Distributed tracking of high-order nonlinear multi-agent systems perturbed by second-order moment processes

• First, tackles high-order, inherently nonlinear dynamics and eases the controller-design burden through flexible inequality scaling; Second, moves beyond classical white-noise assumptions by treating second-order-moment processes, and employs second-moment analysis with expectation estimation to manage coupling with nonlinear terms; Third, enables fully distributed control using only relative output measurements (neighbor-to-neighbor or agent-to-leader), aligning with MAS topology and collaboration constraints rather than requiring full output information. This paper studies the distributed tracking for the nonlinear multi-agent systems perturbed by second-order moment processes. What makes the case here unique from the prior results is that on the one hand, the system is more practical than those with white noise since it is more in line with practical engineering applications, and on the other hand, the system has inherently nonlinear distinguishing from those with second-order moment processes. In this paper, a distributed tracking controller is designed by employing the algebraic graph theorem and the distributed backstepping method, in which, extensive computational skills are taken to offset the difficulties from the system’s high-order. Furthermore, by using stochastic control theory, the tracking errors can be adjusted to an arbitrarily small value while all the states of the closed-loop system composed by the multi-agent systems are bounded in probability. At last, a simulation example with three agents demonstrates the effectiveness of the distributed tracking controller.