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Optimal Control of Logical Control Networks

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3 Author(s)
Yin Zhao ; Key Laboratory of Systems & Control, Institute of Systems Science, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, P. R. China ; Zhiqiang Li ; Daizhan Cheng

This paper considers the infinite horizon optimal control of logical control networks, including Boolean control networks as a special case. Using the framework of game theory, the optimal control problem is formulated. In the sight of the algebraic form of a logical control network, its cycles can be calculated algebraically. Then the optimal control is revealed over a certain cycle. When the games, using memory μ >; 1 (which means the players only consider previous μ steps' action at each step), are considered, the higher order logical control network is introduced and its algebraic form is also presented, which corresponds to a conventional logical control network (i.e., μ = 1 ). Then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this μ-memory case.

Published in:

IEEE Transactions on Automatic Control  (Volume:56 ,  Issue: 8 )