树型变换下高阶多智能体系统鲁棒一致性方法

Robust consensus approach to high-order multi-agent systems based-on tree-type transformation

采用树型变换方法研究了具有变拓扑网络结构的高阶多智能体系统鲁棒一致性控制问题.通过该方法对系统进行降阶,并根据降阶系统动态特征定义恰当的被控输出,将一致性问题转化成鲁棒L2-L∞控制问题.在系统存在不确定时滞情形下,得到一个以线性矩阵不等式形式给出的一致性条件,并求得时变通信时滞的最大容许值.在系统中还存在外部干扰情形下,得到该多智能体系统具有期望抑制扰动性能的一致性条件.通过多智能体系统编队控制的仿真实例验证了所得结论的正确性.

Robust consensus control problem was studied for high-order multi-agent systems with the net- work under switching topologies by the tree-type transformation approach, through which the systems were turn into the reduced-order systems. After defining an appropriate controlled output, the consensus problem was re- formulated as a robust L2-L∞ control problem. For the systems with uncertain time-delays, a consensus condi- tion in terms of linear matrix inequalities （LMIs） is obtained, which could provide the allowable upper bound of delays. Furthermore, a sufficient condition is derived for the robust consensus with the desired disturbance attenuation performance of the systems subject to external disturbances. A simulation example of formation control for multi-agent systems is provided to validate the theoretical results.