Distributed fixed-time and prescribed-time average consensus for multi-agent systems with energy constraints

This paper is devoted to the investigation of the fixed-time and prescribed-time average consensus problem for multi-agent systems (MASs) with energy constraints. For the purpose of the fixed-time and prescribed-time average consensus of MASs, two control algorithms are firstly developed in this paper on the basis of the fixed-time technique and the prescribed-time technique. Then, the time integral of the quadratic function is constructed to calculate the energy consumption by the error between each agent and the reference state. And the sufficient conditions for the stability of the Lyapunov function are provided by designing the parameters and the gain matrix. Ultimately, the theoretical results are effectively and correctly verified by utilizing simulations.