Memory-Based Accelerated Consensus for Second-Order Multi-Agent Systems With Delay

Time delay, which is particularly common in reality, generally has a negative impact on system performance. In order to improve the convergence rate, memory term is adopt to design the fast consensus protocol for second-order multi-agent systems(MASs) with time delay. Through the graph Fourier transform, the consensus problem is transformed to a simultaneous stability problem, and the necessary and sufficient condition to reach consensus is given. Then, a fast consensus algorithm based on gradient descent is proposed to optimize the convergence rate. For MASs with small delay, the explicit formulas of the optimal control gains and the fastest convergence rate are obtained for memory-based and memoryless protocols respectively. Finally, numerical examples are given to illustrate the validity of the theoretical results.