Minimal time bioremediation of natural water resources

We study minimal time strategies for the treatment of pollution in large water volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists of feeding the bioreactor from the resource, with clean output returning to the resource with the same flow rate. We first characterize the optimal policies among constant and feedback controls under the assumption of a uniform concentration in the resource. In the second part, we study the influence of inhomogeneity in the resource, considering two measurement points. With the help of the Maximum Principle, we show that the optimal control law is non-monotonic and terminates with a constant phase, in contrast to the homogeneous case in which the optimal flow rate decreases with time. This study allows decision makers to identify situations in which the benefit of using non-constant flow rates is significant.

[1]  H. Lim,et al.  Computational algorithms for optimal feed rates for a class of fed‐batch fermentation: Numerical results for penicillin and cell mass production , 1986, Biotechnology and bioengineering.

[2]  K. Yamuna Rani,et al.  Control of fermenters : a review , 1999 .

[3]  Carmen G. Moles,et al.  DYNAMIC OPTIMIZATION OF BIOREACTORS: A REVIEW , 2003 .

[4]  Miroslav Krstic,et al.  Optimizing bioreactors by extremum seeking , 1999 .

[5]  John Matthew Santosuosso,et al.  Dynamic optimization of batch processing , 2003 .

[6]  Denis Dochain,et al.  Adaptive extremum seeking control of continuous stirred-tank bioreactors , 2003 .

[7]  D W Spitzer.  Maximization of steady‐state Bacterial production in a chemostat with pH and substrate control , 1976, Biotechnology and bioengineering.

[8]  Jan F. M. Van Impe,et al.  Optimal control of (bio-)chemical reactors: generic properties of time and space dependent optimization , 2002, Math. Comput. Simul..

[9]  Christian Skov,et al.  Lake restoration: successes, failures and long‐term effects , 2007 .

[10]  Antoine Rousseau.  Accounting for spatial inhomogeneity in the minimal-time bioremediation of natural water resources , 2011 .

[11]  Alain Rapaport,et al.  Optimal time switching control for multi‐reaction batch process , 2010 .

[12]  Salah Leulmi,et al.  Optimal control of a CSTR process , 2008 .

[13]  Xiao Dong Chen,et al.  Comparison of Several Periodic Operations of a Continuous Fermentation Process , 1996 .

[14]  S. Shioya,et al.  Optimization and control in fed-batch bioreactors , 1992 .

[15]  Z Kurtanjek.  Optimal nonsingular control of fed‐batch fermentation , 1991, Biotechnology and bioengineering.

[16]  Joseph S. Alford,et al.  Bioprocess control: Advances and challenges , 2006, Comput. Chem. Eng..

[17]  Petar V. Kokotovic,et al.  Optimal Control of Bacterial Growth , 1972 .

[18]  Ramesh D. Gulati,et al.  Lakes in the Netherlands, their origin, eutrophication and restoration: state-of-the-art review* , 2004, Hydrobiologia.

[19]  A. Johnson,et al.  The control of fed-batch fermentation processes - A survey , 1987, Autom..

[20]  Denis Dochain,et al.  Adaptive extremum-seeking control of a continuous stirred tank bioreactor with Haldane's Kinetics , 2004 .

[21]  Mohd Azlan Hussain,et al.  Comparison of optimisation based control techniques for the control of a CSTR , 2000 .

[22]  Jan Van Impe,et al.  Optimal adaptive control of biotechnological processes , 1998 .

[23]  T. Patarinska,et al.  Augmented Lagrange decomposition method for optimal control calculation of batch fermentation processes , 1998 .

[24]  Takashi Asano,et al.  Sequencing batch reactors for biological wastewater treatment , 1989 .

[25]  J Hong,et al.  Optimal substrate feeding policy for a fed batch fermentation with substrate and product inhibition kinetics , 1986, Biotechnology and bioengineering.

[26]  G. Lyberatos,et al.  Periodic optimization of continuous microbial growth processes , 1987, Biotechnology and bioengineering.

[27]  Ying Tan,et al.  On extremum seeking in bioprocesses with multivalued cost functions , 2009, Biotechnology progress.

[28]  Vanina Estrada,et al.  Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches , 2009, Comput. Chem. Eng..

[29]  Alain Rapaport,et al.  Minimal Time Sequential Batch Reactors with Bounded and Impulse Controls for One or More Species , 2008, SIAM J. Control. Optim..

[30]  Jaime A. Moreno.  Optimal time control of bioreactors for the wastewater treatment , 1999 .

[31]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: I. Characterization of the nominal solution , 2003, Comput. Chem. Eng..

[32]  Ilse Smets,et al.  Optimal adaptive control of (bio)chemical reactors: past, present and future , 2004 .

[33]  E. Donk,et al.  Lakes in the Netherlands, their origin, eutrophication and restoration: state-of-the-art review , 2002 .