Optimal Stationary Synchronization of Heterogeneous Linear Multi-Agent Systems
For control engineers designing multi-agent systems, this work relaxes exact synchronization constraints, enabling broader applicability and energy savings, though it is an incremental extension of existing LQT methods.
This paper introduces optimal stationary synchronization (OSS) for heterogeneous linear multi-agent systems, allowing non-zero steady-state synchronization errors to relax standard requirements and save input energy. The method combines bounded exosystem synchronization with local infinite-time linear quadratic tracking, achieving an optimal balance between synchronization error and energy consumption while guaranteeing strict error bounds.
In this paper, we address the output synchronization of heterogeneous linear networks. In the literature, all agents are typically required to synchronize exactly to a common trajectory. Here, we introduce optimal stationary synchronization (OSS) instead which permits non-zero steady-state synchronization errors. As a benefit, we are able to relax standard requirements. E.g., agents are allowed to participate in the network even when they usually cannot synchronize exactly. In addition, OSS enables agents to save input-energy by synchronizing within tolerable error-bounds. Our new method combines the synchronization of bounded exosystems with local infinite-time linear quadratic tracking (LQT). This results in an optimal balance of each agent's synchronization error versus its consumed input-energy. Moreover, we extend recent results in LQT such that the derived time-invariant optimal control guarantees that the synchronization error satisfies given strict bounds. All these aspects are demonstrated by an illustrative simulation example with a detailed analysis.