Semsar-Kazerooni Elham, Khorasani Khashayar
IEEE Trans Syst Man Cybern B Cybern. 2010 Apr;40(2):540-7. doi: 10.1109/TSMCB.2009.2026730. Epub 2009 Oct 9.
In this paper, an optimal control design strategy for guaranteeing consensus achievement in a network of multiagent systems is developed. Minimization of a global cost function for the entire network guarantees a stable consensus with an optimal control effort. In solving the optimization problem, it is shown that the solution of the Riccati equation cannot guarantee consensus achievement. Therefore, a linearmatrix-inequality (LMI) formulation of the problem is used to address the optimization problem and to simultaneously resolve the consensus achievement constraint. Moreover, by invoking an LMI formulation, a semidecentralized controller structure that is based on the neighboring sets, i.e., the network underlying graph, can be imposed as an additional constraint. Consequently, the only information that each controller requires is the one that it receives from agents in its neighboring set. The global cost function formulation provides a deeper understanding and insight into the optimal system performance that would result from the global solution of the entire network of multiagent systems. Simulation results are presented to illustrate the capabilities and characteristics of our proposed multiagent team in achieving consensus.
本文提出了一种用于保证多智能体系统网络中达成一致性的最优控制设计策略。通过最小化整个网络的全局成本函数，可确保在最优控制作用下实现稳定的一致性。在求解优化问题时发现，里卡蒂方程的解无法保证达成一致性。因此，采用该问题的线性矩阵不等式（LMI）形式来解决优化问题，并同时解决达成一致性的约束条件。此外，通过引入LMI形式，可以将基于邻域集（即网络基础图）的半分散控制器结构作为附加约束。这样一来，每个控制器所需的唯一信息就是它从其邻域集中的智能体接收到的信息。全局成本函数形式为深入理解和洞察整个多智能体系统网络的全局解所带来的最优系统性能提供了帮助。给出了仿真结果，以说明我们提出的多智能体团队在达成一致性方面的能力和特性。
