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.
In this article, the synchronization problem for nonlinear hybrid-coupled complex networks with both coupling and internal self-feedback delays is studied. An aperiodically intermittent adaptive control is employed for a fraction of nodes to pin the whole network to the synchronization state. Some sufficient conditions for realizing global synchronization are derived based on Halanay inequality and Lyapunov stability theory. Finally, a simulation example verifies the effectiveness of the proposed control method.
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