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This article investigates observability of Boolean control networks (BCNs) and probabilistic Boolean networks (PBNs). First, weak observability of BCNs is discussed via the nonaugmented approach. The obtained result is then applied to determine (asymptotic) observability of PBNs. Finally, complexity of algorithms based on new criteria is analyzed. Compared with existing ones, time and space complexity do not get worse, even are improved under some mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, the finite horizon tracking control problem of probabilistic Boolean control networks (PBCNs) is studied. For a given reference output trajectory, two trackability definitions are introduced according to whether the tracking probability is 1. Under the framework of the semi-tensor product, some necessary and sufficient conditions are obtained to determine whether the reference output trajectory is trackable with probability (probability one) by a PBCN starting from a given initial state. Based on this, two algorithms are proposed to determine the maximum tracking probability and the corresponding optimal control policy sequence. By determining the tracking error of the reference output trajectory, two related optimal control problems are considered: one is to minimize the expected value of the total tracking error, and the other is to minimize the maximum tracking error. Inspired by dynamic programming, corresponding algorithms are given to solve these two problems. Finally, two examples are given to verify the validity and correctness of the results. [ABSTRACT FROM AUTHOR]

In this paper, the block decoupling of Boolean control networks is investigated via solving logical matrix equations. First, the definition of block decoupling of Boolean control networks is proposed. Second, the block decoupling problem is equivalently converted into the solvability of a set of logical matrix equations. Subsequently, the approaches to solve these equations are designed, based on which the suitable coordinate transformations and open-loop controllers can be determined. Finally, an illustrative example is given to show the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Abstract This paper devotes to introducing and investigating the detectability of probabilistic Boolean networks (PBNs). Two types of detectability, weak detectability and strong detectability, are proposed to deal with different situations. Firstly, by resorting to the semi-tensor product (STP) of matrices, the equivalent algebraic expression of the PBN is converted into another kind of expression, which is called the data form. This data form can estimate the current state distribution from the corresponding output sequence. Then, using this data form constructs the detection form, based on which, two necessary and sufficient conditions are derived for checking weak detectability and strong detectability. Secondly, combining the STP and this detection form, a nice algorithm is established for checking wether a PBN is weak detectability. Finally, for better presentation, two numerical examples are shown to demonstrate the effectiveness of the theoretical results, and the diagnosis of tuberculosis is briefly analyzed. [ABSTRACT FROM AUTHOR]

Derived from a simplified intelligent traffic control system, sampled-data controllability and stabilizability of Boolean control networks are considered. Compared with the existing case of uniform (periodic) sampling in Boolean control networks, the nonuniform one is more general. Using linear span with integral coefficients, the distribution of sampling points can be obtained. Then by constructing novel systems, some necessary and sufficient conditions are proposed to determine sampled-data controllability and stabilizability. Finally, two illustrative examples, which are on apoptosis networks and traffic control systems, respectively, are worked out to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the weighted l 1 -gain analysis and l 1 model reduction problem for Boolean control networks are proposed and investigated via semi-tensor product method. First, the input energy and output energy are described by pseudo-Boolean functions, based on which the definition of the weighted l 1 -gain is introduced. By constructing a co-positive Lyapunov function, a sufficient condition is established to ensure that a Boolean control network is not only internally asymptotically stable, but also has an l 1 -gain no more than a given scalar. Along this line, by virtue of the properties of semi-tensor product, the l 1 model reduction problem of a Boolean control network is defined and converted to the l 1 -gain problem of another Boolean control network with more nodes. A sufficient condition for the l 1 model reduction problem is then derived immediately, and an algorithm is presented to compute the matrices in the reduced order model. Finally, two examples, including the Boolean model for biochemical oscillators in the cell cycle, are displayed to show the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]