Disturbance decoupling control design for Boolean control networks: a Boolean algebra approach

Conversion between Logic and Algebraic Expressions of Boolean Control Networks

“…This paper will provide a constructive and straightforward method with a complexity of O(2 m+n n) to convert the logic expression to the algebraic expression of a BCN. More concretely, the complexity of the STP based method presented in [11] is 2 5(m+n) times that of the method given in this paper, and the Khatri-Rao product based method presented in [26,27] is 2 n /n times that of ours.…”

“…The STP based method has been presented in ([11], Theorem IV.6) for obtaining the algebraic expression of BCNs by introducing the swap matrix, dummy matrix and power reducing matrix, which has a very high computational complexity of O(2 6(m+n) n) (see [3], Theorem 1). Resently, Sarda et al [26,27] proposed a Khatri-Rao product based method to obtain such an algebraic expression.…”

“…It has been calculated in [3] that the complexity of STP based method is O(2 6(m+n) n). Recently, Sarda et al [26,27] proposed a Khatri-Rao product based method to transform the logical form of a BCN into a discrete time bilinear system, which has a complexity of O(2 m+2n ). In other words, the complexity of the STP based method is 2 5m+4n n times that of the Khatri-Rao product based method.…”

Bisimulations for delayed switched Boolean control networks and its application in controllability

“…In other words, we can use some standard mathematical tools in linear state-space models and facilitate exploring BNs and BCNs within the control theory framework. Consequently, many fundamental and important results about BNs and BCNs have emerged, such as controllability and observability [7][8][9][10], optimal control [11][12][13], pinning control [14][15][16], stability and stabilization [13,[17][18][19], tracking control [20][21][22], disturbance decoupling [23], and so on.…”