Neural network-based smooth fixed-time cooperative control of high-Order multi-agent systems with time-varying failures

This article tries to achieve smooth fixed-time cooperative control for high-order multi-agent systems in the presence of nonlinear uncertainties, time-varying failures and single-way communication. Due to the lemma of fixed-time stabilization involving fractional and high-power terms, it is nontrivial to design C-1 smooth controllers for such systems. To eliminate linear growth conditions of uncertainties, neural networks are introduced; To ensure all fixed-time controllers are C-1 continuous, a novel smooth fixedtime cooperative control framework is provided by designing C-1 smooth switching and implementing dynamic surface control such that singularity and chattering problem are eliminated completely; To achieve smooth fixed-time fault-tolerant control, based on bound estimation method, the fixed-time compensation of time-varying failures is made by designing two continuous adaptive laws. Then, a novel smooth fixed-time fault-tolerant cooperative control scheme is proposed to guarantee that all control signals are continuous, smooth and bounded. Meanwhile, all internal errors will converge to arbitrarily small zones of zero within fixed time. To confirm the effectiveness of the proposed smooth fixed-time fault-tolerant cooperative control schemes, simulations based on a numerical example and a practical example are made. (c) 2022 Published by Elsevier Ltd on behalf of The Franklin Institute.