On disturbance decoupling problem of Boolean control networks

Abstract

In this paper, the disturbance decoupling problem for Boolean control networks is investigated in a new viewpoint. A new concept called original disturbance decoupling is proposed and necessary and sufficient conditions for the original disturbance decoupling are given. Similarly, an equivalent condition for the s‐step original disturbance decoupling is obtained. Finally, an algorithm and some simulations for an example are provided to validate the obtained theoretical results.

Finite‐time observability of probabilistic Boolean control networks

“…Its main idea is to rewrite the logical vector as its canonical form, by which BNs can be transformed into algebraic representation. Using this novel framework, many analysis and theoretical results on BNs have been studied, which include but are not limited to, stabilization [12][13][14][15][16][17][18], set stabilization [19,20], robustness analysis [21][22][23][24], observability [25][26][27], decoupling problem [28], state estimation [29], and so on.…”

Matrix expression of Owen values

“…In fact, the STP of matrices, proposed by Cheng et al [13], is an extension of traditional matrix product. In the past few years, this powerful mathematical tool has been successfully applied to the analysis of Boolean control networks and mix-valued logical networks, on which many fundamental control problems have been studied, including stability and stabilization [14][15][16], reachability and observability [17][18][19], optimal control [20,21], and other research topics [22][23][24]. Recently, with STP method in hand, many researchers attempt to investigate cooperative games [12], noncooperative games [25][26][27], and evolutionary games [28][29][30].…”

The equivalence transformation between Galois NFSRs and Fibonacci NFSRs

“…For the community of system sciences, Prof. Cheng and his co-workers developed an algebraic framework for Boolean networks [15], using the STP approach. Thanks to their method, many problems including the controllability [16,17], stability [18,19], observer-bility [20,36], detectability [22,23], disturbance decouping problem [24,25] and bisimulations [26,27] have been well investigated.…”