Bipartite Consensus and Distributed Boundary Control for Multiple Flexible Manipulators Associated With Signed Digraph
研究了通过带符号有向图通信的多柔性机械臂系统，提出分布式边界控制协议实现关节角二部一致并抑制振动，用半群理论证明了降阶系统的指数稳定性。
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.