Research on adaptive practical prescribed-time consensus of multiple mechanical systems with full-state constraints

In this paper, an adaptive practical prescribed-time consensus (PPTC) for multiple mechanical systems with full-state constraints is discussed. We first propose a new nonlinear mapping (NM). By transforming the full state–constrained system with the NM, we can obtain an unconstrained system. Then combined with neural networks, graph theory, and practical prescribed-time control theory, a distributed adaptive PPTC protocol is proposed for the unconstrained system, which can ensure that position errors and speed errors reach a certain region within a prescribed-time and full-state constraints are satisfied. Finally, an example is given to demonstrate that this method can be implemented.