Robust Guaranteed Cost Consensus for High-order Discrete-time Multi-agent Systems With Switching Topologies and Time Delays
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摘要: 研究存在参数不确定性的高阶离散时间多智能体系统在时延和联合连通切换通信拓扑条件下的鲁棒保性能一致性问题，给出一种线性一致性协议的设计方法.1）引入高阶离散时间不确定多智能体系统的鲁棒保性能一致性问题，定义基于智能体邻居状态误差和控制输入的保性能函数；2）通过构造合适的Lyapunov函数并利用离散时间系统稳定性理论，推导出一个使高阶离散时间不确定多智能体系统在该条件下获得保性能一致性的线性矩阵不等式（Linear matrix inequality，LMI）充分条件，并给出相应的保性能上界；3）以一致性序列的形式给出参数不确定条件下的高阶离散时间多智能体系统的一致性收敛结果；4）数值仿真验证了本文理论的正确性和有效性.Abstract: The robust guaranteed cost consensus problem for high-order discrete-time linear multi-agent systems with parameter uncertainties is studied, under the condition of jointly-connected interconnections and time-varying delays. A corresponding linear consensus protocol design is proposed. The idea of robust guaranteed cost control is introduced to the consensus problem. After that, a cost function is defined based on the state errors among neighboring agents and control inputs of all the agents. By constructing a suitable Lyapunov function and using the stability theory of discrete-time linear systems, a sufficient linear matrix inequality (LMI) condition, as well as an upper bound of the cost function, is derived to ensure the robust guaranteed cost consensus of the concerned systems. Then, convergence results are provided as final consensus values for the high-order discrete-time linear multi-agent systems with switching topologies and time-varying delays. Numerical experiment is carried out to demonstrate the correctness and effectiveness of the theoretical results.
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Key words:
- Time delays /
- switching topologies /
- uncertain multi-agent systems /
- consensus /
- guaranteed cost
1) 本文责任编委 夏元清 -
图 2 状态${{\pmb{x}}}_{i1}$在参数${r_j} (j = 1, 2, 3)$变化前后的状态轨迹
Fig. 2 Comparison of state trajectories of ${{\pmb{x}}}_{i1}$ before and after parameters ${r_j}~(j = 1, 2, 3)$ change
图 3 状态${{\pmb{x}}}_{i2}$在参数${r_j}~(j = 1, 2, 3)$变化前后的状态轨迹
Fig. 3 Comparison of state trajectories of ${{\pmb{x}}}_{i2}$ before and after parameters ${r_j}~(j = 1, 2, 3)$ change
图 4 状态${{\pmb{x}}}_{i3}$在参数${r_j}~(j = 1, 2, 3)$变化前后的状态轨迹
Fig. 4 Comparison of state trajectories of ${{\pmb{x}}}_{i3}$ before and after parameters ${r_j}~(j = 1, 2, 3)$ change
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