Distributed Control with Time Transformation: User-Defined Finite Time Convergence and Beyond

View Video Presentation: https://doi.org/10.2514/6.2022-1716.vid

The authors recently focused on time-critical multiagent systems applications over a finite-time interval [0; T) with T in seconds being the user-defined convergence time. These applications involved, for example, cooperative engagement with a target, cooperative landing on a region, and cooperative transportation of loads, where their common denominator was that they were over at T seconds. Predicated on a new time transformation approach, distributed finite-time control architectures were established to perform these applications over [0; T) through local, agent-to-agent information exchange. Considering the fact that there are several other important multiagent systems applications that involve, for example, formation assignment and command tracking, where they are not over at T seconds, the purpose of this paper is to generalize our prior research to allow multiagent systems perform their tasks beyond T seconds. Specifically, we focus on both formation assignment and command tracking problems, and propose a switching distributed control architecture. The key feature of the proposed architecture is that it guarantees agents to establish a desired formation and approach a time-varying command available to a subset of these agents at the user-defined T seconds, and then track the command while keeping the resulting formation beyond T seconds through local information exchange. We present a system-theoretical stability analysis of our architecture using a time transformation approach, Lyapunov stability, and the input-to-state stability, and also illustrate our theoretical contributions in an example.