Improved Prescribed Performance Consensus of Heterogeneous Multiagent Systems: A Dynamic-Shear-Mapping-Based Approach

Prescribed performance (PP) control is widely used in the construction of consensus protocols for multiagent systems (MASs) due to its property of ensuring that the variables of interest are constrained within the prescribed range during the control process. However, when unpredictable faults such as sudden sensor faults occur, or parameters such as the sampling interval are selected improperly, it can cause singularity problems and render the PP protocol ineffective. Introducing shear mapping into the PP mechanism can resolve the singularity problems, but it requires solving complex nonlinear equations, which may heavily occupy agents' computational resources. To address this issue, we propose a novel dynamic shear mapping mechanism, based on which an event-triggered PP consensus protocol is developed for a class of heterogeneous leaderless MASs. Specifically, by constructing a dynamic shear angle related to the constraint performance functions and variables of interest, the need to solve nonlinear equations is reduced, while the hard-soft transition of performance constraint in the control process is achieved. It is proven that, under the proposed protocol, the consensus errors can strictly satisfy the PP requirements during a prescribed stage, and ultimately converge to zero asymptotically. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.