Consensus conditions of continuous-time multi-agent systems under the $G$-expectation frame

Abstract

In this paper, we consider the control problem of multi-agent systems with additive noises in the uncertain situation, (which means we are not sure about a particular probability space.) With mild condition, both $G$-mean square convergence and $G$-mean square steady-state error are analyzed by graph theory and $G$-martingale convergence. Different from classical probability, weak convergence in capacity and weak convergence in capacity 1 are considered.