Stochastic stability and stabilization of n-person random evolutionary Boolean games

Abstract

This paper studies the stochastic stability and stabilization of n-person random evolutionary Boolean games (REBG). Firstly, the n-person REBG is converted to an algebraic form by using the semi-tensor product of matrices. Secondly, a necessary and sufficient condition is presented for the stochastic stability of n-person REBG based on the algebraic form. Thirdly, a constructive procedure is proposed for the state feedback stochastic stabilization control design of n-person REBG by defining a series of stochastic reachable sets. Finally, two illustrative examples are worked out to show the effectiveness of the obtained new results.