Accurate prescribed-time output consensus of heterogeneous multi-agent systems: A bounded time-varying gain approach

In this paper, we develop a bounded time-varying gain approach, consisting of a time base generator (TBG)-based observer and a switching controller, to achieve the accurate prescribed-time output consensus for heterogeneous multi-agent systems (MASs). First, the TBG-based observer is designed for each agent to estimate the leader’s state, and the accurate estimation time can be pre-set arbitrarily. Next, a switching controller is designed, which integrates a TBG-based time-varying feedback and a fractional-order feedback, with a pre-determined switching instant before a prescribed time. Under this switching controller, the accurate prescribed-time output consensus of heterogeneous MASs is achieved, irrespective of agents’ initial states and control parameters. The bounded nature of the TBG gain within the prescribed time interval ensures that the proposed switching controller is non-singular, avoiding the numerical calculation problem associated with unbounded time-varying gains. Moreover, a control optimization algorithm is introduced to select the optimal switching instant, thus solving the accurate prescribed-time output consensus for heterogeneous MASs with minimal control effort. Notably, the proposed approach does not require a temporal scale transformation of the prescribed time intervals and state variables of all agents, simplifying the analysis process. Finally, the theoretical results are validated through a simulation example.