Input‐Output Decoupling of Boolean Control Networks

Abstract

This paper is devoted to the input-output decoupling problem of Boolean control networks (BCNs). First, a necessary and sufficient condition for the existence of comparable output subspaces is obtained as well as an algorithm to construct the comparable output subspaces. Then, two kinds of controllers are designed to solve the decoupling problem, including open-loop controller and state feedback controller. Finally, an example is given to illustrate the effectiveness of the proposed method.

The equivalence transformation between Galois NFSRs and Fibonacci NFSRs

“…We are now in a position to prove that the set  𝑦 is not T-complete for T ≤ 4, by Proposition 2, we only need to prove that the set  𝑦 is not 4-complete. Denoting the output sequence of initial state 𝛿 13 16 ∼ 0011 by p 1 , the output sequence of initial state 𝛿 2 16 ∼ 1110 by p 2 , we have p 1 = {0001101 … }, and p 2 = {10011011 … }. It is easy to see that p 1 (t) = p 2 (t) for 1 ≤ t ≤ 4, but the sequence…”

“…The Boolean network was first introduced by Kauffman in 1969 to model a genetic network whose describing variables take only two values, "on" and "off", or 1 and 0 equivalently [6]. Over the last decades Boolean networks have attracted much attention in many communities, ranging from biology [7][8][9] and physics [10,11], to system sciences [12][13][14]. For the community of system sciences, Prof. Cheng and his co-workers developed an algebraic framework for Boolean networks [15], using the STP approach.…”

Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems

“…In the past decade, based on the algebraic state space representation approach, many theoretic problems of LDSs have been achieved, including controllability [37][38][39][40][41], observability [42][43][44][45][46], stability [47][48][49][50][51], stabilization [52][53][54][55][56], tracking control [57][58][59][60][61], disturbance decoupling [62][63][64][65][66], input-output decoupling [67][68][69][70][71], optimal control [12,[72][73][74], and so on.…”

RobustH∞filtering for singular Markovian jump systems via decoupling and substitution principles

“…Thus, MJSs with partly unknown transition rates have drawn much attention 10,11 . Singular systems can better describe physical models than standard state‐space systems, which have extensive applications in many fields, such as electrical circuits, power systems and networks 12,13 . When singular systems experience abrupt changes in their structures, it is natural to model them as singular Markovian jump systems (SMJSs) 14‐17 .…”