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Two types of controllability of dynamic-algebraic Boolean control networks are first presented. The necessary and sufficient conditions of such controllability are derived. A similar concept of coordinate transformation called special restricted coordinate transformation is posed. It is sufficient to transform the coordinate frame of a dynamic-algebraic Boolean control network and obtain its corresponding equivalent form. The relevant results about special restricted coordinate transformation are proposed. Accordingly, two kinds of controllability decomposition are discussed and the corresponding algorithms are provided, which differs from that of the conventional Boolean networks. A method is provided to guarantee that all the dynamic equations in controllable subsystem are affected by control. A numerical example and a practical example are raised to illustrate the results of this paper, and the latter one is about the programmable logical circuit. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability and set controllability of periodically switched Boolean control networks (PSBCNs) via the semi-tensor product. Firstly, the algebraic form of switching signal is given and a parallel system is formed by combining the switching signal and the state. Then the controllability problem of PSBCNs is transformed into the set controllability problem of the new system, further, the criterion for controllability is obtained. Secondly, the set controllability matrix of PSBCNs is constructed, and the necessary and sufficient condition of set controllability for PSBCNs is presented. In addition, a more general PSBCN is considered and the criteria for its controllability and set controllability are proposed. Finally, a practical example is given to illustrate the obtained results, which shows that our new results are correct and effective. [ABSTRACT FROM AUTHOR]

In actual economic activities, different economic systems usually interact with each other, and the coupled networked evolutionary game is an important theoretical tool to describe and analyse such economic activities. In this paper, we investigate a kind of coupled evolutionary public good games (PGGs) with threshold which have two enhancement factors. First, the algebraic formulation for the dynamics of the given coupled PGGs is constructed by using a semi-tensor product (STP) of matrices. Then, the strategy optimisation problem is considered based on the algebraic expression, and all valid state feedback controls are designed to make the investment of the coupled evolutionary game in each layer reach their own threshold. Finally, an illustrative example is studied to support our new results. [ABSTRACT FROM AUTHOR]