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This paper investigates three kinds of system decompositions of multi-valued Boolean control networks. Based on the algebraic representation of Boolean control networks, some necessary and sufficient graphical conditions for the decomposability are proposed and consequently the system decomposition problems are completely solved. It is revealed that not every Boolean control system has a Kalman decomposition.
In this paper, the observability of probability Boolean networks is studied and several necessary and sufficient conditions are obtained. First, for probabilistic Boolean networks, the observability is defined and their algebraic form is given. Then, several necessary and sufficient conditions are obtained, based on which the observability is solved. Finally, an illustrative example is studied to...
This paper mainly investigates the reachability of a kind of Boolean control networks with delays in both state and control. By a system transformation, the reachability problem of the delayed Boolean control network becomes that of a Boolean control network without delays. The relationship between the transformed network and the original network is revealed. A necessary and sufficient condition for...
This paper considers the fuzzy graph coloring problem. Using the matrix semi-tensor product, two necessary and sufficient conditions are put forward for the fuzzy colorability, based on which a new algorithm is designed to find all the fuzzy coloring schemes for any fuzzy graph. the effectiveness of the results/algorithms presented in this paper is shown by one illustrative example.
In the literatures, to design state feedback controller to partially stabilize Boolean control network is rarely considered. Motivated by this, this paper studies partial stabilization for Boolean network with state feedback control. A sufficient condition for the existence of a state feedback controller to achieve the partial stabilization is established first. Then, the feedback control law is proposed...
In order to take full advantages of multi-sensor information from mobile robot, such as olfaction, vision, wind and so forth for odor source localization, a semi-tensor product based control system is set up. The inputs of the control system are multi-sensor information and the outputs are the relative searching strategies, such as random searching (RS), vision searching (VS), odor source declaration...
This paper investigates the matrix expression of state equation and reachability of a class of Petri nets (PNs) by using the semi-tensor product of matrices (STP). First, we get the formula for the number of states of the PNs based on the combinatorial mathematics method. The states and transitions of the PNs are expressed as vector forms, respectively, then the state equation of the PNs is established...
This paper investigates the evolutionary dynamics of two games which are played within distinct networks of interdependent networks. First, the evolutionary dynamic of the coupled evolutionary games based on biased imitation is expressed as a logical dynamic system and then converted into its algebraic form by using the semi-tensor product of matrices. Second, based on the algebraic form, the final...
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