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

Abstract EN

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.