Stochastic fixed-time formation for nonlinear multi-agent systems under a discontinuous protocol

This article mainly studies the time-varying fixed-time formation (FTF) tracking control problem for stochastically disturbed nonlinear multi-agent systems on detail balanced graphs. First, a novel sufficient condition for ensuring the fixed-time stability in probability of stochastic differential equation is given. Then, using the neighboring information, a simple discontinuous control protocol is designed for achieving time-varying FTF. By means of non-smooth analysis techniques, our control objective is obtained and a proper upper bound for the expectation of the stochastic settling time is estimated. Finally, a numerical illustration demonstrates that the proposed control protocol is effective.