Controller design for disturbance decoupling of Boolean control networks

Observability analysis and observer design for finite automata via matrix approach

“…(3, 1), (3,2), (2,3), (3,4), (4,7), (3,9), (3,10), (3,12), (2,17), (2,19), (4,21), (4,23) and other entries equal to '0'. By (17) we have K 13 (3,9) = K 13(2,35) = 1, K 23(4,36) = 1, K 33(3,13) = 1, K 53(4,51) = 1, K 63(4,52) = 1 with other entries equal to '0', which implies that K i3 are generalised logical matrices for i = 1, .…”

“…, (13,9), (13,10), (13,12), 17), (51, 19), (52, 21), (52, 23) and other entries equal to '0'; 3 is a 4 × 32 matrix with the entries in the following positions equal to '1'…”

“…Based on semi-tensor product (STP) of matrices developed by Cheng [18], the observability problem of Boolean networks, which can be seen as a special case of automata driven by logical relations between states, were considered in [19][20][21][22][23][24]. In spite of these existing results, necessary and sufficient conditions that are readily verifiable for different observability concepts of finite automata are still in need.…”

Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method

“…Up to now, this method has been successfully applied to the analysis and control of Boolean network and mix-valued logical network, and many excellent results have been obtained on calculating fixed points and cycles of Boolean networks (Cheng, 2009), the controllability and observability of Boolean control networks (Cheng & Qi, 2009), the optimal control (Zhao, Li, & Cheng, 2011), and other related issues (Cheng & Qi, 2010;Li & Sun, 2011;Li & Wang, 2012;Wang, Zhang, & Liu, 2012;Yang, Li, & Chu, 2013). Moreover, this method has also been used in the study of dynamical games in Cheng, Zhao, and Mu (2010), where the authors proposed a way called the hill climbing method to find the local ''best'' strategy of dynamical games.…”

Nonsingularity of nonlinear feedback shift registers

“…It is worth noting that the semi-tensor product of matrices [8] has been successfully used in the study of Boolean (control) networks [9][10][11], multi-valued and mix-valued logical networks [12,13], and some other related fields [14][15][16][17][18][19][20]. In [10], authors investigated a matrix expression of a Boolean network, and presented some results about the number of cycles of different lengths, transient period and basin of each attractor.…”