From STP to game-based control

Abstract

This paper provides a comprehensive survey on semi-tensor product (STP) of matrices and its applications to different disciplines. First of all, the STP and its basic properties are introduced. Meanwhile, its inside physical meaning is explained. Second, its application to conventional dynamic systems is presented. As an example, the region of attraction of stable equilibriums is discussed. Third, its application to logical systems is presented. Particularly, the algebraic state space representation of logical systems and the important role it plays in analysis and control of logical systems are emphasized. Fourth, its application to finite games is discussed. The most interesting problems include potential game, evolutionary game, and game theoretic control. Finally, the mathematical essence of STP is briefly introduced.

Impulsive control design for output tracking of probabilistic Boolean control networks

“…Utilising , and , according to the technique proposed in [42], one can find unique structure matrices of , , h and g , denoted by , , , and , respectively. Then, we obtain the following algebraic forms of (1) and (3), respectively: …”

Profile-dynamic based fictitious play

“…This technique was firstly proposed in [4], and it has been successfully applied to investigate Boolean networks and logical systems subsequently [5]. For more details about STP and its applications in games and logical systems, please see [6][7][8].…”

Semitensor Product Approach to Controllability, Reachability, and Stabilizability of Probabilistic Finite Automata

“…In some recent works, a semitensor product (STP) approach [21] has been introduced to the reachability and stabilizability of finite automata [1,2,22]. For other applications of STP in Boolean networks [23][24][25] and game theory [26][27][28], please refer to [29][30][31][32][33][34][35]. Xu et al [1] developed an STPbased method for the reachability of DFA.…”