Containment Control for Upper-Triangular Nonlinear Multi-Agent Systems Perturbed by Second-Order Moment Processes

This paper considers the containment control with multiple leaders for a class of upper-triangular nonlinear multi-agent systems (MASs) perturbed by second-order moment processes. Firstly, we design the distributed controllers for the nominal system of the MASs with multiple leaders. Then, by the low-gain homogeneous domination technique and the stochastic analysis tools, we design a low-gain parameter, choose an appropriate Lyapunov function and prove that the output tracking errors can achieve mean square bounded and all the states of the closed-loop system are bounded in probability. After that, this paper gives an example to demonstrate the effectiveness of the tracking controllers. In addition, this paper gives a simulation example that the dynamics of the system does not satisfy the description of the MASs studied in this paper, but our method is still valid to deal with it.