This paper is concerned with the formation control problem for a class of large-scale mobile sensor networks. The dynamic of mobile sensors are modeled by class of semilinear parabolic system, which is a class of partial differential equation(PDE) and has rich geometric family. In this model, the communication topology of agents is a chain graph and fixed. Leader feedback laws which designed in a manner to the boundary control of semilinear parabolic system allow the mobile sensors stable deployment onto planar curves. By constructing appropriate Lyapunov functional and using linear matrix inequality, several sufficient criteria are derived ensuring the mobile sensor networks to be globally asymptotically stable at the equilibrium. A simulation example is provided to demonstrate the usefulness of the proposed formation control scheme.

This paper investigates the consensus problem of an array of large mobile sensor networks. A new framework for the dynamic of mobile sensors as a continuum which described by parabolic system with boundary disturbance is proposed. The communication topology of agents is a chain graph and fixed. Leader feedback laws which is designed in a manner to the boundary control of large mobile sensor networks allow the mobile sensors achieve the formation steadily. By referring to Lyapunov functional method and employing boundary control approach, a new protocol is established to deal with formation problem for the large mobile sensor networks. Finally, numerical examples are given to illustrate the usefulness of the results.