Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 952310, 10 pages
http://dx.doi.org/10.1155/2015/952310
Research Article

Optimal Control of Probabilistic Logic Networks and Its Application to Real-Time Pricing of Electricity

1Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan
2School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

Received 1 July 2015; Revised 18 October 2015; Accepted 16 November 2015

Academic Editor: Qingling Zhang

Copyright © 2015 Koichi Kobayashi and Kunihiko Hiraishi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Tabuada, Verification and Control of Hybrid Systems, Springer, New York, NY, USA, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. H. D. Jong, “Modeling and simulation of genetic regulatory systems: a literature review,” Journal of Computational Biology, vol. 9, no. 1, pp. 67–103, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. S. A. Kauffman, “Metabolic stability and epigenesis in randomly constructed genetic nets,” Journal of Theoretical Biology, vol. 22, no. 3, pp. 437–467, 1969. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Mochizuki, “An analytical study of the number of steady states in gene regulatory networks,” Journal of Theoretical Biology, vol. 236, no. 3, pp. 291–310, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. C. Chaouiya, A. Naldi, E. Remy, and D. Thieffry, “Petri net representation of multi-valued logical regulatory graphs,” Natural Computing, vol. 10, no. 2, pp. 727–750, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. D. Cheng, H. Qi, and Z. Li, Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach, Springer, London, UK, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. D. Cheng and X. Xu, “Bi-decomposition of multi-valued logical functions and its applications,” Automatica, vol. 49, no. 7, pp. 1979–1985, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. Zhao, Z. Li, and D. Cheng, “Optimal control of logical control networks,” IEEE Transactions on Automatic Control, vol. 56, no. 8, pp. 1766–1776, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang, “Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks,” Bioinformatics, vol. 18, no. 2, pp. 261–274, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. B. Liu, Y. Z. Wang, and H. T. Li, “Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks,” Science China—Information Sciences, vol. 57, no. 5, pp. 1–10, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. Y. Zhao and D. Cheng, “Controllability and stabilizability of probabilistic logical control networks,” in Proceedings of the 51st IEEE Conference on Decision and Control (CDC '12), pp. 6729–6734, Maui, Hawaii, USA, December 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Kobayashi and K. Hiraishi, “Optimal control of gene regulatory networks with effectiveness of multiple drugs: a Boolean network approach,” BioMed Research International, vol. 2013, Article ID 246761, 11 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. K. Kobayashi and K. Hiraishi, “A probabilistic approach to control of complex systems and its application to real-time pricing,” Mathematical Problems in Engineering, vol. 2014, Article ID 906717, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  14. I. Shmulevich, E. R. Dougherty, and W. Zhang, “Control of stationary behavior in probabilistic Boolean networks by means of structural intervention,” Journal of Biological Systems, vol. 10, no. 4, pp. 431–445, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. Y. Xiao and E. R. Dougherty, “The impact of function perturbations in Boolean networks,” Bioinformatics, vol. 23, no. 10, pp. 1265–1273, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. K. Kobayashi and K. Hiraishi, “ILP/SMT-based method for design of Boolean networks based on singleton attractors,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 11, no. 6, pp. 1253–1259, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. X. Chen, T. Akutsu, T. Tamura, and W.-K. Ching, “Finding optimal control policy in probabilistic Boolean networks with hard constraints by using integer programming and dynamic programming,” in Proceedings of the IEEE International Conference on Bioinformatics and Biomedicine (BIBM '10), pp. 240–246, Hong Kong, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Borenstein, M. Jaske, and A. Rosenfeld, Dynamic Pricing, Advanced Metering, and Demand Response in Electricity Markets, Center for the Study of Energy Markets, UC Berkeley, 2002.
  19. M. Roozbehani, M. Dahleh, and S. Mitter, “On the stability of wholesale electricity markets under real-time pricing,” in Proceedings of the 49th IEEE Conference on Decision and Control (CDC '10), pp. 1911–1918, IEEE, Atlanta, Ga, USA, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. P. Samadi, A.-H. Mohsenian-Rad, R. Schober, V. W. S. Wong, and J. Jatskevich, “Optimal real-time pricing algorithm based on utility maximization for smart grid,” in Proceedings of the 1st IEEE International Conference on Smart Grid Communications (SmartGridComm '10), pp. 415–420, Gaithersburg, Md, USA, October 2010. View at Publisher · View at Google Scholar
  21. C. Vivekananthan, Y. Mishra, and G. Ledwich, “A novel real time pricing scheme for demand response in residential distribution systems,” in Proceedings of the 39th Annual Conference of the IEEE Industrial Electronics Society (IECON '13), pp. 1956–1961, Vienna, Austria, November 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. K. Kobayashi and K. Hiraishi, “Optimal control of probabilistic Boolean networks using polynomial optimization,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 95, no. 9, pp. 1512–1517, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. K. Kobayashi and K. Hiraishi, “Algorithm for optimal real-time pricing based on switched Markov chain models,” in Proceedings of the IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT '15), pp. 1–5, Washington, DC, USA, Feburary 2015. View at Publisher · View at Google Scholar
  24. I. Maruta and Y. Takarada, “Modeling of dynamics in demand response for real-time pricing,” in Proceedings of the 5th IEEE International Conference on Smart Grid Communications (SmartGridComm '14), pp. 806–811, Venice, Italy, November 2014. View at Publisher · View at Google Scholar · View at Scopus