An Information Flow Filter Approach to Formation Control for Heterogeneously Scheduled LPV Agents

This paper studies the formation control problem for a group of non-holonomic agents modeled as LPV systems with heterogeneous scheduling. Here we use an approach based on an information flow filter that makes it possible to design the dynamics of the information flow in the network. We propose a synthesis condition in the form of a linear matrix inequality for a distributed control scheme that guarantees stability and a level of ${\mathcal{L}_2}$ performance. Moreover, by using the framework of decomposable systems, the complexity of the synthesis problem can be made independent of the network size; it corresponds to the size of the synthesis problem for a single agent. The work presented here extends earlier work where a similar scheme was proposed, however restricted by the assumption that the LPV agents are scheduled homogeneously. Whereas in that work the agents were modeled as polytopic LPV models, here the extension to heterogeneously scheduled agents is achieved by using LFT representations of the agents and employing the full-block S-procedure for synthesis. The proposed method is illustrated in simulation by applying it to a formation control problem for a group of dynamic unicycles.