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

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  • Koichi Kobayashi
  • Kunihiko Hiraishi

Abstract

In analysis and control of large-scale complex systems, a discrete model plays an important role. In this paper, a probabilistic logic network (PLN) is considered as a discrete model. A PLN is a mathematical model where multivalued logic functions are randomly switched. For a PLN with two kinds of control inputs, the optimal control problem is formulated, and an approximate solution method for this problem is proposed. In the proposed method, using a matrix-based representation for a PLN, this problem is approximated by a mixed integer linear programming problem. In application, real-time pricing of electricity is studied. In real-time pricing, electricity conservation is achieved by setting a high electricity price. A numerical example is presented to show the effectiveness of the proposed method.

Suggested Citation

  • Koichi Kobayashi & Kunihiko Hiraishi, 2015. "Optimal Control of Probabilistic Logic Networks and Its Application to Real-Time Pricing of Electricity," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, December.
    • Handle: RePEc:hin:jnlmpe:952310
    DOI: 10.1155/2015/952310
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