Abstract
This paper considers time-varying formation control for multiagent systems (MASs). The collective dynamics is modeled by a wave partial differential equation (PDE) in an angular symmetric annulus. The dynamical formation formed by a group of agents can be represented by wave PDEs due to the energy conservation property of wave PDEs. To achieve convergence of the MAS to desired time-varying formations, we design a boundary controller and a boundary observer by employing the backstepping method, which turns into a leader-enable actuation mode by using only local information. Closed-loop exponential stability with a desired decay rate in the $H^{1}$ norm is proven for both full state and output feedback designs, which means that the communication topology keeps unchanged and connected over time. Compared with the usual 1-D wave equation, the design of the controller, observer, and their stability proof are more involved due to the Laplace operator in polar coordinates. The effectiveness of the proposed control scheme of time-varying formation for MASs is illustrated via numerical simulations.
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