针对异构多智能体系统的输出包含控制问题，提出一种基于边的事件触发最优控制协议，保证所有跟随者的输出能进入到由领航者的输出所形成的凸包中。同时，使系统达到最优性能，最小化控制代价。考虑到不是所有的跟随者都可获得领航者的信息，提出一种基于边的分布式事件触发观测器，估计领航者输出形成的凸包内点的轨迹。设计加权代价函数评价包含控制的性能，并将输出包含问题转化为最优状态反馈控制设计问题。利用贝尔曼方程和黎卡提方程，给出异构多智能体系统最优输出包含控制的参数设计。选择不同类型的机器人构成多智能体系统，验证算法的有效性。
An edge-based event-triggered optimal control algorithm is proposed to solve the optimal output containment problem of general linear heterogeneous multi-agent systems. The proposed algorithm guarantees that the outputs of all followers enter into the convex hull formed by the outputs of leaders. At the same time, it can also render that the closed-loop system achieves the optimal performance and minimize the cost of control. Considering that the information of the leaders is unavailable to a part of followers, a distributed edge-based event-triggered observer is presented to estimate the trajectory for the interior point in the convex hull. In addition, a weighted performance function is designed to transform the output containment problem into the optimal state-feedback design problem. Based on the proposed function, the Bellman equation and algebraic Riccati equation are derived to solve the optimal output containment control problem of heterogeneous multi-agent systems. Multiple autonomous robots are employed as a group of multi-agent systems to verify the effectiveness of the proposed algorithm.
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