低阶多智能体系统快速一致性优化设计的解析方法

Analytic solutions to the optimal design for fast consensus of low-order multi-agent systems

在实际应用中,一大类的多智能体系统可由二阶和三阶模型描述.鉴于此,研究二阶和三阶多智能体系统在无向图下的一致性和收敛率优化问题.针对在离散时间下的智能体,采取一个定常的控制协议.首先,给出多智能体系统达到一致性的充要条件以及一致性状态的显示表达式;然后,将快速一致性问题转化为收敛率的优化问题,利用劳斯判据的方法得到二阶和三阶系统最优收敛率和控制增益的直接求解公式;最后,通过仿真实验对理论结果的有效性进行验证.

A large class of multi-agent systems can be described by second-order and third-order models in practical applications. This paper consider the consensus and the optimization problem of the convergence rate of second-order and third-order multi-agent systems under undirected topologies. A constant control protocol is applied to discrete-time agents. Firstly, a necessary and sufficient condition for consensus is presented, as well as the explicit formula of the consensus state. Then, the problem of accelerated consensus is transformed into the optimization problem of convergence rate. Explicit formulas for the optimal convergence rate and control gains of second-order and third-order multi-agent systems are obtained by applying the Routh criterion. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.