Performance-Guaranteed Consensus Tracking of Non-Smooth Multiagent Systems: A Low-Complexity Design Approach

This article investigates the leader-follower consensus tracking problem for non-smooth multiagent systems (MASs) with prescribed performance constraints. The non-smooth system is transformed into an equivalent smooth one based on Cellina approximate selection theorem. A novel mapping-based barrier function is introduced to get rid of the sign limitation, which enables us to design a tube-type performance function capable of achieving zero-overshoot consensus, as the initial constraining condition can be naturally satisfied without manual adjustment. The design of the controller is approximation-free by the use of the backstepping technique that can achieve the performance requirements with low computation complexity. Based on the Lyapunov stability analysis, it is proved that all signals of the closed-loop system are uniformly ultimately bounded. The effectiveness of the method is demonstrated with simulation examples.