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A Semi‐Tensor Product Approach to Pseudo‐ B oolean Functions with Application to B oolean Control Networks
Author(s) -
Li Haitao,
Wang Yuzhen,
Liu Zhenbin
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.767
Subject(s) - tensor product , mathematics , product (mathematics) , matrix (chemical analysis) , set (abstract data type) , algebraic number , function (biology) , algebraic expression , tensor (intrinsic definition) , expression (computer science) , optimal control , mathematical optimization , algebra over a field , computer science , pure mathematics , mathematical analysis , materials science , geometry , evolutionary biology , composite material , biology , programming language
Using the semi‐tensor product method, this paper investigates several fundamental problems of general pseudo‐ B oolean functions with application to the optimal control of B oolean control networks, and establishes a new framework to deal with pseudo‐ B oolean inequalities, the optimization problem and the best linear approximation of pseudo‐ B oolean functions. First, the pseudo‐ B oolean function is expressed in the algebraic form via constructing its unique structural matrix. Second, based on the matrix expression, solving pseudo‐ B oolean inequalities is converted into finding solutions to algebraic inequalities, and a set of new formulas are presented. Third, the optimization problem and the linear approximation of the pseudo‐ B oolean function are considered and several new results are established. Finally, as an application, we investigate the optimal control of B oolean control networks, and present a new optimal control design procedure. It is shown through the study of illustrative examples that the new results proposed in this paper work very well.