Stochastic set stabilisation of n ‐person random evolutionary Boolean games and its applications

Abstract

This study studies the stochastic set stabilisation of an n-person random evolutionary Boolean game (REBG). Firstly, the definition of stochastic set stabilisation has been proposed, and the n-person REBG is converted to an equivalent algebraic form by using the semi-tensor product of matrices. Secondly, by defining a series of stochastic reachable sets, a necessary and sufficient condition is presented for the state feedback stochastic set stabilisation of n-person REBG. Thirdly, based on the concept of uniformly one-step reachability with probability one, a constructive procedure is proposed for the calculation of stochastic reachable sets. Finally, as two applications of stochastic set stabilisation, the output tracking control and the strategy consensus of n-person REBG are investigated, respectively, and two necessary and sufficient conditions are presented.