Hybrid formation control for heterogeneous uncertain linear two-time-scale systems

This paper investigates time-varying output formation of interconnected heterogeneous linear two-time-scale systems with model uncertainty. Unlike previous works on the cooperation of interconnected two-time-scale systems, we consider nonidentical dynamics for each agent that may be characterized by different dimensions and time-scaling factors. Additionally, the systems are interconnected through a switching graph with a disconnected topology, rendering more challenging the analysis and the controller design. To address these challenges, a hybrid two-layer hierarchical control protocol is proposed. The upper layer utilizes an impulsive cooperative control strategy to generate local references, enabling discrete-time interactions among agents and thereby reducing the communication burden. The lower layer implements an internal model-based controller for the two-time-scale dynamics to track the generated references, demonstrating robustness against small model uncertainties. Closed-loop analysis is based on input-to-state stability (ISS) results for hybrid systems. Furthermore, the obtained result is extended to achieve the output consensus. Finally, two examples are presented to illustrate the effectiveness of the results.