Optimal Stationary Synchronization of Heterogeneous Linear Multi-Agent Systems

Based on an approach with bounded virtual exosystems, the output synchronization of heterogeneous linear networks is addressed. Instead of exact synchronization with zero steady-state error, we introduce optimal stationary synchronization. Then, each agent is able to balance its synchronization error versus its consumed input-energy. In this regard, a local, time-invariant optimal control is obtained by means of recently developed methods for infinite-time linear quadratic tracking. Extending these methods, we present a parametric optimization problem to obtain an optimal control that guarantees given error-bounds on the synchronization error. In addition, we are able to relax standard assumptions and our approach applies even for agents which usually cannot synchronize exactly, e.g. agents with less inputs than outputs. All these aspects are demonstrated by an illustrative simulation example for which a detailed analysis is provided.