E. Achhab and V. Wertz, Exponential observer for a class of nonlinear distributed parameter systems with application to a nonisothermal tubular reactor, in Proceedings of the 5th International Conference on informatics in Control, Automation & Robotics (ICINCO), Funchal, Madiera, Portugal, May 2008. |
[10] |
N. Barje, M. E. Achhab and V. Wertz, State observers for a class of semilinear infinite-dimensional systems, International Journal of Mathematics & Statistics, 4 (2009), 69-72. |
[11] |
T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford University Press, New York, 1998. |
[12] |
S. Cherkaoui and A. El jai, Consistent estimators for a class of distributed stochastic systems, in Proceedings of the 3rd IFAC Symposium on Control of Distributed parameter Systems, Toulouse, France, 1983, 409-412. |
[13] |
S. Cherkaoui and M. E. Achhab, State estimation for partially observed evolution equations systems with state dependent noise, Preprints of IFAC 9th World Congress. VI, Budapest, Hungary, July 1984, 21-26. |
[14] |
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory, Lecture Notes in Control & Information Sciences, 8, Springer-Verlag, Berlin-New York, 1978. |
[15] |
R. F. Curtain, Finite dimensional compensators for prabonic distributed systems with unbounded control and observation, SIAM J. Control & Optimization, 22 (1984), 255-276.
doi: 10.1137/0322018. |
[16] |
R. F. Curtain and D. Salomon, Finite dimensional compensators for infinite dimensional systems with unbounded input operators, SIAM J. Control & Optimization, 24 (1986), 797-816.
doi: 10.1137/0324050. |
[17] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite-dimensional Linear Systems Theory, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4224-6. |
[18] |
A. El Jai and M. Amouroux, Sur la détermination d'un observateur de dimension finie pour une classe de systèemes linéaires à paramètres répartis, C. R. Acad. Sc. Paris, Série A, 287 (1978), A163-A166. |
[19] |
A. El Jai, M. Amouroux and S. Cherkaoui, A modified Luenberger observer for parabolic systems, in Proceedings of the 8th IFAC World Congress, Kyoto, Japan, 1981. |
[20] |
R. V. Gressang and G. B. Lamont, Observers for systems chracterized by semi-groups, IEEE Trans. Autom. Control, 20 (1975), 523-528. |
[21] |
M. Laabissi, M. E. Achhab, J. J. Winkin and D. Dochain, Trajectory analysis of nonisothermal tubular reactor nonlinear models, Systems & Control Letters, 42 (2001), 169-184.
doi: 10.1016/S0167-6911(00)00088-8. |
[22] |
M. Laabissi, M. E. Achhab, J. J. Winkin and D. Dochain, Multiple equilibrium profiles for nonisothermal tubular reactor nonlinear models, Dynamics of Continuous, Discrete and Impulsive Systems - B, 11 (2004), 339-352. |
[23] |
R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976. |
[24] |
R. Nagel, ed., One-Parameter Semigroups of Positive Operators, Lecture Notes in Mathematics, 1184, Springer-Verlag, New York, 1986. |
[25] |
A. Namir, A. Bennar and M. Laklalech, Asymptotic estimation for retarded stochastic systems, International J. of Pure & Applied Mathematics, 41 (2007), 637-646. |
[26] |
C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. |
[27] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[28] |
J. M. Schumacher, Dynamic Feedback in Finite and Infinite Dimensional Linear Systems, Mathematical Center Tracts, 143, Mathematish Centrum, Amsterdam, 1981. |
[29] |
J. M. Schumacher, A direct approach to compensator design for distributed parameter systems, SIAM J. Control & Optimization, 21 (1983), 823-836.
doi: 10.1137/0321050. |
[30] |
I. Smets, D. Dochain and J. van Impe, Optimal temperature control of a steady-state exothermic plug flow reactor, AIChE Journal, 48 (2002), 279-286.
doi: 10.1002/aic.690480212. |
[31] |
M. Slemrod, Feedback stabilization of a linear control system in Hilbert space with a priori bounded control, Math. Control Signals Syst., 2 (1989), 265-285.
doi: 10.1007/BF02551387. |
[32] |
J. Winkin, D. Dochain and P. Ligarius., Dynamical analysis of distributed parameter tubular reactors, Automatica, 36 (2000), 349-361.
doi: 10.1016/S0005-1098(99)00170-3. |
show all references
References:
[1] |
B. Abouzaid, M. E. Achhab and V. Wertz, Regulator problem for infinite-dimensional linear systems with constraints on control and its rate, European Journal of Control, 17 (2011), 183-190.
doi: 10.3166/ejc.17.183-190. |
[2] |
B. Abouzaid, M. E. Achhab and V. Wertz, Stabilization of a class of partially observed infinite-dimensional systems with control constraints, IMA Journal of Mathematical Control and Information, 26 (2009), 79-94.
doi: 10.1093/imamci/dnn014. |
[3] |
M. E. Achhab, M. Laabissi, J. Winkin and D. Dochain, State trajectory analysis of plug flow nonisothermal reactors using a nonlinear model, Proceedings of the 38th IEEE Conference on Decision and Control. Vol. 1, IEEE, Phoenix, AZ, USA, 1999, 663-667.
doi: 10.1109/CDC.1999.832862. |
[4] |
M. E. Achhab and M. Laabissi, Feedback stabilization of a class of distributed parameter systems with control constraints, Systems & Control Letters, 45 (2002), 163-171.
