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Multivariable boundary PI control and regulation of a fluid flow system
1. | Université de Lyon, LAGEP, Bât. CPE, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France |
2. | Université de Lorraine and Inria Nancy-Grand Est, Bâtiment A, Ile du Saulcy, F-57045 Metz, France |
References:
[1] |
G. Bastin and J. M. Coron, On boundary feedback stabilization of non-uniform linear $2 \times 2$ hyperbolic systems over a bounded interval, Systems & Control Letters, 60 (2011), 900-906.
doi: 10.1016/j.sysconle.2011.07.008. |
[2] |
H. Bounit, H. Hammouri and J. Sau, Regulation of an irrigation channel through the semigroup approach, Proceedings of the workshop on Regulation and Irrigation Canals, (1997), 261-267, Marrakesh, Maroc. |
[3] |
J. M. Coron, B. d'Andréa-Novel and G. Bastin, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Transactions on Automatic Control, 52 ( 2007), 2-11.
doi: 10.1109/TAC.2006.887903. |
[4] |
E. J. Davison, The robust control of a servomechanism problem for linear time-invariant multivariable systems, IEEE Transactions Automatic Control, 21 (1976), 25-34. |
[5] |
V. Dos Santos and C. Prieur, Boundary control of open channels with numerical and experimental validations, IEEE Transactions on Control Systems Technolgy, 16 (2008), 1252-1264. |
[6] |
D. Georegs, Infinite-dimensional nonlinear predictive control design for open hydraulic systems, Networks and Heterogeneous Media - American Institute of Mathematical Sciences, 4 (2009), 267-285.
doi: 10.3934/nhm.2009.4.267. |
[7] |
J. M. Greenberg and T. T. Li, The effect of boundary damping for the quasi-linear wave equation, Journal of Differential Equations, 52 (1984), 66-75.
doi: 10.1016/0022-0396(84)90135-9. |
[8] |
F. L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. of Differential Equations, 1 (1985), 43-56. |
[9] |
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1976. |
[10] |
I. Lasiecka and R. Triggiani, Finite rank, relative bounded perturbation of semigroups - Part I : Well-posedness and boundary feedback hyperbolic dynamics, Annali Scuola Normale Superior-Pisa, Classe di Scienze, Serie IV, XII (4), 12 (1985), 641-668. |
[11] |
X. Litrico and V. Fromion, Boundary control of hyperbolic conservation laws using a frequency domain approach, Automatica, 45 (2009), 647-656.
doi: 10.1016/j.automatica.2008.09.022. |
[12] |
H. Logemann and S. Townley, Low gain control of uncertain regular linear systems, SIAM J. Control Optim., 35 (1997), 78-116.
doi: 10.1137/S0363012994275920. |
[13] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[14] |
S. A. Pohjolainen, Robust multivariable PI-controllers for infinite dimensional systems, IEEE Transaction Automatic Control, 27 (1982), 17-30.
doi: 10.1109/TAC.1982.1102887. |
[15] |
S. Pohjolainen, Robust controller for systems with exponentially stable strongly continuous semigroups, Journal of Mathematical Analysis and Applications, 111 (1985), 622-636.
doi: 10.1016/0022-247X(85)90239-2. |
[16] |
J. Prüss, On the spectrum of $C_0$- semigroups, Trans. Amer. Math. Soc., 284 (1984), 847-857.
doi: 10.2307/1999112. |
[17] |
J. Rauch and M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domain, Indiana University Mathematics Journal, 24 (1974), 79-86.
doi: 10.1512/iumj.1975.24.24004. |
[18] |
D. L. Russell, Controllability and stabilizability theory for linear partial differential equations : Recent progress and open questions, Siam Review, 20 (1978), 639-739.
doi: 10.1137/1020095. |
[19] |
D. L. Russell and G. Weiss, A general necessary condition for exact observability, SIAM J. Control and Optimization, 32 (1994), 1-23.
doi: 10.1137/S036301299119795X. |
[20] |
D. Salamon, Realization theory in Hilbert space, Math. Systems Theory, 21 (1989), 147-164.
doi: 10.1007/BF02088011. |
[21] |
M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Birkhäuser, Boston, 2009.
doi: 10.1007/978-3-7643-8994-9. |
[22] |
G. Weiss, Regular linear systems with feedback, Math. Control, Signals & Systems, 7 (1994), 23-57.
doi: 10.1007/BF01211484. |
[23] |
C. Z. Xu and D. X. Feng, Symmetric hyperbolic systems and applications to exponential stability of heat exchangers and irrigation canals, Proceedings of the Mathematical Theory of Networks and Systems, 2000, Perpignan, France. |
[24] |
C. Z. Xu and H. Jerbi, A robust PI-controller for infinite dimensional systems, Int. J. Control, 61 (1995), 33-45.
doi: 10.1080/00207179508921891. |
[25] |
C. Z. Xu and G. Sallet, Proportional and integral regulation of irrigation canal systems governed by the Saint Venant equation, Proceedings of the 14th IFAC World Congress, 1999, Beijing, China. |
[26] |
C. Z. Xu and G. Sallet, Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems, ESAIM: Control, Optimization and Calculus of Variations, 7 (2002), 421-442.
