This paper develops a cooperative fencing control scheme of networked second-order nonlinear agents with multiple moving targets. A position-only distributed observer is designed to estimate the center state of the targets. Then, to fulfill state estimation, an optimal fencing controller is designed to achieve evenly distributed fencing of multiple targets via output feedback and adaptive neural optimization. Significantly, the asymptotical stability of the closed-loop system governed by the proposed collective fencing control law is guaranteed by the input-to-state (ISS) principle under nonlinear dynamics constraints. Finally, illustrative simulations are provided to show the effectiveness of the proposed fencing scheme.