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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.

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