Minimum-time strategy optimization for networked evolutionary games with bankruptcy mechanism

Abstract

In this paper, the minimum-time strategy optimization problem for NEGs with bankruptcy mechanism is considered based on semi-tensor product of matrices. Firstly, in order to describe the impact of bankruptcy mechanism on evolution, a novel matrix called controlled state transition matrix is constructed by deleting all invalid states, which will also reduce the computational complexity of subsequent analysis and design. Secondly, by assorting to the redefined matrix, the minimum-time strategy optimization problem for NEGs with bankruptcy mechanism can be solved by designing state feedback control which can guarantee the convergence of states without violating the bankruptcy mechanism. Meanwhile, the verification condition is derived to verify the existence of the state feedback control, and an algorithm for seeking all possible minimum-time state feedback controllers is constructed. Finally, a typical example is illustrated to validate the effectiveness of the proposed method.