Containment Control Protocol Design for PDE Agents Subject to External Disturbances

This paper mainly solves the containment control issue for a network of infinite-dimensional agents described by wave equations. To eliminate influences caused by external disturbances, observers based on partial differential equations are proposed. A novel interaction protocol is then designed to reach containment control under a fixed directed communication topology. Different from the existing works, disturbances with unbounded derivatives are allowed in this paper. A proper Lyapunov function is constructed and the sufficient condition assuring containment control is obtained. Finally, the theoretical results are verified via numerical examples.