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A Probabilistic Approach to Control of Complex Systems and Its Application to Real-Time Pricing

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  • Koichi Kobayashi
  • Kunihiko Hiraishi

Abstract

Control of complex systems is one of the fundamental problems in control theory. In this paper, a control method for complex systems modeled by a probabilistic Boolean network (PBN) is studied. A PBN is widely used as a model of complex systems such as gene regulatory networks. For a PBN, the structural control problem is newly formulated. In this problem, a discrete probability distribution appeared in a PBN is controlled by the continuous-valued input. For this problem, an approximate solution method using a matrix-based representation for a PBN is proposed. Then, the problem is approximated by a linear programming problem. Furthermore, the proposed method is applied to design of real-time pricing systems of electricity. Electricity conservation is achieved by appropriately determining the electricity price over time. The effectiveness of the proposed method is presented by a numerical example on real-time pricing systems.

Suggested Citation

  • Koichi Kobayashi & Kunihiko Hiraishi, 2014. "A Probabilistic Approach to Control of Complex Systems and Its Application to Real-Time Pricing," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, September.
    • Handle: RePEc:hin:jnlmpe:906717
    DOI: 10.1155/2014/906717
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