A multi-model approach to Saint-Venant equations: A stability study by LMIs

Alizadeh Moghadam, A., Aksikas, I., Dubljevic, S. and Forbes, J. (2011). LQR control of an in finite dimensional timevarying CSTR-PFR system, 18th IFAC World Congress, Milan, Italy.10.3182/20110828-6-IT-1002.02195Search in Google Scholar

Athans, M., Fekri, S. and Pascoal, A. (2005). Issues on robust adaptive feedback control, Proceedings of the 16th IFAC World Congress, Prague, Czech Republic.10.3182/20050703-6-CZ-1902.01036Search in Google Scholar

Banerjee, A., Arkun, Y., Pearson, R. and Ogunnaike, B. (1995). H∞ control of nonlinear processes using multiple linear models, Proceedings of the European Control Conference, Rome, Italy, pp. 2671-2676.Search in Google Scholar

Bhagwat, A., Srinivasan, R. and Krishnaswamy, P.R. (2003). Multi-linear model-based fault detection during process transitions, Chemical Engineering Science 58: 1649-1670.10.1016/S0009-2509(03)00008-3Search in Google Scholar

Blesa, J., Puig, V. and Bolea, Y. (2010). Fault detection using interval LPV models in an open-flow canal, Control Engineering and Practice 18(5): 460-470.10.1016/j.conengprac.2010.01.002Search in Google Scholar

Cordier, S., Buet, C. and Dos Santos, V. (2004). A conservative and entropy scheme for a simplified model of granular media, Transport Theory and Statistical Physics 33(2): HYKE 2003-021.10.1081/TT-120037804Search in Google Scholar

Coron, J. M., d’Andr´ea Novel, B. and Bastin, G. (2007). A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Transactions on Automatic Control 52(1): 2-11.10.1109/TAC.2006.887903Search in Google Scholar

Curtain, R. and Zwart, H. (1995). An Introduction to Infinite Dimensional Linear Systems, Springer Verlag, New York, NY.10.1007/978-1-4612-4224-6Search in Google Scholar

Dos Santos Martins, V. and Rodrigues, M. (2011). A proportional integral feedback for open channels control trough LMI design, 18th IFAC World Congress, Milan, Italy.10.3182/20110828-6-IT-1002.01037Search in Google Scholar

Dos Santos, V. (2004). Contrˆole Fronti`ere par Mod`ele Interne de Syst`emes Hyperboliques: Application `a la R´egulation de Canaux d’Irrigation, Ph.D. thesis, University of Orl´eans, Orl´eans.Search in Google Scholar

Dos Santos, V., Bastin, G., Coron, J.-M. and d’Andr´ea Novel, B. (2008). Boundary control with integral action for hyperbolic systems of conservation laws: Lyapunov stability analysis and experimental validation, Automatica 44(5): 1310-1318.10.1016/j.automatica.2007.09.022Search in Google Scholar

Dos Santos, V. and Prieur, C. (2008). Boundary control of open channels with numerical and experimental validations, IEEE Transactions on Control Systems Technology 16(99): 1252-1264.10.1109/TCST.2008.919418Search in Google Scholar

Dos Santos, V. and Toure, Y. (2005). Irrigation multireaches regulation problem by internal model boundary control, 44th CDC-ECC05, IEEE Control Systems Society Conference, Seville, Spain, pp. 1905-1910.Search in Google Scholar

Dos Santos, V., Toure, Y., Mendes, E. and Courtial, E. (2005). Multivariable boundary control approach by internal model, applied to irrigations canals regulation, Proceedings of the 16th IFAC World Congress, Prague, Czech Republic.10.3182/20050703-6-CZ-1902.02101Search in Google Scholar

Dulhoste, J.-F., Besanc¸on, G. and Georges, D. (2001). Nonlinear control of water flow dynamics by input-output linearisation based on a collocation model, European Control Conference, Porto, Portugal.10.23919/ECC.2001.7076326Search in Google Scholar

Gatzke, E. and Doyle, F. (2002). Use of multiple models and qualitative knowledge for on-line moving horizon disturbance estimation and fault diagnosis, Journal of Process Control 12(2): 339-352.10.1016/S0959-1524(01)00037-3Search in Google Scholar

Georges (2002). Automatique pour la Gestion des Ressources en Eau, Edts IC2, Syst`emes automatis´es, Herm`es, Paris.Search in Google Scholar

Greenberg, J.-M. and Li, T. (1984). The effect of boundary damping for the quasilinear wave equations, Journal of Differential Equations 52(1): 66-75.10.1016/0022-0396(84)90135-9Search in Google Scholar

Hamdi, H., Rodrigues, M., Mechmeche, C., Theilliol, D. and Braiek, N. B. (2011). Fault detection and isolation in linear parameter varying descriptor systems via proportional integral observer, International Journal of Adaptive Control and Signal Processing 26(3): 224-240, DOI: 10.1002/acs.1260.10.1002/acs.1260Search in Google Scholar

Hante, F. and Sigalotti, M. (2010). Existence of common Lyapunov functions for infinite-dimensional switched linear systems, 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, pp. 5668-5673.Search in Google Scholar