doi: 10.1016/S0167-6911(01)00171-2. |
[5] |
M. E. Achhab and V. Wertz, On stabilization of partially observed infinite-dimensional semilinear systems, in 1st IFAC Workshop on Control of Systems Modeled by Partial Differential Equations CPDE. Vol. 1, Paris, France, 2013, 161-166.
doi: 10.3182/20130925-3-FR-4043.00040. |
[6] |
I. Aksikas, J. Winkin and D. Dochain, Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor, Systems & Control Letters, 56 (2007), 122-132.
doi: 10.1016/j.sysconle.2006.08.012. |
[7] |
R. Al-Saphory and and A. El Jai, Sensors and asymptotic $\omega$-observer for distributed diffusion systems, Sensors, 1 (2001), 161-182. |
[8] |
B. Aylaj, M. E. Achhab and M. Laabissi, Asymptotic behaviour of state trajectories for a class of tubular reactor nonlinear models, IMA Journal of Mathematical Control and Information, 24 (2007), 163-175.
doi: 10.1093/imamci/dnl013. |
[9] |
N. Barje, M. E. Achhab and V. Wertz, Exponential observer for a class of nonlinear distributed parameter systems with application to a nonisothermal tubular reactor, in Proceedings of the 5th International Conference on informatics in Control, Automation & Robotics (ICINCO), Funchal, Madiera, Portugal, May 2008. |
[10] |
N. Barje, M. E. Achhab and V. Wertz, State observers for a class of semilinear infinite-dimensional systems, International Journal of Mathematics & Statistics, 4 (2009), 69-72. |
[11] |
T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford University Press, New York, 1998. |
[12] |
S. Cherkaoui and A. El jai, Consistent estimators for a class of distributed stochastic systems, in Proceedings of the 3rd IFAC Symposium on Control of Distributed parameter Systems, Toulouse, France, 1983, 409-412. |
[13] |
S. Cherkaoui and M. E. Achhab, State estimation for partially observed evolution equations systems with state dependent noise, Preprints of IFAC 9th World Congress. VI, Budapest, Hungary, July 1984, 21-26. |
[14] |
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory, Lecture Notes in Control & Information Sciences, 8, Springer-Verlag, Berlin-New York, 1978. |
[15] |
R. F. Curtain, Finite dimensional compensators for prabonic distributed systems with unbounded control and observation, SIAM J. Control & Optimization, 22 (1984), 255-276.
doi: 10.1137/0322018. |
[16] |
R. F. Curtain and D. Salomon, Finite dimensional compensators for infinite dimensional systems with unbounded input operators, SIAM J. Control & Optimization, 24 (1986), 797-816.
doi: 10.1137/0324050. |
[17] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite-dimensional Linear Systems Theory, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4224-6. |
[18] |
A. El Jai and M. Amouroux, Sur la détermination d'un observateur de dimension finie pour une classe de systèemes linéaires à paramètres répartis, C. R. Acad. Sc. Paris, Série A, 287 (1978), A163-A166. |
[19] |
A. El Jai, M. Amouroux and S. Cherkaoui, A modified Luenberger observer for parabolic systems, in Proceedings of the 8th IFAC World Congress, Kyoto, Japan, 1981. |
[20] |
R. V. Gressang and G. B. Lamont, Observers for systems chracterized by semi-groups, IEEE Trans. Autom. Control, 20 (1975), 523-528. |
[21] |
M. Laabissi, M. E. Achhab, J. J. Winkin and D. Dochain, Trajectory analysis of nonisothermal tubular reactor nonlinear models, Systems & Control Letters, 42 (2001), 169-184.
doi: 10.1016/S0167-6911(00)00088-8. |
[22] |
M. Laabissi, M. E. Achhab, J. J. Winkin and D. Dochain, Multiple equilibrium profiles for nonisothermal tubular reactor nonlinear models, Dynamics of Continuous, Discrete and Impulsive Systems - B, 11 (2004), 339-352. |
[23] |
R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976. |
[24] |
R. Nagel, ed., One-Parameter Semigroups of Positive Operators, Lecture Notes in Mathematics, 1184, Springer-Verlag, New York, 1986. |
[25] |
A. Namir, A. Bennar and M. Laklalech, Asymptotic estimation for retarded stochastic systems, International J. of Pure & Applied Mathematics, 41 (2007), 637-646. |
[26] |
C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. |
[27] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[28] |
J. M. Schumacher, Dynamic Feedback in Finite and Infinite Dimensional Linear Systems, Mathematical Center Tracts, 143, Mathematish Centrum, Amsterdam, 1981. |
[29] |
J. M. Schumacher, A direct approach to compensator design for distributed parameter systems, SIAM J. Control & Optimization, 21 (1983), 823-836.
doi: 10.1137/0321050. |
[30] |
I. Smets, D. Dochain and J. van Impe, Optimal temperature control of a steady-state exothermic plug flow reactor, AIChE Journal, 48 (2002), 279-286.
doi: 10.1002/aic.690480212. |
[31] |
M. Slemrod, Feedback stabilization of a linear control system in Hilbert space with a priori bounded control, Math. Control Signals Syst., 2 (1989), 265-285.
doi: 10.1007/BF02551387. |
[32] |
J. Winkin, D. Dochain and P. Ligarius., Dynamical analysis of distributed parameter tubular reactors, Automatica, 36 (2000), 349-361.
doi: 10.1016/S0005-1098(99)00170-3. |
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