Hierarchical optimization for task-space bipartite coordination of multiple uncertain Lagrange plants

Abstract

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.