Asynchronous Tracking Control of Leader–Follower Multiagent Systems With Input Uncertainties Over Switching Signed Digraphs
研究了在切换符号有向图上，跟随者无法准确测量领导者时变加速度且各智能体异步通信的情况下，如何通过矩阵分析和二元关系组合方法，将异步跟踪问题转化为子随机矩阵乘积的收敛问题，并建立了生成树条件来保证跟踪控制。
Signed digraphs with both positive and negative weighted edges are widely applied to explain cooperative and competitive interactions arising from various social, biological, and physical systems. This article formulates and solves the asynchronous tracking control problem of multiagent systems with input uncertainties on switching signed digraphs. In the interaction setting, we assume that the leader moves at a time-varying acceleration that cannot be measured by the followers accurately, and further suppose that each agent receives its neighbors' states information at certain instants determined by its own clock, which is not necessary to be synchronized with those of other agents. Using dynamically changing spanning subdigraphs of signed digraphs to describe graphically asynchronous interactions, the asynchronous tracking problem is equivalently transformed into a convergence problem of products of general substochastic matrices (PGSSM), in which the matrix elements are not necessarily non-negative and the row sums are less than or equal to 1. With the help of the matrix analysis technique and the composition of binary relations, we propose a new and original method to deal with the convergence problem of PGSSM, and further establish a spanning tree condition for asynchronous tracking control. Finally, the validity of the theoretical findings is verified through several numerical examples.