线性多智能体系统一致性问题的部分稳定性方法

提出了处理高阶线性多智能体系统一致性问题的线性变换.该线性变换将一致性问题转化为一个部分稳定问题.研究了一般线性协议下线性多智能体系统的三个问题: 1) 寻找一致性收敛判据; 2) 计算一致性函数; 3) 设计线性一致性协议的增益矩阵.具体来说,提出了基于矩阵 Hurwitz 稳定的一致性收敛的充分必要条件,给出了一致性函数的解析表达式,同时建立了一致性协议的增益矩阵与多智能体系统收敛时间和一致性精度的关系,并针对预先给定的收敛时间和精度要求设计了增益矩阵.

Partial Stability Approach to Consensus Problem of Linear Multi-agent Systems

A linear transformation is proposed to deal with the consensus problem of high-order linear multi-agent systems (LMASs). In virtue of the linear transformation, the consensus problem is equivalently translated into a partial stability problem. We discuss three issues of the LMASs under a generalized linear protocol: 1) to find criteria of consensus convergence; 2) to calculate consensus function; 3) to design gain matrices in the linear consensus protocol. Precisely, we provide a necessary and sufficient criterion of consensus convergence in terms of Hurwitz stability of a matrix and give an analytical expression of the consensus function. In addition, we set up a relation between the gain matrices in the protocol and the convergence time and consensus accuracy of the agents, and then design the gain matrices with respect to a pre-specified convergence time and a required consensus accuracy.