Optimal control of a bioreactor

Applied Mathematics and Computation

Volumn 216, Issue 9, 2010, Pages 2559-2575

  Alvarez Vázquez, Lino J ^a   Fernández, Francisco J ^b  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Bioreactor; Eutrophication; Existence; Optimal control; Optimality conditions

Indexed keywords

ADJOINT SYSTEM; COMPLEX SYSTEMS; COMPUTATIONAL RESULTS; CONSTRAINED OPTIMAL CONTROL PROBLEMS; CONTROL PROBLEMS; FIRST-ORDER OPTIMALITY CONDITION; NON-SMOOTH; OPTIMAL CONTROL; OPTIMAL CONTROLS; OPTIMAL MANAGEMENT; OPTIMAL SOLUTIONS; OPTIMALITY CONDITIONS; REAL-WORLD PROBLEM; STATE-CONTROL;

BIOCONVERSION; BIOREACTORS; CONTROL; DIFFERENTIAL EQUATIONS; EUTROPHICATION;

OPTIMIZATION;

EID: 77953128279     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.03.097     Document Type: Article

References (19)

1. Adams R.A. Sobolev Spaces (1975), Academic Press, New York
2. Alibert J.-J., and Raymond J.-P. A Lagrange multiplier theorem for control problems with state constraints. Numer. Funct. Anal. Optim. 19 (1998) 697-704
3. Allegretto W., Mocenni C., and Vicino A. Periodic solutions in modelling lagoon ecological interactions. J. Math. Biol. 51 (2005) 367-388
4. L.J. Alvarez-Vázquez, F.J. Fernández, A. Marti{dotless}́nez, Optimal management of a bioreactor for eutrophicated water treatment: A numerical approach, J. Sci. Comput., in press. doi: 10.1007/s10915-009-9344-7.
5. Alvarez-Vázquez L.J., Fernández F.J., and Muñoz-Sola R. Analysis of a multistate control problem related to food technology. J. Differ. Equations 245 (2008) 130-153
6. Alvarez-Vázquez L.J., Fernández F.J., and Muñoz-Sola R. Mathematical analysis of a three-dimensional eutrophication model. J. Math. Anal. Appl. 349 (2009) 135-155
7. Arino O., Boushaba K., and Boussouar A. A mathematical model of the dynamics of the phytoplankton-nutrient system. Nonlinear Anal. Real World Appl. 1 (2000) 69-87
8. Canale R.P. Modeling Biochemical Processes in Aquatic Ecosystems (1976), Ann Arbor Science Publishers, Ann Arbor
9. Casas E. Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31 (1993) 993-1006
10. Chang K.-C. Methods in Nonlinear Analysis (2005), Springer-Verlag, Berlin
11. Cioffi F., and Gallerano F. Management strategies for the control of eutrophication processes in Fogliano lagoon (Italy): a long-term analysis using a mathematical model. Appl. Math. Model. 25 (2001) 385-426
12. Clarke F.H. Optimization and Nonsmooth Analysis (1983), John Wiley & Sons Inc., New York
13. Drago M., Cescon B., and Iovenitti L. A three-dimensional numerical model for eutrophication and pollutant transport. Ecol. Model. 145 (2001) 17-34
14. Garvie M.R., and Trenchea C. Optimal control of a nutrient-phytoplankton-zooplankton-fish system. SIAM J. Control Optim. 46 (2007) 775-791
15. Lunardini F., and Di Cola G. Oxygen dynamics in coastal and lagoon ecosystems. Math. Comput. Model. 31 (2000) 135-141
16. Park K., Jung H.-S., Kim H.-S., and Ahn S.-M. Three-dimensional hydrodynamic-eutrophication model (HEM-3D): application to Kwang-Yang Bay, Korea. Mar. Environ. Res. 60 (2005) 171-193
17. Roubi{dotless}́ček T. Nonlinear Partial Differential Equations with Applications (2005), Birkhäuser Verlag, Basel
18. Wächter A., and Biegler L.T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106 (2006) 25-57
19. Yamashiki Y., Matsumoto M., Tezuka T., Matsui S., and Kumagai M. Three-dimensional eutrophication model for Lake Biwa and its application to the framework design of transferable discharge permits. Hydrol. Process. 17 (2003) 2957-2973