Leith, D.J. and Leithead, W.E. (2000). Survey of gainscheduling analysis and design, International Journal of Control 73(11): 1001-1025.10.1080/002071700411304Search in Google Scholar

Li, T. (1994). Global Classical Solutions for Quasilinear Hyperbolic Systems, Research in Applied Mathematics, Masson and Wiley, Paris/Milan/Barcelona.Search in Google Scholar

Litrico, X., Fromion, V., Baume, J.-P., Arranja, C. and Rijo, M. (2005). Experimental validation of a methodology to control irrigation canals based on Saint-Venant equations, Control Engineering Practice 13(11): 1425-1437.10.1016/j.conengprac.2004.12.010Search in Google Scholar

Litrico, X. and Georges, D. (1999). Robust continuous-time and discrete-time flow control of a dam-river system, I: Modelling, Journal of Applied Mathematical Modelling 23(11): 809-827.10.1016/S0307-904X(99)00014-1Search in Google Scholar

Lopez-Toribio, C., Patton, R. and Daley, S. (1999). A mutiplemodel approach to fault-tolerant control using Takagi-Sugeno fuzzy modelling: Real application to an induction motor drive system, European Control Conference, ECC 99, Karlsruhe, Germany.10.23919/ECC.1999.7100040Search in Google Scholar

Malaterre, P.-O., Rogers, D. and Schuurmans, J. (1998). Classification of canal control algorithms, Journal of Irrigation and Drainage Engineering 124(1): 3-10.10.1061/(ASCE)0733-9437(1998)124:1(3)Search in Google Scholar

Mareels, I., Weyer, E., Ooi, S., Cantoni, M., Li, Y. and Nair, G. (2005). Systems engineering for irrigation systems: Successes and challenges, Annual Reviews in Control 29(2): 191-204.10.1016/j.arcontrol.2005.08.001Search in Google Scholar

Murray-Smith, R. and Johansen, T. (1997). Multiple Model Approaches to Modelling and Control, Taylor and Francis, London.Search in Google Scholar

Narendra, K., Balakrishnan, J. and Kermal, M. (1995). Adaptation and learning using multiple models, switching and tuning, IEEE Control Systems 15(3): 37-51.10.1109/37.387616Search in Google Scholar

Ouarit, H., Lefevre, L. and Georges, D. (2003). Robust optimal control of one-reach open channels, European Control Conference 03, Cambridge, UK.10.23919/ECC.2003.7085328Search in Google Scholar

Papageorgiou, M. and Messmer, A. (1989). Flow control of a long river stretch, Automatica 25(2): 177-183.10.1016/0005-1098(89)90071-XSearch in Google Scholar

Porfirio, C. R., Neito, E. A. and Odloak, D. (2003). Multi-model predictive control of an industrial c3/c4 splitter, Control Engineering Practice 11(7): 765-779.10.1016/S0967-0661(02)00183-1Search in Google Scholar

Rodrigues, M., Theilliol, D., Aberkane, S. and Sauter, D. (2007). Fault tolerant control design for polytopic LPV systems, International Journal of Applied Mathematics and Computer Science 17(1): 27-37, DOI: 10.2478/v10006-007-0004-5.10.2478/v10006-007-0004-5Search in Google Scholar

Rodrigues, M., Theilliol, D., Adam-Medina, M. and Sauter, D. (2008). A fault detection and isolation scheme for industrial systems based on multiple operating models, Control Engineering Practice 16(2): 225-239.10.1016/j.conengprac.2006.02.020Search in Google Scholar

Sakawa, Y. and Matsushita, T. (1975). Feedback stabilization of a class of distributed systems and construction of a state estimator, IEEE Transactions on Automatic Control AC-20 (6): 748-753.10.1109/TAC.1975.1101095Search in Google Scholar

Tour´e, Y. and Rudolph, J. (2002). Controller design for distributed parameter systems, Encyclopedia of LIFE Support on Control Systems, Robotics and Automation, Vol. I, Eolss Publishers, Oxford, pp. 933-979.Search in Google Scholar

Triggiani, R. (1975). On the stability problem in Banach space, Journal of Mathematical Analysis and Applications 52(3): 383-403.10.1016/0022-247X(75)90067-0Search in Google Scholar

Wang, J.-W., Wu, H.-N. and Li, H.-X. (2011). Distributed fuzzy control design of nonlinear hyperbolic PDE systems with application to nonisothermal plug-flow reactor, IEEE Transactions on Fuzzy Systems 19(3): 514-526.10.1109/TFUZZ.2011.2116028Search in Google Scholar

Weyer, E. (2002). Decentralised PI controller of an open water channel, 15th IFAC World Congress, Barcelona, Spain.10.3182/20020721-6-ES-1901.01406Search in Google Scholar

Zaccarian, L., Li, Y., Weyer, E., Cantoni, M. and Teel, A.R. (2007). Anti-windup for marginally stable plants and its application to open water channel control systems, Control Engineering Practice 15(2): 261-272.10.1016/j.conengprac.2006.08.001Search in Google Scholar