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研究了一类异构线性多智能体系统的最优输出跟踪问题.利用非零给定点调节器理论,通过引入适当的性能指标函数,得到了使所有智能体输出变量收敛到期望值的充分必要条件;并指出当个体输出矩阵为单位阵时,最优输出跟踪问题即转化为最优状态跟踪问题;在此基础上,将所得结果推广到了个体状态变量传输具有时滞的情形,得到了问题可解的充要条件,给出了时滞上界.同时,给出了系统实现动态输出跟踪的充分必要条件.利用所得结果,可以确定满足性能指标要求的信息交换拓扑和基于个体的控制器,从而为实现最优输出/状态跟踪的异构多智能体系统的设计提供了工具.仿真结果验证了所得结果的有效性.
The optimal output tracking problem for a class of heterogeneous linear multi-agent systems is studied. By using the non-zero given point controller theory and by introducing appropriate performance index functions, the necessary and sufficient conditions for all the output variables to converge to the expected value are obtained ; And pointed out that when the individual output matrix is a unit matrix, the optimal output tracking problem transforms to the optimal state tracking problem; on this basis, the result is generalized to the case that the individual state variables have time-delay, and the problem can be solved The sufficient and necessary conditions of the solution are given and the upper bound of the delay is given. At the same time, the necessary and sufficient conditions for the system to realize the dynamic output tracking are given.Using the results, we can determine the information exchange topology and individual controller that meet the performance requirements, Which provides a tool for the design of heterogeneous multi-agent systems that achieve optimal output / state tracking.The simulation results verify the effectiveness of the results obtained.