This note is concerned with a suboptimal version of the distributed linear quadratic optimal control problem for multiagent systems. Given a multiagent system with identical agent dynamics and an associated global quadratic cost functional, our objective is to design distributed control laws that achieve consensus and whose cost is smaller than an a priori given upper bound, for all initial states of the network that are bounded in norm by a given radius. A centralized design method is provided to compute such suboptimal controllers, involving the solution of a single Riccati inequality of dimension equal to the dimension of the agent dynamics, and the smallest nonzero and the largest eigenvalue of the Laplacian matrix. Furthermore, we relax the requirement of exact knowledge of the smallest nonzero and largest eigenvalue of the Laplacian matrix by using only lower and upper bounds on these eigenvalues. Finally, a simulation example is provided to illustrate our design method.

中文翻译：

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分布式线性二次最优控制的次优方法

本笔记涉及多智能体系统的分布式线性二次最优控制问题的次优版本。给定一个具有相同代理动态和相关全局二次成本函数的多代理系统，我们的目标是设计分布式控制律，实现共识并且其成本小于先验给定的上限，对于有界网络的所有初始状态以给定半径的范数。提供了一种集中式设计方法来计算这种次优控制器，涉及维数等于代理动力学维数的单个 Riccati 不等式的解，以及拉普拉斯矩阵的最小非零和最大特征值。此外，我们通过仅使用这些特征值的下限和上限，放宽了对拉普拉斯矩阵的最小非零和最大特征值的精确知识的要求。最后，提供了一个仿真实例来说明我们的设计方法。