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http://dx.doi.org/10.14317/jami.2012.30.5_6.883

DYNAMIC AND CONTROLLABILITY OF A NONLINEAR WASTEWATER TREATMENT PROBLEM  

Jourani, Abderrahim (Universite de Bourgogne, Institut de Mathematiques de Bourgogne)
Serhani, Mustapha (Equipe TSI, Department of Mathematics and Informatics, Faculty of Sciences, University Moulay Ismail)
Boutoulout, Ali (Equipe TSI, Department of Mathematics and Informatics, Faculty of Sciences, University Moulay Ismail)
Publication Information
Journal of applied mathematics & informatics / v.30, no.5_6, 2012 , pp. 883-902 More about this Journal
Abstract
In this work we deal with a nonlinear dynamical system, namely the wastewater treatment model. We proceed to a dynamical analysis of the model. Invariance, boundness, controllability and the sensitivity with respect the initial conditions are studied. On the other hand, using the nonsmooth analysis tools, we look for the viability of the model, that is, the necessary and sufficient conditions under which trajectories move in a suitable time-moving sets, to avoid the washing problem (died of bacteria).
Keywords
Wastewater treatment; dynamical system; non-linear analysis; control; viability;
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1 B. Haegeman, C. Lobry and J. Harmand, Modeling bacteria flocculation as density-dependent growth, Aiche Journal 53(2)(2007), 535-539.   DOI
2 A. Jourani, Normality, local controllability and NOC in multiobjective optimal control problems, Contemporary Trends in Nonlinear Geometric Control Theory and its Applications, Eds A. Anzaldo-Meneses, B. Bonnard, J.-P. Gauthier and F. Monroy, World Scientific Publishers, Singapore, 2002.
3 F.N. Koumboulis, N.D. Kouvakas, R.E. King and A. Stathaki, Two-stage robust controlof substrate concentration for an activated sludge process, ISA Transactions 47(3)(2008), 267-278.   DOI
4 S. Marsili-Libelli, Optimal control of the activated sludge process, Trans. Inst. Meas. Control 6(1984), 146-152.   DOI
5 F. Nejjari, G. Roux, B. Dahhou and A. Benhammou, Estimation and optimal control design of a biological wastewater treatment plant, Mathematics and computer in simulation 48(1999), 269-280.   DOI
6 A. Rapaport and D. Dochain, Interval observers for biochemical processes with uncertain kinetics and inputs, Mathematical Biosciences 193(2005), 235-253.   DOI
7 M. Serhani, P. Cartigny and N. Raissi, Robust feedback design of wastewater treatment problem, J. of Math. Model. Nat. Ph. 4(5)(2009), 1139-143.
8 M. Serhani, J.L. Gouze and N. Raissi, Dynamical study and robustness of a nonlinear wastewater treatment problem, J. of Nonlinear analysis RWA, 12(2011), 487-500.   DOI
9 H.L. Smith, Monotone dynamical systems : an introduction to the theory of competitive and cooperative systems, American Matheatical society, 1995.
10 J.F. Andrews, Kinetic models of biological waste treatment process, Biotech. Bioeng. Symp. 2(1971), 5-34.
11 J.P. Aubin, Viability Theory, Birkhuser, Boston, 1991.
12 F. Clarke, Yu. Ledyaev, R. Stern and P.Wolenski, Nonsmooth Analysis and Control Theory, Springer, NewYork, 1998.
13 T. Donchev, V. Ros and P. Wolenski, Strong invariance and one-sided Lipschitz multifunctions, J. Nonlinear Analysis 60(2005), 849862.   DOI
14 M. Fikar, B. Chachuat and M.A. Latifi, Optimal operation of alternating activated sludge processes, J. Control Engineering Practice 13(2005), 853861.   DOI
15 H. Frankowska, S. Plaskacs and T. Rzezuchowski, Measurable viability theorems and the Hamilton JacobiBellman equation, J. Differ. Equations 116(1995), 265305.   DOI
16 H. Frankowska and S. Plaskacs, Measurable upper semicontinuous viability theorem for tubes, J. Nonlinear Anal., Theory, Methods and Aplications 26(3)(1996), 565-582.   DOI
17 M.Z. Hadj-Sadok and J.L. Gouze, Estimation of uncertain models of activated sludge processes with interval observers, J. of Process Control 11(2001), 299-310.   DOI