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Neural Networks Simulation of Feeding Adaptations of Daphnia

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Algorithms for Computational Biology (AlCoB 2016)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9702))

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Abstract

In this article we present a neutral network based optimal control synthesis for solving distributed optimal control problems for systems governed by parabolic differential equations with control and state constraints and discrete time delay. The optimal control problem is transcribed into nonlinear programming problem which is implemented with feed forward adaptive critic neural network to find optimal control and optimal trajectory. The developed simulation method is demonstrated on the optimal control problem of feeding adaptation of Daphnia model with diffusion and discrete time delay of nutrient uptake. Results show that adaptive critic based systematic approaches are promising in obtaining the optimal distributed control with discrete time delays in state and control variables subject to control and state constraints.

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References

  1. Borzi, A.: Multigrid methods for parabolic distributed optimal control problems. J. Comput. Appl. Math. 157, 365–382 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Buskens, C., Maurer, H.: SQP-methods for solving optimal control problems with control and state constraints: adjoint variable, sensitivity analysis and real-time control. J. Comput. Appl. Math. 120, 85–108 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chryssoverghi, I.: Discretization methods for semilinear parabolic optimal control problems. Int. J. Numer. Anal. Model. 3, 437–458 (2006)

    MathSciNet  MATH  Google Scholar 

  4. Clever, D., Lang, J., Ulbrich, S., Ziems, J.C.: Combination of an adaptive multilevel SQP method and a space-time adaptive PDAE solver for optimal control problems. Procedia Comput. Sci. 1, 1435–1443 (2012)

    Article  MATH  Google Scholar 

  5. Gollman, L., Kern, D., Mauer, H.: Optimal control problem with delays in state and control variables subject to mixed control-state constraints. Optim. Control Appl. Meth. 30, 341–365 (2009)

    Article  MathSciNet  Google Scholar 

  6. Hornik, M., Stichcombe, M., White, H.: Multilayer feed forward networks are universal approximators. Neural Netw. 3, 256–366 (1989)

    Google Scholar 

  7. Kmet, T., Kmetova, M.: Adaptive critic neural network solution of optimal control problems with discrete time delays. In: Mladenov, V., Koprinkova-Hristova, P., Palm, G., Villa, A.E.P., Appollini, B., Kasabov, N. (eds.) ICANN 2013. LNCS, vol. 8131, pp. 483–494. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Kmet, T., Straskraba, M.: Feeding adaptation of filter feeders: Daphnia. Ecol. Model. 178, 313–327 (2004)

    Article  Google Scholar 

  9. Knowles, G.: Finite element approximation of parabolic time optimal control problems. SIAM J. Control Optim. 20, 414–427 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu, W., Yan, N.: A posteriori error estimates for optimal control problems governed by parabolic equations. Numer. Math. 93, 497–521 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mittelmann, H.D.: Solving elliptic control problems with interior point and SQP methods: control and state constraints. J. Comput. Appl. Math. 120, 175–195 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Padhi, R., Unnikrishnan, N., Wang, X., Balakrishnan, S.N.: Adaptive-critic based optimal control synthesis for distributed parameter systems. Automatica 37, 1223–1234 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rumelhart, D.F., Hinton, G.E., Wiliams, R.J.: Learning internal representation by error propagation. In: Rumelhart, D.E., McClelland, D.E., Group, P.R. (eds.) Parallel Distributed Processing: Foundation Observation of Strains, vol. 1, pp. 318–362. The MIT Press, Cambridge (1987)

    Google Scholar 

  14. Straskraba, M., Gnauck, P.: Freshwater Ecosystems: Developments in Environmental Modelling, Modelling and Simulation. Elsevier, Amsterdam (1985)

    Google Scholar 

  15. Werbos, P.J.: Approximate dynamic programming for real-time control and neural modelling. In: White, D.A., Sofge, D.A. (eds.) Handbook of Intelligent Control: Neural Fuzzy, and Adaptive Approaches, pp. 493–525. Van Nostrand, New York (1992)

    Google Scholar 

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Acknowledgments

The paper was worked out as a part of the solution of the scientific project number KEGA 010UJS-4/2014.

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Authors and Affiliations

  1. Department of Informatics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74, Nitra, Slovakia

    Tibor Kmet

  2. Department of Mathematics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74, Nitra, Slovakia

    Maria Kmetova

Authors
  1. Tibor Kmet
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  2. Maria Kmetova
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Correspondence to Tibor Kmet .

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Editors and Affiliations

  1. CETA-Ciemat, Trujillo, Spain

    María Botón-Fernández

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Extremadura, Cáceres, Spain

    Sergio Santander-Jiménez

  4. University of Extremadura, Cáceres, Spain

    Miguel A. Vega-Rodríguez

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Kmet, T., Kmetova, M. (2016). Neural Networks Simulation of Feeding Adaptations of Daphnia. In: Botón-Fernández, M., Martín-Vide, C., Santander-Jiménez, S., Vega-Rodríguez, M.A. (eds) Algorithms for Computational Biology. AlCoB 2016. Lecture Notes in Computer Science(), vol 9702. Springer, Cham. https://doi.org/10.1007/978-3-319-38827-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-38827-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38826-7

  • Online ISBN: 978-3-319-38827-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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