In this paper, we investigate the algorithm of distributed optimization and control for task-space bipartite coordination of multiple uncertain Lagrange plants (MULPs) with unavailable dynamical parameters. We establish the global cost function based on the sum of the user-defined local cost functions, which are respectively presented for all the individuals within the MULPs. We present a hierarchical optimization algorithm, involving the distributed optimized estimators and the adaptive local controllers in different layers, to force the task-space outputs of the MULPs to achieve the bipartite coordination at some specified points where the global cost function is minimized in a distributed manner. Particularly, the presented algorithm is fully-distributed, namely, no global information is employed in achieving the above-mentioned goal. Additionally, the hierarchical algorithm is also designed in the manner of privacy protection, since only the estimated state of each plant is assumed to be accessible for its neighbors, namely, the actual state of each one is inaccessible to others. Finally, the simulation studies are carried out to verify the effectiveness of the main results.

在本文中，我们研究了具有不可用动态参数的多个不确定拉格朗日对象 (MULP) 的任务空间二分协调的分布式优化和控制算法。我们根据用户定义的局部成本函数的总和建立全局成本函数，这些局部成本函数分别呈现给 MULP 中的所有个体。我们提出了一种分层优化算法，涉及不同层中的分布式优化估计器和自适应局部控制器，以强制 MULP 的任务空间输出在某些指定点实现双向协调，其中全局成本函数在分布式中最小化方式。特别地，所提出的算法是完全分布式的，即在实现上述目标时不使用全局信息。此外，分层算法还以隐私保护的方式设计，因为仅假设每个植物的估计状态对其邻居是可访问的，即每个植物的实际状态是其他人无法访问的。最后通过仿真研究验证了主要结果的有效性。