Abstract
This article investigates the networked multiple one-link flexible manipulators system communicating through a signed digraph, in which the dynamic of each submanipulator is described by the PDE-ODE hybrid model. A distributed boundary control protocol is proposed to realize bipartite consensus of joint angles and vibration suppression. To overcome the flexible dynamics, novel variables are introduced in the protocol to suppress the vibrations. The single zero eigenvalue brought by the Laplacian matrix is ignored for avoiding singularity, and the exponential stability of the reduced-order system is strictly proven by means of semigroup theory. Based on the estimations of integral terms in the novel variables, the necessary and sufficient conditions are finally obtained. Numerical simulations are presented to illustrate the effectiveness of the proposed protocol.
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