doi: 10.1051/cocv:2002062. |
show all references
References:
[1] |
G. Bastin and J. M. Coron, On boundary feedback stabilization of non-uniform linear $2 \times 2$ hyperbolic systems over a bounded interval, Systems & Control Letters, 60 (2011), 900-906.
doi: 10.1016/j.sysconle.2011.07.008. |
[2] |
H. Bounit, H. Hammouri and J. Sau, Regulation of an irrigation channel through the semigroup approach, Proceedings of the workshop on Regulation and Irrigation Canals, (1997), 261-267, Marrakesh, Maroc. |
[3] |
J. M. Coron, B. d'Andréa-Novel and G. Bastin, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Transactions on Automatic Control, 52 ( 2007), 2-11.
doi: 10.1109/TAC.2006.887903. |
[4] |
E. J. Davison, The robust control of a servomechanism problem for linear time-invariant multivariable systems, IEEE Transactions Automatic Control, 21 (1976), 25-34. |
[5] |
V. Dos Santos and C. Prieur, Boundary control of open channels with numerical and experimental validations, IEEE Transactions on Control Systems Technolgy, 16 (2008), 1252-1264. |
[6] |
D. Georegs, Infinite-dimensional nonlinear predictive control design for open hydraulic systems, Networks and Heterogeneous Media - American Institute of Mathematical Sciences, 4 (2009), 267-285.
doi: 10.3934/nhm.2009.4.267. |
[7] |
J. M. Greenberg and T. T. Li, The effect of boundary damping for the quasi-linear wave equation, Journal of Differential Equations, 52 (1984), 66-75.
doi: 10.1016/0022-0396(84)90135-9. |
[8] |
F. L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. of Differential Equations, 1 (1985), 43-56. |
[9] |
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1976. |
[10] |
I. Lasiecka and R. Triggiani, Finite rank, relative bounded perturbation of semigroups - Part I : Well-posedness and boundary feedback hyperbolic dynamics, Annali Scuola Normale Superior-Pisa, Classe di Scienze, Serie IV, XII (4), 12 (1985), 641-668. |
[11] |
X. Litrico and V. Fromion, Boundary control of hyperbolic conservation laws using a frequency domain approach, Automatica, 45 (2009), 647-656.
doi: 10.1016/j.automatica.2008.09.022. |
[12] |
H. Logemann and S. Townley, Low gain control of uncertain regular linear systems, SIAM J. Control Optim., 35 (1997), 78-116.
doi: 10.1137/S0363012994275920. |
[13] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[14] |
S. A. Pohjolainen, Robust multivariable PI-controllers for infinite dimensional systems, IEEE Transaction Automatic Control, 27 (1982), 17-30.
doi: 10.1109/TAC.1982.1102887. |
[15] |
S. Pohjolainen, Robust controller for systems with exponentially stable strongly continuous semigroups, Journal of Mathematical Analysis and Applications, 111 (1985), 622-636.
doi: 10.1016/0022-247X(85)90239-2. |
[16] |
J. Prüss, On the spectrum of $C_0$- semigroups, Trans. Amer. Math. Soc., 284 (1984), 847-857.
doi: 10.2307/1999112. |
[17] |
J. Rauch and M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domain, Indiana University Mathematics Journal, 24 (1974), 79-86.
doi: 10.1512/iumj.1975.24.24004. |
[18] |
D. L. Russell, Controllability and stabilizability theory for linear partial differential equations : Recent progress and open questions, Siam Review, 20 (1978), 639-739.
doi: 10.1137/1020095. |
[19] |
D. L. Russell and G. Weiss, A general necessary condition for exact observability, SIAM J. Control and Optimization, 32 (1994), 1-23.
doi: 10.1137/S036301299119795X. |
[20] |
D. Salamon, Realization theory in Hilbert space, Math. Systems Theory, 21 (1989), 147-164.
doi: 10.1007/BF02088011. |
[21] |
M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Birkhäuser, Boston, 2009.
doi: 10.1007/978-3-7643-8994-9. |
[22] |
G. Weiss, Regular linear systems with feedback, Math. Control, Signals & Systems, 7 (1994), 23-57.
doi: 10.1007/BF01211484. |
[23] |
C. Z. Xu and D. X. Feng, Symmetric hyperbolic systems and applications to exponential stability of heat exchangers and irrigation canals, Proceedings of the Mathematical Theory of Networks and Systems, 2000, Perpignan, France. |
[24] |
C. Z. Xu and H. Jerbi, A robust PI-controller for infinite dimensional systems, Int. J. Control, 61 (1995), 33-45.
doi: 10.1080/00207179508921891. |
[25] |
C. Z. Xu and G. Sallet, Proportional and integral regulation of irrigation canal systems governed by the Saint Venant equation, Proceedings of the 14th IFAC World Congress, 1999, Beijing, China. |
[26] |
C. Z. Xu and G. Sallet, Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems, ESAIM: Control, Optimization and Calculus of Variations, 7 (2002), 421-442.
doi: 10.1051/cocv:2002062. |
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