Robust Inverse Optimal Cooperative Control for Uncertain Linear Multiagent Systems

This article studies robust inverse optimal control design for cooperative control of uncertain linear multiagent systems (MASs) on directed graph. While designing optimal cooperative control solutions are desired and have been widely considered, ignoring the system uncertainties during the design phase can jeopardize their performance and even cause instability during the operation phase. To alleviate this issue, distributed controllers are designed that are robust to uncertainty and are optimal with respect to some meaningful performance index (referred to as being inverse optimal). It is shown that using the presented distributed robust inverse optimal controller the network of agents converge to a common value of interest or follow the trajectory of a leader node despite uncertainties. A comprehensive study is performed with the time varying bounded parameters uncertainties on the drift and the input matrices of the state-space representation of the MASs. Sufficient conditions for stability analysis are provided using the Lyapunov theory to show that the distributed controller can stabilize the MAS globally. The proposed ideas are confirmed via numerical examples.